{"CFDocument":{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2019-02-16T14:58:14+00:00","CFPackageURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFPackages\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"licenseURI":{"title":"CC BY 3.0 US","identifier":"887091d4-43f5-11e8-8f3c-5da5460dc2fb","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFLicenses\/887091d4-43f5-11e8-8f3c-5da5460dc2fb"},"officialSourceURL":"http:\/\/www.uen.org\/core\/math\/","creator":"PCG Copy","title":"PCG - Utah Core Standards for Mathematics","version":"2016","language":"en","adoptionStatus":"Private Draft"},"CFItems":[{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3d5130-f280-11e8-9cff-0242ac140002","identifier":"5b3d5130-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Course","CFItemTypeURI":{"title":"Course","identifier":"eaaba9be-9fdf-56b0-9be5-053d48e28cd4","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/eaaba9be-9fdf-56b0-9be5-053d48e28cd4"},"educationLevel":["09","10","11","12"],"fullStatement":"Secondary Mathematics I","notes":"**THE FUNDAMENTAL PURPOSE OF SECONDARY MATHEMATICS I** is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Secondary Mathematics I uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades. The final unit in the course ties together the algebraic and geometric ideas studied. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.\r\n\r\n**CRITICAL AREA 1**: By the end of eighth grade, students have had a variety of experiences working with expressions and creating equations. Students continue this work by using quantities to model and analyze situations, to interpret expressions, and by creating equations to describe situations.\r\n\r\n**CRITICAL AREA 2:** In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. Students will learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs, and start viewing functions as objects in their own right. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Their work includes functions that can be described or approximated by formulas, as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.\r\n\r\n**CRITICAL AREA 3:** By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This area builds on these earlier experiences by asking students to analyze and explain the process of solving an equation and to justify the process used in solving a system of equations. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. Students explore systems of equations and inequalities, and they find and interpret their solutions. All of this work is grounded on understanding quantities and on relationships between them.\r\n\r\n**CRITICAL AREA 4:** This area builds upon students\u2019 prior experiences with data, providing students with more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.\r\n\r\n**CRITICAL AREA 5:** In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions (translations, reflections, and rotations) and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.\r\n\r\n**CRITICAL AREA 6:** Building on their work with the Pythagorean Theorem in eighth grade to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3dd49f-f280-11e8-9cff-0242ac140002","identifier":"5b3dd49f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Course","CFItemTypeURI":{"title":"Course","identifier":"eaaba9be-9fdf-56b0-9be5-053d48e28cd4","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/eaaba9be-9fdf-56b0-9be5-053d48e28cd4"},"educationLevel":["09","10","11","12"],"fullStatement":"Secondary Mathematics III","notes":"**THE FOCUS OF SECONDARY MATHEMATICS II** is on quadratic expressions, equations, and functions and on comparing their characteristics and behavior to those of linear and exponential relationships from Secondary Mathematics I as organized into six critical areas, or units. The need for extending the set of rational numbers arises, and real and complex numbers are introduced so that all quadratic equations can be solved. The link between probability and data is explored through conditional probability and counting methods, including their use in making and evaluating decisions. The study of similarity leads to an understanding of right triangle trigonometry and connects to quadratics through Pythagorean relationships. Circles, with their quadratic algebraic representations, round out the course. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.\r\n\r\n**CRITICAL AREA 1:** Students extend the laws of exponents to rational exponents and explore distinctions between rational and irrational numbers by considering their decimal representations. Students learn that when quadratic equations do not have real solutions the number system must be extended so that solutions exist, analogous to the way in which extending the whole numbers to the negative numbers allows x+1 = 0 to have a solution. Students explore relationships between number systems: whole numbers, integers, rational numbers, real numbers, and complex numbers. The guiding principle is that equations with no solutions in one number system may have solutions in a larger number system.\r\n\r\n**CRITICAL AREA 2:** Students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. When quadratic equations do not have real solutions, students learn that the graph of the related quadratic function does not cross the horizontal axis. They expand their experience with functions to include more specialized functions\u2014absolute value, step, and those that are piecewise-defined.\r\n\r\n**CRITICAL AREA 3:** Students begin this unit by focusing on the structure of expressions, rewriting expressions to clarify and reveal aspects of the relationship they represent. They create and solve equations, inequalities, and systems of equations involving exponential and quadratic expressions.\r\n\r\n**CRITICAL AREA 4**: Building on probability concepts that began in the middle grades, students use the languages of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for compound events, attending to mutually exclusive events, independent events, and conditional probability. Students should make use of geometric probability models wherever possible. They use probability to make informed decisions.\r\n\r\n**CRITICAL AREA 5:** Students apply their earlier experience with dilations and proportional reasoning to build a formal understanding of similarity. They identify criteria for similarity of triangles, use similarity to solve problems, and apply similarity in right triangles to understand right triangle trigonometry, with particular attention to special right triangles and the Pythagorean Theorem. It is in this unit that students develop facility with geometric proof. They use what they know about congruence and similarity to prove theorems involving lines, angles, triangles, and other polygons. They explore a variety of formats for writing proofs.\r\n\r\n**CRITICAL AREA 6:** Students prove basic theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem, and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the coordinates of its center, and the equation of a parabola with vertical axis when given an equation of its directrix and the coordinates of its focus. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations to determine intersections between lines and circles or a parabola and between two circles. Students develop informal arguments justifying common formulas for circumference, area, and volume of geometric objects, especially those related to circles.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3e4bd9-f280-11e8-9cff-0242ac140002","identifier":"5b3e4bd9-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Course","CFItemTypeURI":{"title":"Course","identifier":"eaaba9be-9fdf-56b0-9be5-053d48e28cd4","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/eaaba9be-9fdf-56b0-9be5-053d48e28cd4"},"educationLevel":["09","10","11","12"],"fullStatement":"Secondary Mathematics III","notes":"**IN SECONDARY MATHEMATICS III** students pull together and apply the accumulation of learning that they have from their previous courses, with content grouped into four critical areas, organized into units. They apply methods from probability and statistics to draw inferences and conclusions from data. Students expand their repertoire of functions to include polynomial, rational, and radical functions. They expand their study of right triangle trigonometry to include general triangles. And, finally, students bring together all of their experience with functions and geometry to create models and solve contextual problems. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.\r\n\r\n**CRITICAL AREA 1:** Students see how the visual displays and summary statistics they learned in earlier grades relate to different types of data and to probability distributions. They identify different ways of collecting data - including sample surveys, experiments, and simulations\u2014and the role that randomness and careful design play in the conclusions that can be drawn.\r\n\r\n**CRITICAL AREA 2:** This area develops the structural similarities between the system of polynomials and the system of integers. Students draw on analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students connect multiplication of polynomials with multiplication of multi-digit integers, and division of polynomials with long division of integers. Students identify zeros of polynomials and make connections between zeros of polynomials and solutions of polynomial equations. The unit culminates with the fundamental theorem of algebra. Rational numbers extend the arithmetic of integers by allowing division by all numbers except 0. Similarly, rational expressions extend the arithmetic of polynomials by allowing division by all polynomials except the zero polynomial. A central theme of this unit is that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.\r\n\r\n**CRITICAL AREA 3:** Students develop the Laws of Sines and Cosines in order to find missing measures of general (not necessarily right) triangles. They are able to distinguish whether three given measures (angles or sides) define 0, 1, 2, or infinitely many triangles. This discussion of general triangles opens up the idea of trigonometry applied beyond the right triangle\u2014that is, at least to obtuse angles. Students build on this idea to develop the notion of radian measure for angles and extend the domain of the trigonometric functions to all real numbers. They apply this knowledge to model simple periodic phenomena.\r\n\r\n**CRITICAL AREA 4:** Students synthesize and generalize what they have learned about a variety of function families. They extend their work with exponential functions to include solving exponential equations with logarithms. They explore the effects of transformations on graphs of diverse functions, including functions arising in an application, in order to abstract the general principle that transformations on a graph always have the same effect regardless of the type of the underlying functions. They identify appropriate types of functions to model a situation, adjust parameters to improve the model, and compare models by analyzing the appropriateness of the fit and making judgments about the domain over which a model is a good fit. The description of modeling as \u201cthe process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions\u201d is at the heart of this area. The narrative discussion and diagram of the modeling cycle should be considered when knowledge of functions, statistics, and geometry is applied in a modeling context.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3eb336-f280-11e8-9cff-0242ac140002","identifier":"5b3eb336-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Course","CFItemTypeURI":{"title":"Course","identifier":"eaaba9be-9fdf-56b0-9be5-053d48e28cd4","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/eaaba9be-9fdf-56b0-9be5-053d48e28cd4"},"educationLevel":["09","10","11","12"],"fullStatement":"Precalculus","notes":"**Number and Quantity**\r\n\r\n* Vector and Matrix Quantities\r\n* Complex Number System\r\n\r\n**Algebra**\r\n\r\n* Reasoning With Equations and Inequalities\r\n\r\n**Functions**\r\n\r\n* Interpreting Functions\r\n* Building Functions\r\n* Trigonometric Functions\r\n\r\n**Geometry**\r\n\r\n* Geometric Measurement and Dimension\r\n* Expressing Geometric Properties with Equations\r\n\r\n**Statistics**\r\n\r\n* Conditional Probability and the Rules of Probability","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3effcc-f280-11e8-9cff-0242ac140002","identifier":"5b3effcc-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/8047d85d-6c8e-5231-bd6d-050731684413"},"educationLevel":["09","10","11","12"],"fullStatement":"Standards for HS Math Content","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b415443-f280-11e8-9cff-0242ac140002","identifier":"5b415443-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/8047d85d-6c8e-5231-bd6d-050731684413"},"educationLevel":["KG"],"fullStatement":"Kindergarten","notes":"In kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects; (2) describing shapes and space. More learning time in kindergarten should be devoted to number than to other topics.\r\n\r\n(1) Students will use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 \u2013 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but is not required.) Students will choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away.\r\n\r\n(2) Students will describe their physical world using geometric ideas (for example, shape, orientation, spatial relations) and vocabulary. They will identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (for example, with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They will use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41559a-f280-11e8-9cff-0242ac140002","identifier":"5b41559a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["KG"],"fullStatement":"Know number names and the counting sequence","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4156f2-f280-11e8-9cff-0242ac140002","identifier":"5b4156f2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["KG"],"fullStatement":"Count to tell the number of objects","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41582b-f280-11e8-9cff-0242ac140002","identifier":"5b41582b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["KG"],"fullStatement":"Identify and compare quantities of objects and numerals","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41594d-f280-11e8-9cff-0242ac140002","identifier":"5b41594d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["KG"],"fullStatement":"Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b415a6b-f280-11e8-9cff-0242ac140002","identifier":"5b415a6b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["KG"],"fullStatement":"Compose and decompose numbers 11\u201319 to gain foundations for place value","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b415b82-f280-11e8-9cff-0242ac140002","identifier":"5b415b82-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["KG"],"fullStatement":"Describe and compare measurable attributes of objects","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b415c9c-f280-11e8-9cff-0242ac140002","identifier":"5b415c9c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["KG"],"fullStatement":"Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.","notes":"Limit the category counts to less than or equal to 10.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b415dc3-f280-11e8-9cff-0242ac140002","identifier":"5b415dc3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["KG"],"fullStatement":"Identify and describe shapes, including squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b415ef2-f280-11e8-9cff-0242ac140002","identifier":"5b415ef2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["KG"],"fullStatement":"Analyze, compare, create, and compose shapes","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b416017-f280-11e8-9cff-0242ac140002","identifier":"5b416017-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/8047d85d-6c8e-5231-bd6d-050731684413"},"educationLevel":["01"],"fullStatement":"Grade 1","notes":"In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.