- 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.<\/li>
- 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.<\/li><\/ul>*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02f05c-f280-11e8-9cff-0242ac140002","identifier":"5d02f05c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.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\/5d02f1fc-f280-11e8-9cff-0242ac140002","identifier":"5d02f1fc-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.4a","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. What is its width?*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02f31f-f280-11e8-9cff-0242ac140002","identifier":"5d02f31f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.4b","fullStatement":"Solve word problems leading to inequalities of the form *px + q > r or px + q < r*, where *p*, *q*, and *r* are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. *For example, as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02f435-f280-11e8-9cff-0242ac140002","identifier":"5d02f435-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.EE.4c","fullStatement":"Solve real-world and mathematical problems by writing and solving equations of the form *x + p = q* and *px = q* in which *p* and *q* are rational numbers.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02f53b-f280-11e8-9cff-0242ac140002","identifier":"5d02f53b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.G.1","fullStatement":"Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02f644-f280-11e8-9cff-0242ac140002","identifier":"5d02f644-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.G.2","fullStatement":"Explore various geometric shapes with given conditions. Focus on creating triangles from three measures of angles and\/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02f74e-f280-11e8-9cff-0242ac140002","identifier":"5d02f74e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.G.3","fullStatement":"Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms, right rectangular pyramids, cones, cylinders, and spheres.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02f854-f280-11e8-9cff-0242ac140002","identifier":"5d02f854-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.G.4","fullStatement":"Given the formulas for the area and circumference of a circle, use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02f96c-f280-11e8-9cff-0242ac140002","identifier":"5d02f96c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.G.5","fullStatement":"Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02fa75-f280-11e8-9cff-0242ac140002","identifier":"5d02fa75-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.G.6","fullStatement":"Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02fc4b-f280-11e8-9cff-0242ac140002","identifier":"5d02fc4b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1","fullStatement":"Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02fd8c-f280-11e8-9cff-0242ac140002","identifier":"5d02fd8c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1a","fullStatement":"Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0. *For example, your bank account balance is -$25.00. You deposit $25.00 into your account. The net balance is $0.00.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02feb2-f280-11e8-9cff-0242ac140002","identifier":"5d02feb2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1b","fullStatement":"Understand *p + q* as the number located a distance |*q*| from *p*, in the positive or negative direction depending on whether *q* is positive or negative. Interpret sums of rational numbers by describing real-world contexts.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d02ffd3-f280-11e8-9cff-0242ac140002","identifier":"5d02ffd3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1c","fullStatement":"Understand subtraction of rational numbers as adding the additive inverse, *p - q* = *p + (-q)*. Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0300dd-f280-11e8-9cff-0242ac140002","identifier":"5d0300dd-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.1d","fullStatement":"Apply properties of operations as strategies to add and subtract rational numbers.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0301df-f280-11e8-9cff-0242ac140002","identifier":"5d0301df-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2","fullStatement":"Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0302e3-f280-11e8-9cff-0242ac140002","identifier":"5d0302e3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2a","fullStatement":"Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (\u2013 1)(\u2013 1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0303f0-f280-11e8-9cff-0242ac140002","identifier":"5d0303f0-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2b","fullStatement":"Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If *p* and *q* are integers then *\u2013(p\/q) = (\u2013p)\/q = p\/(\u2013q)*. Interpret quotients of rational numbers by describing real-world contexts.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0304fb-f280-11e8-9cff-0242ac140002","identifier":"5d0304fb-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2c","fullStatement":"Apply properties of operations as strategies to multiply and divide rational numbers.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030601-f280-11e8-9cff-0242ac140002","identifier":"5d030601-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.2d","fullStatement":"Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030703-f280-11e8-9cff-0242ac140002","identifier":"5d030703-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.NS.3","fullStatement":"Solve real-world and mathematical problems involving the four operations with rational numbers.