\r\n\r\n(1) Students will develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They will use a variety of models, including discrete objects and length-based models (for example, cubes connected to form lengths), to model add-to, take-from, put-together, and take-apart; compare situations to develop meaning for the operations of addition and subtraction; and develop strategies to solve arithmetic problems with these operations. Students will understand connections between counting and addition and subtraction (for example, adding two is the same as counting on two). They will use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (for example, \"making tens\") to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children will build their understanding of the relationship between addition and subtraction.\r\n\r\n(2) Students will develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They will compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They will think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they will understand the order of the counting numbers and their relative magnitudes.\r\n\r\n(3) Students will develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.\r\n\r\n(4) Students will compose and decompose plane or solid figures (for example, put two triangles together to make a quadrilateral) and build understanding of part-whole relationships, as well as the properties of the original and composite shapes. As they combine shapes, they will recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b416161-f280-11e8-9cff-0242ac140002","identifier":"5b416161-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["01"],"fullStatement":"Represent and solve problems involving addition and subtraction within 20","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b416375-f280-11e8-9cff-0242ac140002","identifier":"5b416375-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["01"],"fullStatement":"Understand and apply properties of operations and the relationship between addition and subtraction","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4164d1-f280-11e8-9cff-0242ac140002","identifier":"5b4164d1-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["01"],"fullStatement":"Work with addition and subtraction equations","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b416601-f280-11e8-9cff-0242ac140002","identifier":"5b416601-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["01"],"fullStatement":"Extend the counting sequence","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4167ef-f280-11e8-9cff-0242ac140002","identifier":"5b4167ef-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["01"],"fullStatement":"Understand place value","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b416936-f280-11e8-9cff-0242ac140002","identifier":"5b416936-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"fullStatement":"Tell and write time","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b416dc4-f280-11e8-9cff-0242ac140002","identifier":"5b416dc4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["01"],"fullStatement":"Represent and interpret data","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b416ee7-f280-11e8-9cff-0242ac140002","identifier":"5b416ee7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["01"],"fullStatement":"Identify the value of coins","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b416ffb-f280-11e8-9cff-0242ac140002","identifier":"5b416ffb-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["01"],"fullStatement":"Reason with shapes and their attributes","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b417111-f280-11e8-9cff-0242ac140002","identifier":"5b417111-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/8047d85d-6c8e-5231-bd6d-050731684413"},"educationLevel":["02"],"fullStatement":"Grade 2","notes":"In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.\r\n\r\n(1) Students will extend their understanding of the base-ten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students will understand multi-digit numbers (up to 1,000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (for example, 853 is 8 hundreds + 5 tens + 3 ones).\r\n\r\n(2) Students will use their understanding of addition to develop fluency with addition and subtraction within 100. They will solve problems within 1,000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in base-ten notation, using their understanding of place value and the properties of operations. They will select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.\r\n\r\n(3) Students will recognize the need for standard units of measure (such as centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves an iteration of units. They will recognize that the smaller the unit, the more iterations they need to cover a given length.\r\n\r\n(4) Students will describe and analyze shapes by examining their sides and angles. Students will investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students will develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b417254-f280-11e8-9cff-0242ac140002","identifier":"5b417254-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["02"],"fullStatement":"Represent and solve problems involving addition and subtraction","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41736a-f280-11e8-9cff-0242ac140002","identifier":"5b41736a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students will use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.\r\n\r\n(2) Students will develop an understanding of fractions, beginning with unit fractions. Students will view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1\/2 of the paint in a small bucket could be less paint than 1\/3 of the paint in a larger bucket, but 1\/3 of a ribbon is longer than 1\/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students will be able to use fractions to represent numbers equal to, less than, and greater than one. They will solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.\r\n\r\n(3) Students will recognize area as an attribute of two-dimensional regions. They will measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students will understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students will connect area to multiplication and justify using multiplication to determine the area of a rectangle.\r\n\r\n(4) Students will describe, analyze, and compare properties of two-dimensional shapes. They will compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students will also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4181cd-f280-11e8-9cff-0242ac140002","identifier":"5b4181cd-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["03"],"fullStatement":"Represent and solve problems involving multiplication and division within 100","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4182e2-f280-11e8-9cff-0242ac140002","identifier":"5b4182e2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["03"],"fullStatement":"Demonstrate understanding of the properties of multiplication and the relationship between multiplication and division","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4183f5-f280-11e8-9cff-0242ac140002","identifier":"5b4183f5-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["03"],"fullStatement":"Use the four operations to identify and explain patterns in arithmetic","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4184fe-f280-11e8-9cff-0242ac140002","identifier":"5b4184fe-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["03"],"fullStatement":"Use place value understanding and properties of operations to perform multi-digit arithmetic.","notes":"A range of algorithms may be used","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41860e-f280-11e8-9cff-0242ac140002","identifier":"5b41860e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["03"],"fullStatement":"Develop understanding of fractions as numbers.","notes":"Denominators are limited to 2, 3, 4, 6, and 8 in third grade.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b418727-f280-11e8-9cff-0242ac140002","identifier":"5b418727-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["03"],"fullStatement":"Understand concepts of area and relate area to multiplication and addition","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b418a5e-f280-11e8-9cff-0242ac140002","identifier":"5b418a5e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["03"],"fullStatement":"Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b418b72-f280-11e8-9cff-0242ac140002","identifier":"5b418b72-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["03"],"fullStatement":"Reason with shapes and their attributes","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b418c88-f280-11e8-9cff-0242ac140002","identifier":"5b418c88-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/8047d85d-6c8e-5231-bd6d-050731684413"},"educationLevel":["04"],"fullStatement":"Grade 4","notes":"In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; and (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.\r\n\r\n(1) Students will generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They will apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they will select and accurately apply appropriate methods to estimate or mentally calculate products. They will develop fluency with efficient procedures for multiplying whole numbers, understand and explain why the procedures work based on place value and properties of operations, and use them to solve problems. Students will apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They will select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context.\r\n\r\n(2) Students will develop understanding of fraction equivalence and operations with fractions. They will recognize that two different fractions can be equal (for example, 15\/9 = 5\/3), and they will develop methods for generating and recognizing equivalent fractions. Students will extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number.\r\n\r\n(3) Students will describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students will deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b418e9b-f280-11e8-9cff-0242ac140002","identifier":"5b418e9b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["04"],"fullStatement":"Use the four operations with whole numbers (addition, subtraction, multiplication, and division) to solve problems","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b418fe3-f280-11e8-9cff-0242ac140002","identifier":"5b418fe3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["04"],"fullStatement":"Gain familiarity with factors and multiples","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b419107-f280-11e8-9cff-0242ac140002","identifier":"5b419107-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["04"],"fullStatement":"Generate and analyze numeric and shape patterns","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4192d8-f280-11e8-9cff-0242ac140002","identifier":"5b4192d8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["04"],"fullStatement":"Generalize place value understanding for multi-digit whole numbers by analyzing patterns, writing whole numbers in a variety of ways, making comparisons, and rounding","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41940c-f280-11e8-9cff-0242ac140002","identifier":"5b41940c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["04"],"fullStatement":"Use place value understanding and properties of operations to perform multidigit addition, subtraction, multiplication, and division using a one-digit divisor","notes":"Expectations in this strand are limited to whole numbers less than or equal to 1,000,000.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b419540-f280-11e8-9cff-0242ac140002","identifier":"5b419540-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/8047d85d-6c8e-5231-bd6d-050731684413"},"educationLevel":["05"],"fullStatement":"Grade 5","notes":"In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to two-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.\r\n\r\n(1) Students will apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They will develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students will also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: This is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)\r\n\r\n(2) Students will develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They will finalize fluency with multi-digit addition, subtraction, multiplication, and division. They will apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They will develop fluency in these computations, and make reasonable estimates of their results. Students will use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (e.g., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They will compute products and quotients of decimals to hundredths efficiently and accurately.\r\n\r\n(3) Students will recognize volume as an attribute of three-dimensional space. They will understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They will understand that a one-unit by one-unit by one-unit cube is the standard unit for measuring volume. They will select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They will decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They will measure necessary attributes of shapes in order to determine volumes to solve real-world and mathematical problems.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b419f0b-f280-11e8-9cff-0242ac140002","identifier":"5b419f0b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["05"],"fullStatement":"Write and interpret numerical expressions","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41a01e-f280-11e8-9cff-0242ac140002","identifier":"5b41a01e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Grade Level","CFItemTypeURI":{"title":"Grade Level","identifier":"8047d85d-6c8e-5231-bd6d-050731684413","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/8047d85d-6c8e-5231-bd6d-050731684413"},"educationLevel":["06"],"fullStatement":"Grade 6","notes":"In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.\r\n\r\n(1) Students will use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students will connect their understanding of multiplication and division with ratios and rates. Thus students will expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students will solve a wide variety of problems involving ratios and rates.\r\n\r\n(2) Students will use the meaning of fractions, the meanings of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for dividing fractions make sense. Students will use these operations to solve problems. Students will extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, and in particular negative integers. They will reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.\r\n\r\n(3) Students will understand the use of variables in mathematical expressions. They will write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students will understand that expressions in different forms can be equivalent, and they will use the properties of operations to rewrite expressions in equivalent forms. Students will know that the solutions of an equation are the values of the variables that make the equation true. Students will use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students will construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they will use equations (such as 3x = y) to describe relationships between quantities.\r\n\r\n(4) Building on and reinforcing their understanding of number, students will begin to develop their ability to think statistically. Students will recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students will recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students will learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.\r\n\r\n(5) Students in Grade 6 will also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They will find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students will discuss, develop, and justify formulas for areas of triangles and parallelograms. Students will find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They will reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They will prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41acef-f280-11e8-9cff-0242ac140002","identifier":"5b41acef-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["06"],"fullStatement":"Understand ratio concepts and use ratio reasoning to solve problems","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41ae33-f280-11e8-9cff-0242ac140002","identifier":"5b41ae33-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships.\r\n\r\n(2) Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.\r\n\r\n(3) Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In preparation for work on congruence and similarity in Grade 8 they reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and they gain familiarity with the relationships between angles formed by intersecting lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.\r\n\r\n(4) Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41b9f2-f280-11e8-9cff-0242ac140002","identifier":"5b41b9f2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["07"],"fullStatement":"Analyze proportional relationships and use them to solve real-world and mathematical problems","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41bb15-f280-11e8-9cff-0242ac140002","identifier":"5b41bb15-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Students recognize equations for proportions (y\/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m\u00b7A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation.\r\n\r\nStudents strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems.\r\n\r\n(2) Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations.\r\n\r\n(3) Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41c5be-f280-11e8-9cff-0242ac140002","identifier":"5b41c5be-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Cluster","CFItemTypeURI":{"title":"Cluster","identifier":"d77602ec-0098-5b60-b0c0-531cc61709e3","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/d77602ec-0098-5b60-b0c0-531cc61709e3"},"educationLevel":["08"],"fullStatement":"Know that there are numbers that are not rational, and approximate them by rational numbers","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41c715-f280-11e8-9cff-0242ac140002","identifier":"5b41c715-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b400724-f280-11e8-9cff-0242ac140002","identifier":"5b400724-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.MP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Make sense of quantities and their relationships in problem situations. Contextualize quantities and operations by using images or stories. Decontextualize a given situation and represent it symbolically. Interpret symbols as having meaning, not just as directions to carry out a procedure. Know and flexibly use different properties of operations, numbers, and geometric objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40084c-f280-11e8-9cff-0242ac140002","identifier":"5b40084c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.MP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b400978-f280-11e8-9cff-0242ac140002","identifier":"5b400978-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.MP.4","fullStatement":"Model with mathematics.","notes":"Identify the mathematical elements of a situation and create a mathematical model that shows the relationships among them. Identify important quantities in a contextual situation, use mathematical models to show the relationships of those quantities, analyze the relationships, and draw conclusions. Models may be verbal, contextual, visual, symbolic, or physical.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b400aa2-f280-11e8-9cff-0242ac140002","identifier":"5b400aa2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.MP.5","fullStatement":"Use appropriate tools strategically.","notes":"Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as physical objects, drawings, diagrams, physical tools, technologies, or mathematical tools, such as estimation or a particular strategy or algorithm.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b400c66-f280-11e8-9cff-0242ac140002","identifier":"5b400c66-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.MP.6","fullStatement":"Attend to precision.","notes":"Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b400da9-f280-11e8-9cff-0242ac140002","identifier":"5b400da9-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.MP.7","fullStatement":"Look for and make use of structure.","notes":"Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b400ed1-f280-11e8-9cff-0242ac140002","identifier":"5b400ed1-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.MP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b401c76-f280-11e8-9cff-0242ac140002","identifier":"5b401c76-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["01"],"humanCodingScheme":"1.NBT","fullStatement":"Number and Operations in Base Ten","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b401d9c-f280-11e8-9cff-0242ac140002","identifier":"5b401d9c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.NBT.1","fullStatement":"Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b401fd3-f280-11e8-9cff-0242ac140002","identifier":"5b401fd3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.NBT.2","fullStatement":"Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b401eb8-f280-11e8-9cff-0242ac140002","identifier":"5b401eb8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["01"],"humanCodingScheme":"1.NBT.2.a","fullStatement":"10 can be thought of as a bundle of ten ones, called a \"ten.\"","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4020ed-f280-11e8-9cff-0242ac140002","identifier":"5b4020ed-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["01"],"humanCodingScheme":"1.NBT.2.b","fullStatement":"The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40220a-f280-11e8-9cff-0242ac140002","identifier":"5b40220a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["01"],"humanCodingScheme":"1.NBT.2.c","fullStatement":"The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40232a-f280-11e8-9cff-0242ac140002","identifier":"5b40232a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.NBT.3","fullStatement":"Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols > , = , and < .","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b402442-f280-11e8-9cff-0242ac140002","identifier":"5b402442-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.NBT.4","fullStatement":"Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and\/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens to tens and ones to ones, and that it is sometimes necessary to compose a ten.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b402569-f280-11e8-9cff-0242ac140002","identifier":"5b402569-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.NBT.5","fullStatement":"Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b402685-f280-11e8-9cff-0242ac140002","identifier":"5b402685-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.NBT.6","fullStatement":"Subtract multiples of 10 in the range 10\u201390 from multiples of 10 in the range 10\u201390 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and\/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b400ff4-f280-11e8-9cff-0242ac140002","identifier":"5b400ff4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["01"],"humanCodingScheme":"1.OA","fullStatement":"Operations and Algebraic Thinking","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b401119-f280-11e8-9cff-0242ac140002","identifier":"5b401119-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.OA.1","fullStatement":"Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. *For example, use objects, drawings, and equations with a symbol for the unknown number to represent the problem.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40123b-f280-11e8-9cff-0242ac140002","identifier":"5b40123b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.OA.2","fullStatement":"Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20. *For example, use objects, drawings, and equations with a symbol for the unknown number to represent the problem.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b401366-f280-11e8-9cff-0242ac140002","identifier":"5b401366-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.OA.3","fullStatement":"Apply properties of operations as strategies to add and subtract.* For example: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 =12. (Associative property of addition.)* First grade students need not use formal terms for these properties.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40148b-f280-11e8-9cff-0242ac140002","identifier":"5b40148b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["01"],"humanCodingScheme":"1.OA.4","fullStatement":"Understand subtraction as an unknown-addend problem. 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Sizes are compared directly or visually, not compared by measuring. 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Solve simple put-together, take-apart, and comparison problems using information presented in a bar graph.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40677e-f280-11e8-9cff-0242ac140002","identifier":"5b40677e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.MD.2","fullStatement":"Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b406933-f280-11e8-9cff-0242ac140002","identifier":"5b406933-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40388b-f280-11e8-9cff-0242ac140002","identifier":"5b40388b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["02"],"humanCodingScheme":"2.MP","fullStatement":"Mathematical Practices","notes":"The Standards for Mathematical Practice in Second Grade describe mathematical habits of mind that teachers should seek to develop in their students. Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4039db-f280-11e8-9cff-0242ac140002","identifier":"5b4039db-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.MP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"Explain the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. When a solution pathway does not make sense, look for another pathway that does. Explain connections between various solution strategies and representations. Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b403b11-f280-11e8-9cff-0242ac140002","identifier":"5b403b11-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.MP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Make sense of quantities and their relationships in problem situations. Contextualize quantities and operations by using images or stories. Decontextualize a given situation and represent it symbolically. Interpret symbols as having meaning, not just as directions to carry out a procedure. Know and flexibly use different properties of operations, numbers, and geometric objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b403c40-f280-11e8-9cff-0242ac140002","identifier":"5b403c40-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.MP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b403d74-f280-11e8-9cff-0242ac140002","identifier":"5b403d74-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.MP.4","fullStatement":"Model with mathematics.","notes":"Identify the mathematical elements of a situation and create a mathematical model that shows the relationships among them. Identify important quantities in a contextual situation, use mathematical models to show the relationships of those quantities, analyze the relationships, and draw conclusions. Models may be verbal, contextual, visual, symbolic, or physical.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b403eab-f280-11e8-9cff-0242ac140002","identifier":"5b403eab-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.MP.5","fullStatement":"Use appropriate tools strategically.","notes":"Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b403fd8-f280-11e8-9cff-0242ac140002","identifier":"5b403fd8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.MP.6","fullStatement":"Attend to precision.","notes":"Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4040fb-f280-11e8-9cff-0242ac140002","identifier":"5b4040fb-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.MP.7","fullStatement":"Look for and make use of structure.","notes":"Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40421a-f280-11e8-9cff-0242ac140002","identifier":"5b40421a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.MP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b405572-f280-11e8-9cff-0242ac140002","identifier":"5b405572-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["02"],"humanCodingScheme":"2.NBT","fullStatement":"Number and Operations in Base Ten","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4057db-f280-11e8-9cff-0242ac140002","identifier":"5b4057db-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.1","fullStatement":"Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; *for example, 706 equals 7 hundreds, 0 tens, and 6 ones.* Understand the following as special cases:","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4056b2-f280-11e8-9cff-0242ac140002","identifier":"5b4056b2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.1.a","fullStatement":"100 can be thought of as a bundle of ten tens called a \"hundred.\"","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4058fa-f280-11e8-9cff-0242ac140002","identifier":"5b4058fa-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.1.b","fullStatement":"The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b405ac9-f280-11e8-9cff-0242ac140002","identifier":"5b405ac9-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.2","fullStatement":"Count within 1,000; skip-count by fives, tens, and hundreds.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b405bf9-f280-11e8-9cff-0242ac140002","identifier":"5b405bf9-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.3","fullStatement":"Read and write numbers to 1,000 using base-ten numerals, number names, and expanded form.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b405d13-f280-11e8-9cff-0242ac140002","identifier":"5b405d13-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.4","fullStatement":"Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b405e2c-f280-11e8-9cff-0242ac140002","identifier":"5b405e2c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.5","fullStatement":"Fluently add and subtract within 100 using strategies based on place value, properties of operations, and\/or the relationship between addition and subtraction.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b405f57-f280-11e8-9cff-0242ac140002","identifier":"5b405f57-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.6","fullStatement":"Add up to four two-digit numbers using strategies based on place value and properties of operations.