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030807-f280-11e8-9cff-0242ac140002","identifier":"5d030807-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.1","fullStatement":"Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1\/2 mile in each 1\/4 hour, compute the unit rate as the complex fraction (1\/2)\/(1\/4) miles per hour, equivalently 2 miles per hour.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030916-f280-11e8-9cff-0242ac140002","identifier":"5d030916-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2","fullStatement":"Recognize and represent proportional relationships between quantities.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030a1b-f280-11e8-9cff-0242ac140002","identifier":"5d030a1b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2a","fullStatement":"Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030b1f-f280-11e8-9cff-0242ac140002","identifier":"5d030b1f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2b","fullStatement":"Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030c25-f280-11e8-9cff-0242ac140002","identifier":"5d030c25-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2c","fullStatement":"Represent proportional relationships by equations. *For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030d29-f280-11e8-9cff-0242ac140002","identifier":"5d030d29-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.2d","fullStatement":"Explain what a point (*x,y*) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,*r*) where *r* is the unit rate.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030e32-f280-11e8-9cff-0242ac140002","identifier":"5d030e32-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.RP.3","fullStatement":"Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, and fees.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d030f37-f280-11e8-9cff-0242ac140002","identifier":"5d030f37-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.1","fullStatement":"Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d031044-f280-11e8-9cff-0242ac140002","identifier":"5d031044-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.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\/5d031155-f280-11e8-9cff-0242ac140002","identifier":"5d031155-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.3","fullStatement":"Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the medians by expressing it as a multiple of the interquartile range.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d03125d-f280-11e8-9cff-0242ac140002","identifier":"5d03125d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.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\/5d03136c-f280-11e8-9cff-0242ac140002","identifier":"5d03136c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.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\/5d031479-f280-11e8-9cff-0242ac140002","identifier":"5d031479-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.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. 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\/5d031585-f280-11e8-9cff-0242ac140002","identifier":"5d031585-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.7","fullStatement":"Develop a probability model and use it to find probabilities of events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d03168a-f280-11e8-9cff-0242ac140002","identifier":"5d03168a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.7a","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\/5d03179b-f280-11e8-9cff-0242ac140002","identifier":"5d03179b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.7b","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\/5d031987-f280-11e8-9cff-0242ac140002","identifier":"5d031987-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.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\/5d031a99-f280-11e8-9cff-0242ac140002","identifier":"5d031a99-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.8a","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\/5d031ba2-f280-11e8-9cff-0242ac140002","identifier":"5d031ba2-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.8b","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\/5d031cac-f280-11e8-9cff-0242ac140002","identifier":"5d031cac-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["07"],"humanCodingScheme":"MGSE7.SP.8c","fullStatement":"Explain ways to set up a simulation and use the simulation to generate frequencies for compound events. *For example, if 40% of donors have type A blood, create a simulation to predict 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\/5d031db7-f280-11e8-9cff-0242ac140002","identifier":"5d031db7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.1","fullStatement":"Know and apply the properties of integer exponents to generate equivalent numerical expressions. *For example, $3^2 \\times 3^{(-5)} = 3^{(-3)} = \\frac{1}{(3^3)} = \\frac{1}{27}$.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d031eba-f280-11e8-9cff-0242ac140002","identifier":"5d031eba-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.2","fullStatement":"Use square root and cube root symbols to represent solutions to equations. Recognize that x\u00b2 = p (where p is a positive rational number and |x| \u2264 25) has 2 solutions and x\u00b3 = p (where p is a negative or positive rational number and |x| \u2264 10) has one solution. Evaluate square roots of perfect squares \u2264 625 and cube roots of perfect cubes \u2265 -1000 and \u2264 1000.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d031fcb-f280-11e8-9cff-0242ac140002","identifier":"5d031fcb-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.3","fullStatement":"Use numbers expressed in scientific notation 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 $3 \\times 10^8$ and the population of the world as $7 \\times 10^9$, and determine that the world population is more than 20 times larger.