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b406077-f280-11e8-9cff-0242ac140002","identifier":"5b406077-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.7","fullStatement":"Add and subtract within 1,000 using concrete models or drawings and strategies based on place value, properties of operations, and\/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, and ones and ones, and that it is sometimes necessary to compose or decompose tens or hundreds.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b406282-f280-11e8-9cff-0242ac140002","identifier":"5b406282-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.8","fullStatement":"Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4063dc-f280-11e8-9cff-0242ac140002","identifier":"5b4063dc-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.NBT.9","fullStatement":"Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b404337-f280-11e8-9cff-0242ac140002","identifier":"5b404337-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["02"],"humanCodingScheme":"2.OA","fullStatement":"Operations and Algebraic Thinking","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b404461-f280-11e8-9cff-0242ac140002","identifier":"5b404461-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.OA.1","fullStatement":"Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, *for example, by using drawings and equations with a symbol for the unknown number to represent the problem.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4047af-f280-11e8-9cff-0242ac140002","identifier":"5b4047af-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.OA.2","fullStatement":"Fluently add and subtract within 20.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40458a-f280-11e8-9cff-0242ac140002","identifier":"5b40458a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["02"],"humanCodingScheme":"2.OA.2.a","fullStatement":"Add and subtract within 20 using mental strategies such as counting on; making ten (*for example, 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14*); decomposing a number leading to a ten (*for example, 13 \u2013 4 = 13 \u2013 3 \u2013 1 = 10 \u2013 1 = 9*); using the relationship between addition and subtraction (*for example, knowing that 8 + 4 = 12, one knows 12 \u2013 8 = 4*); and creating equivalent but easier or known sums (*for example, adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13*).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b404b2e-f280-11e8-9cff-0242ac140002","identifier":"5b404b2e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["02"],"humanCodingScheme":"2.OA.2.b","fullStatement":"By the end of Grade 2, know from memory all sums of two one-digit numbers.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40515d-f280-11e8-9cff-0242ac140002","identifier":"5b40515d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.OA.3","fullStatement":"Determine whether a group of objects (up to 20) has an odd or even number of members, (*for example, by pairing objects or counting them by twos*). Write an equation to express an even number as a sum of two equal addends.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4053a0-f280-11e8-9cff-0242ac140002","identifier":"5b4053a0-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["02"],"humanCodingScheme":"2.OA.4","fullStatement":"Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40bab5-f280-11e8-9cff-0242ac140002","identifier":"5b40bab5-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["03"],"humanCodingScheme":"3.G","fullStatement":"Geometry","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40bbda-f280-11e8-9cff-0242ac140002","identifier":"5b40bbda-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.G.1","fullStatement":"Understand that shapes in different categories (*for example, rhombuses, rectangles, and others*) may share attributes (*for example, having four sides*), and that the shared attributes can define a larger category (*for example, quadrilaterals*). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40bdee-f280-11e8-9cff-0242ac140002","identifier":"5b40bdee-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.G.2","fullStatement":"Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. *For example, partition a shape into four parts with equal area, and describe the area of each part as 1\/4 of the area of the shape.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40a7b4-f280-11e8-9cff-0242ac140002","identifier":"5b40a7b4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["03"],"humanCodingScheme":"3.MD","fullStatement":"Measurement and Data","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40a914-f280-11e8-9cff-0242ac140002","identifier":"5b40a914-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MD.1","fullStatement":"Tell and write time to the nearest minute and measure time intervals in minutes. *Solve word problems involving addition and subtraction of time intervals in minutes, for example, by representing the problem on a number line diagram.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40aa50-f280-11e8-9cff-0242ac140002","identifier":"5b40aa50-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MD.2","fullStatement":"Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), milliliters (ml), and liters (l). (Excludes compound units such as cubic centimeters [cc or cm\u00b3] and finding the geometric volume of a container.) *Add, subtract, multiply, or divide to solve one-step word problems involving masses of objects or volumes of liquids that are given in the same units, for example, by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems.)*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40ab92-f280-11e8-9cff-0242ac140002","identifier":"5b40ab92-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MD.3","fullStatement":"Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step \"how many more\" and \"how many less\" problems using information presented in scaled bar graphs. *For example, draw a bar graph in which each square in the bar graph might represent five pets.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40acc0-f280-11e8-9cff-0242ac140002","identifier":"5b40acc0-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MD.4","fullStatement":"Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40af0a-f280-11e8-9cff-0242ac140002","identifier":"5b40af0a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MD.5","fullStatement":"Recognize area as an attribute of plane figures and understand concepts of area measurement.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40ade6-f280-11e8-9cff-0242ac140002","identifier":"5b40ade6-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Use area models to represent the distributive property in mathematical reasoning.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40b86f-f280-11e8-9cff-0242ac140002","identifier":"5b40b86f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["03"],"humanCodingScheme":"3.MD.7.d","fullStatement":"Recognize area as additive. Find areas of rectilinear figures by decomposing them into non- overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40b994-f280-11e8-9cff-0242ac140002","identifier":"5b40b994-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MD.8","fullStatement":"Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4076cb-f280-11e8-9cff-0242ac140002","identifier":"5b4076cb-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["03"],"humanCodingScheme":"3.MP","fullStatement":"Mathematical Practices","notes":"The Standards for Mathematical Practice in Third Grade describe mathematical habits of mind that teachers should seek to develop in their students. 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Contextualize quantities and operations by using images or stories. Decontextualize a given situation and represent it symbolically. Interpret symbols as having meaning, not just as directions to carry out a procedure. Know and flexibly use different properties of operations, numbers, and geometric objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b407a67-f280-11e8-9cff-0242ac140002","identifier":"5b407a67-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b407b96-f280-11e8-9cff-0242ac140002","identifier":"5b407b96-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MP.4","fullStatement":"Model with mathematics.","notes":"Identify the mathematical elements of a situation and create a mathematical model that shows the relationships among them. Identify important quantities in a contextual situation, use mathematical models to show the relationships of those quantities, analyze the relationships, and draw conclusions. Models may be verbal, contextual, visual, symbolic, or physical.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b407cc8-f280-11e8-9cff-0242ac140002","identifier":"5b407cc8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MP.5","fullStatement":"Use appropriate tools strategically.","notes":"Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b407df6-f280-11e8-9cff-0242ac140002","identifier":"5b407df6-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MP.6","fullStatement":"Attend to precision.","notes":"Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b407f1f-f280-11e8-9cff-0242ac140002","identifier":"5b407f1f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MP.7","fullStatement":"Look for and make use of structure.","notes":"Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4080dc-f280-11e8-9cff-0242ac140002","identifier":"5b4080dc-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.MP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4094c6-f280-11e8-9cff-0242ac140002","identifier":"5b4094c6-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["03"],"humanCodingScheme":"3.NBT","fullStatement":"Number and Operations in Base Ten","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4095f3-f280-11e8-9cff-0242ac140002","identifier":"5b4095f3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Fractions","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b409ba7-f280-11e8-9cff-0242ac140002","identifier":"5b409ba7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.NF.1","fullStatement":"Understand that a unit fraction has a numerator of one and a non-zero denominator.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b409a80-f280-11e8-9cff-0242ac140002","identifier":"5b409a80-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["03"],"humanCodingScheme":"3.NF.1.a","fullStatement":"Understand a fraction 1\/b as the quantity formed by one part when a whole is partitioned into b equal parts.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b409ccb-f280-11e8-9cff-0242ac140002","identifier":"5b409ccb-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["03"],"humanCodingScheme":"3.NF.1.b","fullStatement":"Understand a fraction a\/b as the quantity formed by a parts of size 1\/b. *For example: 1\/4 + 1\/4 + 1\/4 = 3\/4. *","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b409f1d-f280-11e8-9cff-0242ac140002","identifier":"5b409f1d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Recognize that each part has size 1\/b and that the endpoint of the part based at 0 locates the number 1\/b on the number line.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40a043-f280-11e8-9cff-0242ac140002","identifier":"5b40a043-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["03"],"humanCodingScheme":"3.NF.2.b","fullStatement":"Represent a fraction a\/b on a number line diagram by marking off a lengths 1\/b from 0. Recognize that the resulting interval has size a\/b and that its endpoint locates the number a\/b on the number line.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40a28c-f280-11e8-9cff-0242ac140002","identifier":"5b40a28c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-12-18T13:00:10+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.NF.3","fullStatement":"Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40a168-f280-11e8-9cff-0242ac140002","identifier":"5b40a168-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["03"],"humanCodingScheme":"3.NF.3.a","fullStatement":"Understand two fractions as equivalent if they are the same size, or the same point on a number line.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40a3b2-f280-11e8-9cff-0242ac140002","identifier":"5b40a3b2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["03"],"humanCodingScheme":"3.NF.3.b","fullStatement":"Recognize and generate simple equivalent fractions, such as 1\/2 = 2\/4, 4\/6 = 2\/3. *Explain why the fractions are equivalent by using a visual fraction model, for example. *","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40a4e1-f280-11e8-9cff-0242ac140002","identifier":"5b40a4e1-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["03"],"humanCodingScheme":"3.NF.3.c","fullStatement":"Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. *For example, express 3 in the form 3 = 3\/1; recognize that 6\/1 = 6; locate 4\/4 and 1 at the same point of a number line diagram. *","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40a609-f280-11e8-9cff-0242ac140002","identifier":"5b40a609-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["03"],"humanCodingScheme":"3.NF.3.d","fullStatement":"Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. *Record the results of comparisons with the symbols > , = , or < , and justify the conclusions, for example, by using a visual fraction model.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b408224-f280-11e8-9cff-0242ac140002","identifier":"5b408224-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["03"],"humanCodingScheme":"3.OA","fullStatement":"Operations and Algebraic Thinking","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b408354-f280-11e8-9cff-0242ac140002","identifier":"5b408354-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.OA.1","fullStatement":"Interpret products of whole numbers, such as interpret 5 \u00d7 7 as the total number of objects in 5 groups of 7 objects each. *For example, describe a context in which a total number of objects can be expressed as 5 \u00d7 7.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b408471-f280-11e8-9cff-0242ac140002","identifier":"5b408471-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.OA.2","fullStatement":"Interpret whole-number quotients of whole numbers. *For example, interpret 56 \u00f7 8 as the number of objects in each share when 56 objects are partitioned equally into eight shares (partitive), or as a number of shares when 56 objects are partitioned into equal shares of eight objects each (quotative).*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40859b-f280-11e8-9cff-0242ac140002","identifier":"5b40859b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.OA.3","fullStatement":"Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. *For example, use drawings and equations with a symbol for the unknown number to represent the problem.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4086c2-f280-11e8-9cff-0242ac140002","identifier":"5b4086c2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.OA.4","fullStatement":"Determine the unknown whole number in a multiplication or division equation relating three whole numbers. *For example, determine the unknown number - product, factor, quotient, dividend, or divisor - that makes the equation true in each of the equations 8 x ? = 48, 5 = ? \u00f7 3, 6 x 6 = ?.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4087eb-f280-11e8-9cff-0242ac140002","identifier":"5b4087eb-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.OA.5","fullStatement":"Apply properties of operations as strategies to multiply and divide. *For example: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known (commutative property of multiplication). 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30 (associative property of multiplication). Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56 (distributive property). (Third grade students may, but need not, use formal terms for these properties.)*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b408919-f280-11e8-9cff-0242ac140002","identifier":"5b408919-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["03"],"humanCodingScheme":"3.OA.6","fullStatement":"Understand division as an unknown-factor problem. 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Sketch angles of specified measure.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b410084-f280-11e8-9cff-0242ac140002","identifier":"5b410084-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.MD.7","fullStatement":"Recognize angle measure as additive.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40fddf-f280-11e8-9cff-0242ac140002","identifier":"5b40fddf-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["04"],"humanCodingScheme":"4.MD.7.a","fullStatement":"Understand that when an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4101c4-f280-11e8-9cff-0242ac140002","identifier":"5b4101c4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["04"],"humanCodingScheme":"4.MD.7.b","fullStatement":"Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems, *for example by using an equation with a symbol for the unknown angle measure.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40bf55-f280-11e8-9cff-0242ac140002","identifier":"5b40bf55-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["04"],"humanCodingScheme":"4.MP","fullStatement":"Mathematical Practices","notes":"The Standards for Mathematical Practice in Fourth Grade describe mathematical habits of mind that teachers should seek to develop in their students. Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40c0a7-f280-11e8-9cff-0242ac140002","identifier":"5b40c0a7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.MP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"Explain the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. 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Contextualize quantities and operations by using images or stories. Decontextualize a given situation and represent it symbolically. Interpret symbols as having meaning, not just as directions to carry out a procedure. Know and flexibly use different properties of operations, numbers, and geometric objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40c316-f280-11e8-9cff-0242ac140002","identifier":"5b40c316-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.MP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40c43f-f280-11e8-9cff-0242ac140002","identifier":"5b40c43f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.MP.4","fullStatement":"Model with mathematics.","notes":"Identify the mathematical elements of a situation and create a mathematical model that shows the relationships among them. Identify important quantities in a contextual situation, use mathematical models to show the relationships of those quantities, analyze the relationships, and draw conclusions. Models may be verbal, contextual, visual, symbolic, or physical.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40c568-f280-11e8-9cff-0242ac140002","identifier":"5b40c568-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.MP.5","fullStatement":"Use appropriate tools strategically.","notes":"Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40c68e-f280-11e8-9cff-0242ac140002","identifier":"5b40c68e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.MP.6","fullStatement":"Attend to precision.","notes":"Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40c7b4-f280-11e8-9cff-0242ac140002","identifier":"5b40c7b4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.MP.7","fullStatement":"Look for and make use of structure.","notes":"Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40c8d0-f280-11e8-9cff-0242ac140002","identifier":"5b40c8d0-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.MP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40d3ed-f280-11e8-9cff-0242ac140002","identifier":"5b40d3ed-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["04"],"humanCodingScheme":"4.NBT","fullStatement":"Number and Operations in Base Ten","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40d50d-f280-11e8-9cff-0242ac140002","identifier":"5b40d50d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NBT.1","fullStatement":"Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. *For example, recognize that 700 \u00f7 70 = 10 by applying concepts of place value and division.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40d627-f280-11e8-9cff-0242ac140002","identifier":"5b40d627-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NBT.2","fullStatement":"Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using > , = , and < symbols to record the results of comparisons.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40d749-f280-11e8-9cff-0242ac140002","identifier":"5b40d749-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NBT.3","fullStatement":"Use place value understanding to round multi-digit whole numbers to any place.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40d863-f280-11e8-9cff-0242ac140002","identifier":"5b40d863-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NBT.4","fullStatement":"Fluently add and subtract multi-digit whole numbers using the standard algorithm.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40d983-f280-11e8-9cff-0242ac140002","identifier":"5b40d983-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NBT.5","fullStatement":"Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and\/or area models.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40dab3-f280-11e8-9cff-0242ac140002","identifier":"5b40dab3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NBT.6","fullStatement":"Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and\/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and\/or area models.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40dbdc-f280-11e8-9cff-0242ac140002","identifier":"5b40dbdc-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["04"],"humanCodingScheme":"4.NF","fullStatement":"Number and Operations - Fractions","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40dcfc-f280-11e8-9cff-0242ac140002","identifier":"5b40dcfc-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NF.1","fullStatement":"Explain why a fraction a\/b is equivalent to a fraction (n x a)\/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40de1d-f280-11e8-9cff-0242ac140002","identifier":"5b40de1d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NF.2","fullStatement":"Compare two fractions with different numerators and different denominators, *for example, by creating common denominators or numerators*, or by comparing to a benchmark fraction such as 1\/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols > = , or < , and justify the conclusions, *for example, by using a visual fraction model.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40e060-f280-11e8-9cff-0242ac140002","identifier":"5b40e060-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NF.3","fullStatement":"Understand a fraction a\/b with a >1 as a sum of fractions 1\/b. In other words, any fraction is a sum of unit fractions.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40df43-f280-11e8-9cff-0242ac140002","identifier":"5b40df43-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["04"],"humanCodingScheme":"4.NF.3.a","fullStatement":"Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40e17b-f280-11e8-9cff-0242ac140002","identifier":"5b40e17b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["04"],"humanCodingScheme":"4.NF.3.b","fullStatement":"Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, *for example, by using a visual fraction model. For example, 3\/8 = 1\/8 + 1\/8 + 1\/8; 3\/8 = 1\/8 + 2\/8; 2 1\/8 = 1 + 1 + 1\/8; 2 1\/8 = 8\/8 + 8\/8 + 1\/8. *","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40e2a5-f280-11e8-9cff-0242ac140002","identifier":"5b40e2a5-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["04"],"humanCodingScheme":"4.NF.3.c","fullStatement":"Add and subtract mixed numbers with like denominators, for example, by replacing each mixed number with an equivalent fraction, and\/or by using properties of operations and the relationship between addition and subtraction. *For example, 3 1\/4 + 2 1\/4 = 13\/4 + 9\/4 = 22\/4; 3 1\/4 + 2 1\/4 = (3+ 2) + (1\/4 + 1\/4) = 5 + 2\/4 = 5 2\/4, which is equivalent to 22\/4. *","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40e49f-f280-11e8-9cff-0242ac140002","identifier":"5b40e49f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["04"],"humanCodingScheme":"4.NF.3.d","fullStatement":"Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, *for example, by using visual fraction models and equations to represent the problem.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40e906-f280-11e8-9cff-0242ac140002","identifier":"5b40e906-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NF.4","fullStatement":"Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40e6ee-f280-11e8-9cff-0242ac140002","identifier":"5b40e6ee-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["04"],"humanCodingScheme":"4.NF.4.a","fullStatement":"Understand a fraction a\/b as a multiple of 1\/b. *For example, use a visual fraction model to represent 5\/4 as the product 5 x (1\/4), recording the conclusion by the equation 5\/4 = 5 x (1\/4). *","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40eb00-f280-11e8-9cff-0242ac140002","identifier":"5b40eb00-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["04"],"humanCodingScheme":"4.NF.4.b","fullStatement":"Understand a multiple of a\/b as a multiple of 1\/b, and use this understanding to multiply a fraction by a whole number. *For example, use a visual fraction model to express 3 x (2\/5) as 6 x (1\/5), recognizing this product as 6\/5. (In general, n x (a\/b) = (n x a)\/b).*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40ec3d-f280-11e8-9cff-0242ac140002","identifier":"5b40ec3d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["04"],"humanCodingScheme":"4.NF.4.c","fullStatement":"Solve word problems involving multiplication of a fraction by a whole number *(for example, by using visual fraction models and equations to represent the problem). For example, if each person at a party will eat 3\/8 of a pound of roast beef, and there will be five people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40ed67-f280-11e8-9cff-0242ac140002","identifier":"5b40ed67-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NF.5","fullStatement":"Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. *For example, express 3\/10 as 30\/100, and add 3\/10 + 4\/100 = 34\/100.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40ee80-f280-11e8-9cff-0242ac140002","identifier":"5b40ee80-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NF.6","fullStatement":"Use decimal notation for fractions with denominators 10 or 100. *For example, rewrite 0.62 as 62\/100, describe a length as 0.62 meters; locate 0.62 on a number line diagram.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40ef9c-f280-11e8-9cff-0242ac140002","identifier":"5b40ef9c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.NF.7","fullStatement":"Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols > , = , or < , and justify the conclusions,* for example, by using a visual model.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40c9ef-f280-11e8-9cff-0242ac140002","identifier":"5b40c9ef-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["04"],"humanCodingScheme":"4.OA","fullStatement":"Operations and Algebraic Thinking","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b40cb11-f280-11e8-9cff-0242ac140002","identifier":"5b40cb11-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["04"],"humanCodingScheme":"4.OA.1","fullStatement":"Interpret a multiplication equation as a comparison (*for example, interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5*). 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Represent threefold whole-number products as volumes, *for example, to represent the associative property of multiplication.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4148ac-f280-11e8-9cff-0242ac140002","identifier":"5b4148ac-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["05"],"humanCodingScheme":"5.MD.5.b","fullStatement":"Apply the formulas *V = l x w x h* and *V = b x h* for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4149cb-f280-11e8-9cff-0242ac140002","identifier":"5b4149cb-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["05"],"humanCodingScheme":"5.MD.5.c","fullStatement":"Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b410760-f280-11e8-9cff-0242ac140002","identifier":"5b410760-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["05"],"humanCodingScheme":"5.MP","fullStatement":"Mathematical Practices","notes":"The Standards for Mathematical Practice in Fifth Grade describe mathematical habits of mind that teachers should seek to develop in their students. Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41088e-f280-11e8-9cff-0242ac140002","identifier":"5b41088e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.MP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"Explain the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. When a solution pathway does not make sense, look for another pathway that does. Explain connections between various solution strategies and representations. Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4109b8-f280-11e8-9cff-0242ac140002","identifier":"5b4109b8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.MP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Make sense of quantities and their relationships in problem situations. Contextualize quantities and operations by using images or stories. Decontextualize a given situation and represent it symbolically. Interpret symbols as having meaning, not just as directions to carry out a procedure. Know and flexibly use different properties of operations, numbers, and geometric objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b410adf-f280-11e8-9cff-0242ac140002","identifier":"5b410adf-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.MP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. 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Identify important quantities in a contextual situation, use mathematical models to show the relationships of those quantities, analyze the relationships, and draw conclusions. Models may be verbal, contextual, visual, symbolic, or physical.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b410d41-f280-11e8-9cff-0242ac140002","identifier":"5b410d41-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.MP.5","fullStatement":"Use appropriate tools strategically.","notes":"Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b410e6b-f280-11e8-9cff-0242ac140002","identifier":"5b410e6b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.MP.6","fullStatement":"Attend to precision.","notes":"Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41116f-f280-11e8-9cff-0242ac140002","identifier":"5b41116f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.MP.7","fullStatement":"Look for and make use of structure.","notes":"Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b411348-f280-11e8-9cff-0242ac140002","identifier":"5b411348-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.MP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b411ba0-f280-11e8-9cff-0242ac140002","identifier":"5b411ba0-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["05"],"humanCodingScheme":"5.NBT","fullStatement":"Number and Operations in Base Ten","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b411d57-f280-11e8-9cff-0242ac140002","identifier":"5b411d57-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NBT.1","fullStatement":"Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1\/10 of what it represents in the place to its left.