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0321ad-f280-11e8-9cff-0242ac140002","identifier":"5d0321ad-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.4","fullStatement":"Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Understand 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 (e.g. calculators).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d032306-f280-11e8-9cff-0242ac140002","identifier":"5d032306-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.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\/5d03242b-f280-11e8-9cff-0242ac140002","identifier":"5d03242b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.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\/5d03254a-f280-11e8-9cff-0242ac140002","identifier":"5d03254a-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.7","fullStatement":"Solve linear equations in one variable.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d03264f-f280-11e8-9cff-0242ac140002","identifier":"5d03264f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.7a","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\/5d03275c-f280-11e8-9cff-0242ac140002","identifier":"5d03275c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.7b","fullStatement":"Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d03285c-f280-11e8-9cff-0242ac140002","identifier":"5d03285c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.8","fullStatement":"Analyze and solve pairs of simultaneous linear equations (systems of linear equations).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d032964-f280-11e8-9cff-0242ac140002","identifier":"5d032964-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.8a","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\/5d032a66-f280-11e8-9cff-0242ac140002","identifier":"5d032a66-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.8b","fullStatement":"Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. *For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d032b6f-f280-11e8-9cff-0242ac140002","identifier":"5d032b6f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.EE.8c","fullStatement":"Solve real-world and mathematical problems leading to two linear equations in two variables. *For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d032c73-f280-11e8-9cff-0242ac140002","identifier":"5d032c73-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.F.1","fullStatement":"Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d032d77-f280-11e8-9cff-0242ac140002","identifier":"5d032d77-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.F.2","fullStatement":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). *For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d032e88-f280-11e8-9cff-0242ac140002","identifier":"5d032e88-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.F.3","fullStatement":"Interpret the equation *y = mx + b* as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. *For example, the function A = s\u00b2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d032f95-f280-11e8-9cff-0242ac140002","identifier":"5d032f95-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.F.4","fullStatement":"Construct a function to model a linear relationship between two quantities. 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\/5d0330a4-f280-11e8-9cff-0242ac140002","identifier":"5d0330a4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.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\/5d0331ab-f280-11e8-9cff-0242ac140002","identifier":"5d0331ab-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.G.1","fullStatement":"Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0332b6-f280-11e8-9cff-0242ac140002","identifier":"5d0332b6-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.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\/5d0333bf-f280-11e8-9cff-0242ac140002","identifier":"5d0333bf-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.G.3","fullStatement":"Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0334be-f280-11e8-9cff-0242ac140002","identifier":"5d0334be-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.G.4","fullStatement":"Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0335c8-f280-11e8-9cff-0242ac140002","identifier":"5d0335c8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.G.5","fullStatement":"Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. *For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0336d5-f280-11e8-9cff-0242ac140002","identifier":"5d0336d5-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.G.6","fullStatement":"Explain a proof of the Pythagorean Theorem and its converse.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0337d3-f280-11e8-9cff-0242ac140002","identifier":"5d0337d3-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.G.7","fullStatement":"Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0338d6-f280-11e8-9cff-0242ac140002","identifier":"5d0338d6-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.G.8","fullStatement":"Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0339e0-f280-11e8-9cff-0242ac140002","identifier":"5d0339e0-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.G.9","fullStatement":"Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d033ae1-f280-11e8-9cff-0242ac140002","identifier":"5d033ae1-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.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\/5d033bec-f280-11e8-9cff-0242ac140002","identifier":"5d033bec-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.NS.2","fullStatement":"Use rational approximation of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., estimate *\u03c0*\u00b2 to the nearest tenth). *For example, by truncating the decimal expansion of \u221a2 (square root of 2), 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\/5d033cf7-f280-11e8-9cff-0242ac140002","identifier":"5d033cf7-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.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\/5d033dfd-f280-11e8-9cff-0242ac140002","identifier":"5d033dfd-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.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\/5d034088-f280-11e8-9cff-0242ac140002","identifier":"5d034088-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.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.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d034234-f280-11e8-9cff-0242ac140002","identifier":"5d034234-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.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.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d03434c-f280-11e8-9cff-0242ac140002","identifier":"5d03434c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.SP.4a","fullStatement":"Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d034451-f280-11e8-9cff-0242ac140002","identifier":"5d034451-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08"],"humanCodingScheme":"MGSE8.SP.4b","fullStatement":"Use relative frequencies calculated for rows or columns to describe possible association between the two variables. *For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d034564-f280-11e8-9cff-0242ac140002","identifier":"5d034564-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d034756-f280-11e8-9cff-0242ac140002","identifier":"5d034756-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d034ad8-f280-11e8-9cff-0242ac140002","identifier":"5d034ad8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d034be8-f280-11e8-9cff-0242ac140002","identifier":"5d034be8-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d034ced-f280-11e8-9cff-0242ac140002","identifier":"5d034ced-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.1","fullStatement":"Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d034df4-f280-11e8-9cff-0242ac140002","identifier":"5d034df4-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.2","fullStatement":"Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x \u2013 a is p(a), so p(a) = 0 if and only if (x \u2013 a) is a factor of p(x).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d034f0f-f280-11e8-9cff-0242ac140002","identifier":"5d034f0f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.2","fullStatement":"Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x \u2013 a is p(a), so p(a) = 0 if and only if (x \u2013 a) is a factor of p(x).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035019-f280-11e8-9cff-0242ac140002","identifier":"5d035019-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.3","fullStatement":"Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035323-f280-11e8-9cff-0242ac140002","identifier":"5d035323-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.3","fullStatement":"Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035429-f280-11e8-9cff-0242ac140002","identifier":"5d035429-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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For example, the polynomial identity $(x^2 + y^2)^2$ = $(x^2 - y^2)^2$ + $(2xy)^2$ can be used to generate Pythagorean triples.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d03552f-f280-11e8-9cff-0242ac140002","identifier":"5d03552f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.4","fullStatement":"Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity $(x^2 + y^2)^2$ = $(x^2 - y^2)^2$ + $(2xy)^2$ can be used to generate Pythagorean triples.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035638-f280-11e8-9cff-0242ac140002","identifier":"5d035638-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.4","fullStatement":"Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity $(x^2 + y^2)^2$ = $(x^2 - y^2)^2$ + $(2xy)^2$ can be used to generate Pythagorean triples.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d03573d-f280-11e8-9cff-0242ac140002","identifier":"5d03573d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.5","fullStatement":"Know and apply that the Binomial Theorem gives the expansion of ${(x + y)}^n$ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined using Pascal\u2019s Triangle.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035845-f280-11e8-9cff-0242ac140002","identifier":"5d035845-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.5","fullStatement":"Know and apply that the Binomial Theorem gives the expansion of ${(x + y)}^n$ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined using Pascal\u2019s Triangle.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035946-f280-11e8-9cff-0242ac140002","identifier":"5d035946-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.5","fullStatement":"Know and apply that the Binomial Theorem gives the expansion of ${(x + y)}^n$ in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined using Pascal\u2019s Triangle.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035a47-f280-11e8-9cff-0242ac140002","identifier":"5d035a47-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["08","09","10","11"],"humanCodingScheme":"MGSE9-12.A.APR.6","fullStatement":"Rewrite simple rational expressions in different forms using inspection, long division, or a computer algebra system; write a(x)\/b(x) in the form q(x) + r(x)\/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035b54-f280-11e8-9cff-0242ac140002","identifier":"5d035b54-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.6","fullStatement":"Rewrite simple rational expressions in different forms using inspection, long division, or a computer algebra system; write a(x)\/b(x) in the form q(x) + r(x)\/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035c5e-f280-11e8-9cff-0242ac140002","identifier":"5d035c5e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.6","fullStatement":"Rewrite simple rational expressions in different forms using inspection, long division, or a computer algebra system; write a(x)\/b(x) in the form q(x) + r(x)\/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035d61-f280-11e8-9cff-0242ac140002","identifier":"5d035d61-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.7","fullStatement":"Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035e6b-f280-11e8-9cff-0242ac140002","identifier":"5d035e6b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.7","fullStatement":"Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d035f73-f280-11e8-9cff-0242ac140002","identifier":"5d035f73-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.APR.7","fullStatement":"Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d036079-f280-11e8-9cff-0242ac140002","identifier":"5d036079-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions (~~integer inputs only~~).