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b411e91-f280-11e8-9cff-0242ac140002","identifier":"5b411e91-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NBT.2","fullStatement":"Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. 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Illustrate and explain the calculation by using equations, rectangular arrays, and\/or area models.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b412670-f280-11e8-9cff-0242ac140002","identifier":"5b412670-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NBT.7","fullStatement":"Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and\/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. In this standard, dividing decimals is limited to a whole number dividend with a decimal divisor or a decimal dividend with a whole number divisor. Compare the value of the quotient on the basis of the values of the dividend and divisor.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41279c-f280-11e8-9cff-0242ac140002","identifier":"5b41279c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["05"],"humanCodingScheme":"5.NF","fullStatement":"Number and Operations - Fractions","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4128c2-f280-11e8-9cff-0242ac140002","identifier":"5b4128c2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NF.1","fullStatement":"Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. *For example, 2\/3 + 5\/4 = 8\/12 + 15\/12 = 23\/12. (In general, a\/b + c\/d = (ad + bc)\/bd.)*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b412a9f-f280-11e8-9cff-0242ac140002","identifier":"5b412a9f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NF.2","fullStatement":"Solve real-world problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators by, *for example, using visual fraction models or equations to represent the problem*. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. *For example, recognize 2\/5 + 1\/2 = 3\/7 as an incorrect result, by observing that 3\/7 < 1\/2.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b412cb3-f280-11e8-9cff-0242ac140002","identifier":"5b412cb3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NF.3","fullStatement":"Interpret a fraction as division of the numerator by the denominator (a\/b = a \u00f7 b). Solve real-world problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, through the use of visual fraction models or equations to represent the problem. *For example, interpret 3\/4 as the result of dividing three by four, noting that 3\/4 multiplied by four equals three, and that when three wholes are shared equally among four people each person has a share of size 3\/4. If nine people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b412f61-f280-11e8-9cff-0242ac140002","identifier":"5b412f61-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NF.4","fullStatement":"Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b412e32-f280-11e8-9cff-0242ac140002","identifier":"5b412e32-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["05"],"humanCodingScheme":"5.NF.4.a","fullStatement":"Interpret the product (a\/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q \u00f7 b using a visual fraction model. *For example, use a fraction model to show (2\/3) x 4 = 8\/3, and create a story context for this equation. Do the same with (2\/3) x (4\/5) = 8\/15. (In general, (a\/b) x (c\/d) = ac\/bd.)*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41307d-f280-11e8-9cff-0242ac140002","identifier":"5b41307d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["05"],"humanCodingScheme":"5.NF.4.b","fullStatement":"Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4132d8-f280-11e8-9cff-0242ac140002","identifier":"5b4132d8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NF.5","fullStatement":"Interpret multiplication as scaling.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4131a7-f280-11e8-9cff-0242ac140002","identifier":"5b4131a7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["05"],"humanCodingScheme":"5.NF.5.a","fullStatement":"Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. *For example, the products of expressions such as 5 x 3 or \u00bd x 3 can be interpreted in terms of a quantity, three, and a scaling factor, five or \u00bd. Thus in addition to knowing that 5 x 3 = 15, they can also say that 5 x 3 is five times as big as three, without evaluating the product. Likewise they see \u00bd x 3 as half the size of three.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4133f2-f280-11e8-9cff-0242ac140002","identifier":"5b4133f2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["05"],"humanCodingScheme":"5.NF.5.b","fullStatement":"Explain why multiplying a given number by a fraction greater than one results in a product greater than the given number (recognizing multiplication by whole numbers greater than one as a familiar case); explain why multiplying a given number by a fraction less than one results in a product smaller than the given number; and relate the principle of fraction equivalence. *For example, 6\/10 = (2x3)\/(2x5). In general, a\/b = (n x a)\/(n x b) has the effect of multiplying a\/b by one.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41351b-f280-11e8-9cff-0242ac140002","identifier":"5b41351b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NF.6","fullStatement":"Solve real-world problems involving multiplication of fractions and mixed numbers,*for example, by using visual fraction models or equations to represent the problem.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b41374f-f280-11e8-9cff-0242ac140002","identifier":"5b41374f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["05"],"humanCodingScheme":"5.NF.7","fullStatement":"Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Use strategies to divide fractions by reasoning about the relationship between multiplication and division. Division of a fraction by a fraction is not a requirement at this grade.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b413631-f280-11e8-9cff-0242ac140002","identifier":"5b413631-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["05"],"humanCodingScheme":"5.NF.7.a","fullStatement":"Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. *For example, create a story context for (1\/3) \u00f7 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1\/3) \u00f7 4 = 1\/12 because (1\/12) x 4 = 1\/3.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b413872-f280-11e8-9cff-0242ac140002","identifier":"5b413872-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["05"],"humanCodingScheme":"5.NF.7.b","fullStatement":"Interpret division of a whole number by a unit fraction, and compute such quotients. *For example, create a story context for 4 \u00f7 (1\/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 \u00f7 (1\/5) = 20 because 20 x (1\/5) = 4.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4139a4-f280-11e8-9cff-0242ac140002","identifier":"5b4139a4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["05"],"humanCodingScheme":"5.NF.7.c","fullStatement":"Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, *for example, by using visual fraction models and equations to represent the problem.* *For example, how much chocolate will each person get if three people share 1\/2 lb. of chocolate equally? How many 1\/3-cup servings are in two cups of raisins?*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b411493-f280-11e8-9cff-0242ac140002","identifier":"5b411493-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["05"],"humanCodingScheme":"5.OA","fullStatement":"Operations and Algebraic Thinking","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b4115ff-f280-11e8-9cff-0242ac140002","identifier":"5b4115ff-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. *For example, given the rule \"add 3\" and the starting number 0, and given the rule \"add 6\" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f2d5b-f280-11e8-9cff-0242ac140002","identifier":"5b3f2d5b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["06"],"humanCodingScheme":"6.EE","fullStatement":"Expressions and Equations","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f2e81-f280-11e8-9cff-0242ac140002","identifier":"5b3f2e81-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.EE.1","fullStatement":"Write and evaluate numerical expressions involving whole-number exponents.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f30c5-f280-11e8-9cff-0242ac140002","identifier":"5b3f30c5-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.EE.2","fullStatement":"Write, read, and evaluate expressions in which letters stand for numbers.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f2f9d-f280-11e8-9cff-0242ac140002","identifier":"5b3f2f9d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.EE.2.a","fullStatement":"Write expressions that record operations with numbers and with letters representing numbers. *For example, express the calculation \"Subtract y from 5\" as 5 \u2013 y and express \"Jane had $105.00 in her bank account. One year later, she had x dollars more. Write an expression that shows her new balance\" as $105.00 + x.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f31dd-f280-11e8-9cff-0242ac140002","identifier":"5b3f31dd-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.EE.2.b","fullStatement":"Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. *For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f32ff-f280-11e8-9cff-0242ac140002","identifier":"5b3f32ff-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.EE.2.c","fullStatement":"Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, applying the Order of Operations when there are no parentheses to specify a particular order. *For example, use the formulas V = s\u00b3 and A = 6s\u00b2 to find the volume and surface area of a cube with sides of length s = 1\/2.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f34eb-f280-11e8-9cff-0242ac140002","identifier":"5b3f34eb-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.EE.3","fullStatement":"Apply the properties of operations to generate equivalent expressions. *For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f363b-f280-11e8-9cff-0242ac140002","identifier":"5b3f363b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.EE.4","fullStatement":"Identify when two expressions are equivalent. *For example, the expressions y + y + y and 3y are equivalent because they name the same number, regardless of which number y represents.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f376d-f280-11e8-9cff-0242ac140002","identifier":"5b3f376d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.EE.5","fullStatement":"Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f38a5-f280-11e8-9cff-0242ac140002","identifier":"5b3f38a5-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.EE.6","fullStatement":"Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f39cd-f280-11e8-9cff-0242ac140002","identifier":"5b3f39cd-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.EE.7","fullStatement":"Solve real-world and mathematical problems by writing and solving equations of the form *x + a = b* and *ax = b* for cases in which a, b and x are all non-negative rational numbers.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f3aee-f280-11e8-9cff-0242ac140002","identifier":"5b3f3aee-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.EE.8","fullStatement":"Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f3c01-f280-11e8-9cff-0242ac140002","identifier":"5b3f3c01-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.EE.9","fullStatement":"Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. *For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f3d18-f280-11e8-9cff-0242ac140002","identifier":"5b3f3d18-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["06"],"humanCodingScheme":"6.G","fullStatement":"Geometry","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f3e3e-f280-11e8-9cff-0242ac140002","identifier":"5b3f3e3e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.G.1","fullStatement":"Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f3f5d-f280-11e8-9cff-0242ac140002","identifier":"5b3f3f5d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.G.2","fullStatement":"Find the volume of a right rectangular prism with appropriate unit fraction edge lengths by packing it with cubes of the appropriate unit fraction edge lengths *(for example, 3\u00bd x 2 x 6*), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas* V = kWh* and *V = bh* to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.","notes":"(Note: Model the packing using drawings and diagrams.)","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f4087-f280-11e8-9cff-0242ac140002","identifier":"5b3f4087-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.G.3","fullStatement":"Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 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Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f0222-f280-11e8-9cff-0242ac140002","identifier":"5b3f0222-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.MP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, \"Does this make sense?\" Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f0346-f280-11e8-9cff-0242ac140002","identifier":"5b3f0346-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.MP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representations by contextualizing and decontextualizing quantitative relationships. This includes the ability to decontextualize a given situation, representing it algebraically and manipulating symbols fluently as well as the ability to contextualize algebraic representations to make sense of the problem.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f0461-f280-11e8-9cff-0242ac140002","identifier":"5b3f0461-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.MP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f057b-f280-11e8-9cff-0242ac140002","identifier":"5b3f057b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.MP.4","fullStatement":"Model with mathematics.","notes":"Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f068e-f280-11e8-9cff-0242ac140002","identifier":"5b3f068e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.MP.5","fullStatement":"Use appropriate tools strategically.","notes":"Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f07a7-f280-11e8-9cff-0242ac140002","identifier":"5b3f07a7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.MP.6","fullStatement":"Attend to precision.","notes":"Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, and express numerical answers with a degree of precision appropriate for the problem context.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f08bf-f280-11e8-9cff-0242ac140002","identifier":"5b3f08bf-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.MP.7","fullStatement":"Look for and make use of structure.","notes":"Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, see 5 \u2013 3(x \u2013 y)\u00b2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f0aa4-f280-11e8-9cff-0242ac140002","identifier":"5b3f0aa4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.MP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f1526-f280-11e8-9cff-0242ac140002","identifier":"5b3f1526-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["06"],"humanCodingScheme":"6.NS","fullStatement":"The Number System","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f175e-f280-11e8-9cff-0242ac140002","identifier":"5b3f175e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.NS.1","fullStatement":"Interpret and compute quotients of fractions.