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d03617c-f280-11e8-9cff-0242ac140002","identifier":"5d03617c-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, ~~simple rational,~~ and exponential functions (integer inputs only).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d036283-f280-11e8-9cff-0242ac140002","identifier":"5d036283-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. 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Include equations arising from linear, quadratic, simple rational, and exponential functions ~~(integer inputs only).~~","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d03648d-f280-11e8-9cff-0242ac140002","identifier":"5d03648d-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. Include equations arising from ~~linear,~~ quadratic, ~~simple rational, and exponential~~ functions ~~(integer inputs only).~~","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d036590-f280-11e8-9cff-0242ac140002","identifier":"5d036590-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, ~~quadratic, simple rational,~~ and exponential functions (integer inputs only).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d036737-f280-11e8-9cff-0242ac140002","identifier":"5d036737-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. 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Include equations arising from linear, quadratic, ~~simple rational,~~ and exponential functions (integer inputs only).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d036956-f280-11e8-9cff-0242ac140002","identifier":"5d036956-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.1","fullStatement":"Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, ~~quadratic, simple rational,~~ and exponential functions (integer inputs only).","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d036a5e-f280-11e8-9cff-0242ac140002","identifier":"5d036a5e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.2","fullStatement":"Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (*The phrase \u201cin two or more variables\u201d refers to formulas like the compound interest formula, in which $A = P(1 + r\/n)^{(nt)}$ has multiple variables*.)","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d036b6e-f280-11e8-9cff-0242ac140002","identifier":"5d036b6e-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.2","fullStatement":"Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase \u201cin two or more variables\u201d refers to formulas like the compound interest formula, in which $A = P(1 + r\/n)^{(nt)}$ has multiple variables.)","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d036d4b-f280-11e8-9cff-0242ac140002","identifier":"5d036d4b-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.2","fullStatement":"Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 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(The phrase \u201cin two or more variables\u201d refers to formulas like the compound interest formula, in which $A = P(1 + r\/n)^{(nt)}$ has multiple variables.)","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d0371fd-f280-11e8-9cff-0242ac140002","identifier":"5d0371fd-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.2","fullStatement":"Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 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(The phrase \u201cin two or more variables\u201d refers to formulas like the compound interest formula, in which $A = P(1 + r\/n)^{(nt)}$ has multiple variables.)","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d037524-f280-11e8-9cff-0242ac140002","identifier":"5d037524-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.3","fullStatement":"Represent constraints by equations or inequalities, and by systems of equation and\/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d037640-f280-11e8-9cff-0242ac140002","identifier":"5d037640-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.3","fullStatement":"Represent constraints by equations or inequalities, and by systems of equation and\/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d037d77-f280-11e8-9cff-0242ac140002","identifier":"5d037d77-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - Mathematics - Georgia Standards of Excellence","identifier":"4d6f978d-f280-11e8-9cff-0242ac140002","uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFDocuments\/4d6f978d-f280-11e8-9cff-0242ac140002"},"educationLevel":["09","10","11","12"],"humanCodingScheme":"MGSE9-12.A.CED.4","fullStatement":"Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. *Examples: Rearrange Ohm's law V = IR to highlight resistance R; Rearrange area of a circle formula A = \u03c0 r\u00b2 to highlight the radius r.*","language":"en"},{"uri":"https:\/\/opensalt.net\/ims\/case\/v1p0\/CFItems\/5d037e7f-f280-11e8-9cff-0242ac140002","identifier":"5d037e7f-f280-11e8-9cff-0242ac140002","lastChangeDateTime":"2018-11-27T20:09:36+00:00","CFDocumentURI":{"title":"PCG - 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