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f1642-f280-11e8-9cff-0242ac140002","identifier":"5b3f1642-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.1.a","fullStatement":"Compute quotients of fractions by fractions, *for example, by applying strategies such as visual fraction models, equations, and the relationship between multiplication and division, to represent problems. *","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f187d-f280-11e8-9cff-0242ac140002","identifier":"5b3f187d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.1.b","fullStatement":"Solve real-world problems involving division of fractions by fractions. *For example, how much chocolate will each person get if three people share 1\/2 pound of chocolate equally? How many 3\/4-cup servings are in 2\/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3\/4 mile and area 1\/2 square mile?*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f199f-f280-11e8-9cff-0242ac140002","identifier":"5b3f199f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.1.c","fullStatement":"Explain the meaning of quotients in fraction division problems. *For example, create a story context for (2\/3) \u00f7 (3\/4) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (2\/3) \u00f7 (3\/4) = 8\/9 because 3\/4 of 8\/9 is 2\/3. 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Use the distributive property to express a sum of two whole numbers 1\u2013100 with a common factor as a multiple of a sum of two whole numbers with no common factor. *For example, express 36 + 8 as 4 (9 + 2).*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f2056-f280-11e8-9cff-0242ac140002","identifier":"5b3f2056-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.NS.5","fullStatement":"Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (*for example, temperature above\/below zero, elevation above\/below sea level, credits\/debits, positive\/negative electric charge*); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f233d-f280-11e8-9cff-0242ac140002","identifier":"5b3f233d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.NS.6","fullStatement":"Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f220e-f280-11e8-9cff-0242ac140002","identifier":"5b3f220e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.6.a","fullStatement":"Recognize opposite signs of numbers as indicating locations on opposite sides of zero on the number line; recognize that the opposite of the opposite of a number is the number itself. *For example, -(-3) = 3, and zero is its own opposite.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f245b-f280-11e8-9cff-0242ac140002","identifier":"5b3f245b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.6.b","fullStatement":"Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f257c-f280-11e8-9cff-0242ac140002","identifier":"5b3f257c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.6.c","fullStatement":"Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f27b8-f280-11e8-9cff-0242ac140002","identifier":"5b3f27b8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.NS.7","fullStatement":"Understand ordering and absolute value of rational numbers.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f2697-f280-11e8-9cff-0242ac140002","identifier":"5b3f2697-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.7.a","fullStatement":"Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. *For example, interpret \u20133 > \u20137 as a statement that \u20133 is located to the right of \u20137 on a number line oriented from left to right.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f28ce-f280-11e8-9cff-0242ac140002","identifier":"5b3f28ce-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.7.b","fullStatement":"Write, interpret, and explain statements of order for rational numbers in real-world contexts. *For example, write \u20133 \u00b0C > \u20137 \u00b0C to express the fact that \u20133 \u00b0C is warmer than \u20137 \u00b0C.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f29e8-f280-11e8-9cff-0242ac140002","identifier":"5b3f29e8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.7.c","fullStatement":"Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world context. *For example, for an account balance of \u201330 dollars, write |\u201330| = 30 to describe the size of the debt in dollars.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f2b19-f280-11e8-9cff-0242ac140002","identifier":"5b3f2b19-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.NS.7.d","fullStatement":"Distinguish comparisons of absolute value from statements about order. *For example, recognize that an account balance less than \u201330 dollars represents a debt greater than 30 dollars.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f2c39-f280-11e8-9cff-0242ac140002","identifier":"5b3f2c39-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.NS.8","fullStatement":"Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. 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The following are examples of ratio language: *\u201cThe ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.\u201d \u201cFor every vote candidate A received, candidate C received nearly three votes.\u201d*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f0e85-f280-11e8-9cff-0242ac140002","identifier":"5b3f0e85-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.RP.2","fullStatement":"Understand the concept of a unit rate a\/b associated with a ratio a:b with b \u2260 0, and use rate language in the context of a ratio relationship. The following are examples of rate language: *\"This recipe has a ratio of four cups of flour to two cups of sugar, so the rate is two cups of flour for each cup of sugar.\" \u201cWe paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.\" (In sixth grade, unit rates are limited to non-complex fractions.)*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f10cf-f280-11e8-9cff-0242ac140002","identifier":"5b3f10cf-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.RP.3","fullStatement":"Use ratio and rate reasoning to solve real-world (with a context) and mathematical (void of context) problems, using strategies such as reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations involving unit rate problems.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f0fb7-f280-11e8-9cff-0242ac140002","identifier":"5b3f0fb7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.RP.3.a","fullStatement":"Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f11e2-f280-11e8-9cff-0242ac140002","identifier":"5b3f11e2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.RP.3.b","fullStatement":"Solve unit rate problems including those involving unit pricing and constant speed. *For example, if it took four hours to mow eight lawns, how many lawns could be mowed in 32 hours? 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Solve problems involving finding the whole, given a part and the percent. *(For example, 30% of a quantity means 30\/100 times the quantity.)*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f1413-f280-11e8-9cff-0242ac140002","identifier":"5b3f1413-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["06"],"humanCodingScheme":"6.RP.3.d","fullStatement":"Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f42c6-f280-11e8-9cff-0242ac140002","identifier":"5b3f42c6-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Choose the most appropriate graph\/plot for the data collected.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f4a57-f280-11e8-9cff-0242ac140002","identifier":"5b3f4a57-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["06"],"humanCodingScheme":"6.SP.5","fullStatement":"Summarize numerical data sets in relation to their context, such as by:","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f4933-f280-11e8-9cff-0242ac140002","identifier":"5b3f4933-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. *For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1\/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3\/4 inches long in the center of a door that is 27 1\/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f7764-f280-11e8-9cff-0242ac140002","identifier":"5b3f7764-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["07"],"humanCodingScheme":"7.EE.4","fullStatement":"Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f7641-f280-11e8-9cff-0242ac140002","identifier":"5b3f7641-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["07"],"humanCodingScheme":"7.EE.4.a","fullStatement":"Solve word problems leading to equations of the form *px + q = r* and *p(x + q) = r*, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. *For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. 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Understand that random sampling is more likely to produce representative samples and support valid inferences.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f84de-f280-11e8-9cff-0242ac140002","identifier":"5b3f84de-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["07"],"humanCodingScheme":"7.SP.2","fullStatement":"Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. *For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f8621-f280-11e8-9cff-0242ac140002","identifier":"5b3f8621-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["07"],"humanCodingScheme":"7.SP.3","fullStatement":"Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. *For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, approximately twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f875f-f280-11e8-9cff-0242ac140002","identifier":"5b3f875f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["07"],"humanCodingScheme":"7.SP.4","fullStatement":"Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. *For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f8887-f280-11e8-9cff-0242ac140002","identifier":"5b3f8887-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["07"],"humanCodingScheme":"7.SP.5","fullStatement":"Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1\/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f89a4-f280-11e8-9cff-0242ac140002","identifier":"5b3f89a4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["07"],"humanCodingScheme":"7.SP.6","fullStatement":"Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. *For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f8be9-f280-11e8-9cff-0242ac140002","identifier":"5b3f8be9-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["07"],"humanCodingScheme":"7.SP.7","fullStatement":"Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f8ac7-f280-11e8-9cff-0242ac140002","identifier":"5b3f8ac7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["07"],"humanCodingScheme":"7.SP.7.a","fullStatement":"Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. *For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f8d07-f280-11e8-9cff-0242ac140002","identifier":"5b3f8d07-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["07"],"humanCodingScheme":"7.SP.7.b","fullStatement":"Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. *For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f8f4d-f280-11e8-9cff-0242ac140002","identifier":"5b3f8f4d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["07"],"humanCodingScheme":"7.SP.8","fullStatement":"Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f8e30-f280-11e8-9cff-0242ac140002","identifier":"5b3f8e30-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["07"],"humanCodingScheme":"7.SP.8.a","fullStatement":"Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f906a-f280-11e8-9cff-0242ac140002","identifier":"5b3f906a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["07"],"humanCodingScheme":"7.SP.8.b","fullStatement":"Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., \u201crolling double sixes\u201d), identify the outcomes in the sample space which compose the event.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f918c-f280-11e8-9cff-0242ac140002","identifier":"5b3f918c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["07"],"humanCodingScheme":"7.SP.8.c","fullStatement":"Design and use a simulation to generate frequencies for compound events. *For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fa27f-f280-11e8-9cff-0242ac140002","identifier":"5b3fa27f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["08"],"humanCodingScheme":"8.EE","fullStatement":"Expressions and Equations","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fa42c-f280-11e8-9cff-0242ac140002","identifier":"5b3fa42c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.EE.1","fullStatement":"Know and apply the properties of integer exponents to generate equivalent numerical expressions. *For example, 3\u00b2 \u00d7 3\u20135<\/sup> = 3\u20133<\/sup> = 1\/3\u00b3 = 1\/27.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fa619-f280-11e8-9cff-0242ac140002","identifier":"5b3fa619-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.EE.2","fullStatement":"Use square root and cube root symbols to represent solutions to equations of the form x\u00b2 = p and x\u00b3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that \u221a2 is irrational.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fa854-f280-11e8-9cff-0242ac140002","identifier":"5b3fa854-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.EE.3","fullStatement":"Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. *For example, estimate the population of the United States as 3 \u00d7 108<\/sup> and the population of the world as 7 \u00d7 109<\/sup>, and determine that the world population is more than 20 times larger.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fa9be-f280-11e8-9cff-0242ac140002","identifier":"5b3fa9be-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.EE.4","fullStatement":"Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3faaff-f280-11e8-9cff-0242ac140002","identifier":"5b3faaff-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.EE.5","fullStatement":"Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. *For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fac44-f280-11e8-9cff-0242ac140002","identifier":"5b3fac44-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.EE.6","fullStatement":"Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation *y = mx* for a line through the origin and the equation *y = mx + b* for a line intercepting the vertical axis at b.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fae9e-f280-11e8-9cff-0242ac140002","identifier":"5b3fae9e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.EE.7","fullStatement":"Solve linear equations and inequalities in one variable.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fad73-f280-11e8-9cff-0242ac140002","identifier":"5b3fad73-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["08"],"humanCodingScheme":"8.EE.7.a","fullStatement":"Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form *x = a*, *a = a*, or *a = b* results (where a and b are different numbers).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fafb9-f280-11e8-9cff-0242ac140002","identifier":"5b3fafb9-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["08"],"humanCodingScheme":"8.EE.7.b","fullStatement":"Solve single-variable linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and collecting like terms.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fb0db-f280-11e8-9cff-0242ac140002","identifier":"5b3fb0db-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["08"],"humanCodingScheme":"8.EE.7.c","fullStatement":"Solve single-variable absolute value equations.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fb31b-f280-11e8-9cff-0242ac140002","identifier":"5b3fb31b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.EE.8","fullStatement":"Analyze and solve pairs of simultaneous linear equations.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fb1f7-f280-11e8-9cff-0242ac140002","identifier":"5b3fb1f7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["08"],"humanCodingScheme":"8.EE.8.a","fullStatement":"Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fb434-f280-11e8-9cff-0242ac140002","identifier":"5b3fb434-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["08"],"humanCodingScheme":"8.EE.8.b","fullStatement":"Solve systems of two linear equations in two variables graphically, approximating when solutions are not integers and estimate solutions by graphing the equations. 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The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 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Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fbc4d-f280-11e8-9cff-0242ac140002","identifier":"5b3fbc4d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.F.5","fullStatement":"Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fbe18-f280-11e8-9cff-0242ac140002","identifier":"5b3fbe18-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["08"],"humanCodingScheme":"8.G","fullStatement":"Geometry","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fc0d8-f280-11e8-9cff-0242ac140002","identifier":"5b3fc0d8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.G.1","fullStatement":"Verify experimentally the properties of rotations, reflections, and translations:","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fbf5c-f280-11e8-9cff-0242ac140002","identifier":"5b3fbf5c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["08"],"humanCodingScheme":"8.G.1.a","fullStatement":"Lines are taken to lines, and line segments to line segments of the same length.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fc2b5-f280-11e8-9cff-0242ac140002","identifier":"5b3fc2b5-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["08"],"humanCodingScheme":"8.G.1.b","fullStatement":"Angles are taken to angles of the same measure.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fc3e4-f280-11e8-9cff-0242ac140002","identifier":"5b3fc3e4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["08"],"humanCodingScheme":"8.G.1.c","fullStatement":"Parallel lines are taken to parallel lines.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fc506-f280-11e8-9cff-0242ac140002","identifier":"5b3fc506-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.G.2","fullStatement":"Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fc62b-f280-11e8-9cff-0242ac140002","identifier":"5b3fc62b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.G.3","fullStatement":"Observe that orientation of the plane is preserved in rotations and translations, but not with reflections. 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Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f93e6-f280-11e8-9cff-0242ac140002","identifier":"5b3f93e6-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.MP.1","fullStatement":"Make sense of problems and persevere in solving them.","notes":"Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, \"Does this make sense?\" Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f9516-f280-11e8-9cff-0242ac140002","identifier":"5b3f9516-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.MP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representations by contextualizing and decontextualizing quantitative relationships. This includes the ability to decontextualize a given situation, representing it algebraically and manipulating symbols fluently as well as the ability to contextualize algebraic representations to make sense of the problem.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f96cc-f280-11e8-9cff-0242ac140002","identifier":"5b3f96cc-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.MP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f981a-f280-11e8-9cff-0242ac140002","identifier":"5b3f981a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.MP.4","fullStatement":"Model with mathematics.","notes":"Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f9949-f280-11e8-9cff-0242ac140002","identifier":"5b3f9949-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.MP.5","fullStatement":"Use appropriate tools strategically.","notes":"Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f9a6f-f280-11e8-9cff-0242ac140002","identifier":"5b3f9a6f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.MP.6","fullStatement":"Attend to precision.","notes":"Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f9b9c-f280-11e8-9cff-0242ac140002","identifier":"5b3f9b9c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.MP.7","fullStatement":"Look for and make use of structure.","notes":"Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, see 5 \u2013 3(x \u2013 y)\u00b2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f9cc2-f280-11e8-9cff-0242ac140002","identifier":"5b3f9cc2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.MP.8","fullStatement":"Look for and express regularity in repeated reasoning.","notes":"Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f9de9-f280-11e8-9cff-0242ac140002","identifier":"5b3f9de9-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["08"],"humanCodingScheme":"8.NS","fullStatement":"The Number System","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3f9f11-f280-11e8-9cff-0242ac140002","identifier":"5b3f9f11-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.NS.1","fullStatement":"Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fa033-f280-11e8-9cff-0242ac140002","identifier":"5b3fa033-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.NS.2","fullStatement":"Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., \u03c0\u00b2). *For example, by truncating the decimal expansion of \u221a2, show that \u221a2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fa15e-f280-11e8-9cff-0242ac140002","identifier":"5b3fa15e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.NS.3","fullStatement":"Understand how to perform operations and simplify radicals with emphasis on square roots.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fce0f-f280-11e8-9cff-0242ac140002","identifier":"5b3fce0f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["08"],"humanCodingScheme":"8.SP","fullStatement":"Statistics and Probability","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fcf33-f280-11e8-9cff-0242ac140002","identifier":"5b3fcf33-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.SP.1","fullStatement":"Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fd052-f280-11e8-9cff-0242ac140002","identifier":"5b3fd052-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.SP.2","fullStatement":"Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fd178-f280-11e8-9cff-0242ac140002","identifier":"5b3fd178-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.SP.3","fullStatement":"Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. *For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm\/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.* (Calculating equations for a linear model is not expected in grade 8.)","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fd2ac-f280-11e8-9cff-0242ac140002","identifier":"5b3fd2ac-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["08"],"humanCodingScheme":"8.SP.4","fullStatement":"Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. 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Is there evidence that those who have a curfew also tend to have chores?*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3deea3-f280-11e8-9cff-0242ac140002","identifier":"5b3deea3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"A.APR","fullStatement":"Algebra - Arithmetic With Polynomials and Rational Expressions","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3e652c-f280-11e8-9cff-0242ac140002","identifier":"5b3e652c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Describe several measurable attributes of a single object.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3ff953-f280-11e8-9cff-0242ac140002","identifier":"5b3ff953-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["KG"],"humanCodingScheme":"K.MD.2","fullStatement":"Directly compare two objects with a measurable attribute in common, to see which object has \"more of\"\/\"less of\" the attribute, and describe the difference. *For example, directly compare the length of two pencils and describe one as shorter or longer.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3ffa83-f280-11e8-9cff-0242ac140002","identifier":"5b3ffa83-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["KG"],"humanCodingScheme":"K.MD.3","fullStatement":"Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. 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Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fd781-f280-11e8-9cff-0242ac140002","identifier":"5b3fd781-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["KG"],"humanCodingScheme":"K.MP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Make sense of quantities and their relationships in problem situations. 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Know and flexibly use different properties of operations, numbers, and geometric objects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fd8cc-f280-11e8-9cff-0242ac140002","identifier":"5b3fd8cc-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["KG"],"humanCodingScheme":"K.MP.3","fullStatement":"Construct viable arguments and critique the reasoning of others.","notes":"Use stated assumptions, definitions, and previously established results to construct arguments. 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Use observations and reasoning to find shortcuts or generalizations. 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Use objects or drawings and record each composition or decomposition by a drawing or equation. *For example, 18 = 10 + 8.* Understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fee08-f280-11e8-9cff-0242ac140002","identifier":"5b3fee08-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Strand","CFItemTypeURI":{"title":"Strand","identifier":"95eec4ae-ca04-58f4-b52e-052ea81a9034","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/95eec4ae-ca04-58f4-b52e-052ea81a9034"},"educationLevel":["KG"],"humanCodingScheme":"K.OA","fullStatement":"Operations and Algebraic Thinking","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3fef28-f280-11e8-9cff-0242ac140002","identifier":"5b3fef28-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["KG"],"humanCodingScheme":"K.OA.1","fullStatement":"Represent addition and subtraction with objects, fingers, mental images, simple drawings, or sounds.*For example, use clapping, act out situations, and use verbal explanations, expressions, or equations.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3ff03e-f280-11e8-9cff-0242ac140002","identifier":"5b3ff03e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["KG"],"humanCodingScheme":"K.OA.2","fullStatement":"Solve addition and subtraction word problems within 10. Use objects or drawings to represent the problem.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3ff15b-f280-11e8-9cff-0242ac140002","identifier":"5b3ff15b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["KG"],"humanCodingScheme":"K.OA.3","fullStatement":"Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings. 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Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3dc7aa-f280-11e8-9cff-0242ac140002","identifier":"5b3dc7aa-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"N.VM.5","fullStatement":"Multiply a vector by a scalar.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3ec83f-f280-11e8-9cff-0242ac140002","identifier":"5b3ec83f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"N.VM.5","fullStatement":"Multiply a vector by a scalar.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3dc8b9-f280-11e8-9cff-0242ac140002","identifier":"5b3dc8b9-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"N.VM.5.a","fullStatement":"Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as *c(vx , vy ) = (cvx , cry)*.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3ec948-f280-11e8-9cff-0242ac140002","identifier":"5b3ec948-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"N.VM.5.a","fullStatement":"Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, *e.g., as c(vx , vy ) = (cvx, cry ).*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3dc9c5-f280-11e8-9cff-0242ac140002","identifier":"5b3dc9c5-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"N.VM.5.b","fullStatement":"Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v \u2260 0, the direction of cv is either along v (for c > 0) or against vs (for c < 0).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3eca5f-f280-11e8-9cff-0242ac140002","identifier":"5b3eca5f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Component","CFItemTypeURI":{"title":"Component","identifier":"1f1afd62-66cd-51cb-8299-1fe5ced9df16","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/1f1afd62-66cd-51cb-8299-1fe5ced9df16"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"N.VM.5.b","fullStatement":"Compute the magnitude of a scalar multiple cv using *||cv|| = |c|v*. Compute the direction of cv knowing that when *|c|v \u2260 0*, the direction of cv is either along v (for c > 0) or against vs (for c < 0).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3dcad3-f280-11e8-9cff-0242ac140002","identifier":"5b3dcad3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"N.VM.6","fullStatement":"Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3ecb72-f280-11e8-9cff-0242ac140002","identifier":"5b3ecb72-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Check answers to problems using a different method.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3eb7e0-f280-11e8-9cff-0242ac140002","identifier":"5b3eb7e0-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"P.MP.2","fullStatement":"Reason abstractly and quantitatively.","notes":"Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representations by contextualizing and decontextualizing quantitative relationships. 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Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3eba50-f280-11e8-9cff-0242ac140002","identifier":"5b3eba50-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"P.MP.4","fullStatement":"Model with mathematics.","notes":"Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3ebb6f-f280-11e8-9cff-0242ac140002","identifier":"5b3ebb6f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"P.MP.5","fullStatement":"Use appropriate tools strategically.","notes":"Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. 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Do the same for other subjects and compare the results.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3e34ba-f280-11e8-9cff-0242ac140002","identifier":"5b3e34ba-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Utah Core Standards for Mathematics","identifier":"4d6ddc0f-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6ddc0f-f280-11e8-9cff-0242ac140002"},"CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"3de18277-9ce2-523b-a70d-e572220eab56","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItemTypes\/3de18277-9ce2-523b-a70d-e572220eab56"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"S.CP.5","fullStatement":"Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. *For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5b3e35c5-f280-11e8-9cff-0242ac140002","identifier":"5b3e35c5-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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