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They analyze givens, constraints, relationships, and goals. They make\nconjectures about the form and meaning of the solution and plan a solution pathway rather than simply\njumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms\nof the original problem in order to gain insight into its solution. They monitor and evaluate their progress\nand change course if necessary. Older students might, depending on the context of the problem, transform\nalgebraic expressions or change the viewing window on their graphing calculator to get the information they\nneed. Mathematically proficient students can explain correspondences between equations, verbal\ndescriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and\nsearch for regularity or trends. Younger students might rely on using concrete objects or pictures to help\nconceptualize and solve a problem. Mathematically proficient students check their answers to problems\nusing a different method, and they continually ask themselves, \"Does this make sense?\" They can\nunderstand the approaches of others to solving complex problems and identify correspondences between\ndifferent approaches.","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2024-07-30T17:32:52+00:00"},{"identifier":"5b7918f5-39a1-4f02-97e1-8a1cbb6b86c0","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItems/5b7918f5-39a1-4f02-97e1-8a1cbb6b86c0","fullStatement":"Reason abstractly and quantitatively.","CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"743c37b9-9a66-4e4e-ba6a-1eca60778834","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItemTypes/743c37b9-9a66-4e4e-ba6a-1eca60778834"},"humanCodingScheme":"MP2","notes":"Mathematically proficient students make sense of quantities and their relationships in problem situations.\nThey bring two complementary abilities to bear on problems involving quantitative relationships: the ability\nto decontextualize\u2014to abstract a given situation and represent it symbolically and manipulate the\nrepresenting symbols as if they have a life of their own, without necessarily attending to their referents\u2014\nand the ability to contextualize, to pause as needed during the manipulation process in order to probe into\nthe referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent\nrepresentation of the problem at hand; considering the units involved; attending to the meaning of\nquantities, not just how to compute them; and knowing and flexibly using different properties of operations\nand objects.","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2024-07-30T17:32:59+00:00"},{"identifier":"a1600e7b-4dd8-4c15-baed-cbd327f06fd2","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItems/a1600e7b-4dd8-4c15-baed-cbd327f06fd2","fullStatement":"Construct viable arguments and critique the reasoning of others.","CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"743c37b9-9a66-4e4e-ba6a-1eca60778834","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItemTypes/743c37b9-9a66-4e4e-ba6a-1eca60778834"},"humanCodingScheme":"MP3","notes":"Mathematically proficient students understand and use stated assumptions, definitions, and previously\nestablished results in constructing arguments. They make conjectures and build a logical progression of\nstatements to explore the truth of their conjectures. They are able to analyze situations by breaking them\ninto cases, and can recognize and use counterexamples. They justify their conclusions, communicate them\nto others, and respond to the arguments of others. They reason inductively about data, making plausible\narguments that take into account the context from which the data arose. Mathematically proficient students\nare also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning\nfrom that which is flawed, and\u2014if there is a flaw in an argument\u2014explain what it is. Elementary students\ncan construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such\narguments can make sense and be correct, even though they are not generalized or made formal until later\ngrades. Later, students learn to determine domains to which an argument applies. Students at all grades can\nlisten or read the arguments of others, decide whether they make sense, and ask useful questions to clarify\nor improve the arguments.","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2024-07-30T17:33:05+00:00"},{"identifier":"5c5b0a15-4eb6-49fe-bb02-a795707b98d3","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItems/5c5b0a15-4eb6-49fe-bb02-a795707b98d3","fullStatement":"Model with mathematics.","CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"743c37b9-9a66-4e4e-ba6a-1eca60778834","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItemTypes/743c37b9-9a66-4e4e-ba6a-1eca60778834"},"humanCodingScheme":"MP4","notes":"Mathematically proficient students can apply the mathematics they know to solve problems arising in\neveryday life, society, and the workplace. In early grades, this might be as simple as writing an addition\nequation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a\nschool event or analyze a problem in the community. By high school, a student might use geometry to solve\na design problem or use a function to describe how one quantity of interest depends on another.\nMathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are\nable to identify important quantities in a practical situation and map their relationships using such tools as\ndiagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships\nmathematically to draw conclusions. They routinely interpret their mathematical results in the context of\nthe situation and reflect on whether the results make sense, possibly improving the model if it has not\nserved its purpose.","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2024-07-30T17:33:23+00:00"},{"identifier":"5609f6b6-b8bd-40e6-aa0d-8ce53ea8e81c","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItems/5609f6b6-b8bd-40e6-aa0d-8ce53ea8e81c","fullStatement":"Use appropriate tools strategically.","CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"743c37b9-9a66-4e4e-ba6a-1eca60778834","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItemTypes/743c37b9-9a66-4e4e-ba6a-1eca60778834"},"humanCodingScheme":"MP5","notes":"Mathematically proficient students consider the available tools when solving a mathematical problem.\nThese tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a\nspreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient\nstudents are sufficiently familiar with tools appropriate for their grade or course to make sound decisions\nabout when each of these tools might be helpful, recognizing both the insight to be gained and their\nlimitations. For example, mathematically proficient high school students analyze graphs of functions and\nsolutions generated using a graphing calculator. They detect possible errors by strategically using estimation\nand other mathematical knowledge. When making mathematical models, they know that technology can\nenable them to visualize the results of varying assumptions, explore consequences, and compare predictions\nwith data. Mathematically proficient students at various grade levels are able to identify relevant external\nmathematical resources, such as digital content located on a website, and use them to pose or solve\nproblems. They are able to use technological tools to explore and deepen their understanding of concepts.","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2024-07-30T17:33:31+00:00"},{"identifier":"996672df-f747-4233-9f57-16037f2d0f8f","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItems/996672df-f747-4233-9f57-16037f2d0f8f","fullStatement":"Attend to precision.","CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"743c37b9-9a66-4e4e-ba6a-1eca60778834","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItemTypes/743c37b9-9a66-4e4e-ba6a-1eca60778834"},"humanCodingScheme":"MP6","notes":"Mathematically proficient students try to communicate precisely to others. They try to use clear definitions\nin discussion with others and in their own reasoning. They state the meaning of the symbols they choose,\nincluding using the equal sign consistently and appropriately. They are careful about specifying units of\nmeasure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate\naccurately and efficiently, express numerical answers with a degree of precision appropriate for the problem\ncontext. In the elementary grades, students give carefully formulated explanations to each other. By the\ntime they reach high school they have learned to examine claims and make explicit use of definitions.","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2024-07-30T17:33:38+00:00"},{"identifier":"48b6e7eb-b44b-4078-91ef-9b5a674fe296","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItems/48b6e7eb-b44b-4078-91ef-9b5a674fe296","fullStatement":"Look for and make use of structure.","CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"743c37b9-9a66-4e4e-ba6a-1eca60778834","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItemTypes/743c37b9-9a66-4e4e-ba6a-1eca60778834"},"humanCodingScheme":"MP7","notes":"Mathematically proficient students look closely to discern a pattern or structure. Young students, for\nexample, might notice that three and seven more is the same amount as seven and three more, or they may\nsort a collection of shapes according to how many sides the shapes have. Later, students will see 7 \u00d7 8\nequals the well remembered 7 \u00d7 5 + 7 \u00d7 3, in preparation for learning about the distributive property. In the\nexpression x2 + 9x + 14, older students can see the 14 as 2 \u00d7 7 and the 9 as 2 + 7. They recognize the\nsignificance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for\nsolving problems. They also can step back for an overview and shift perspective. They can see complicated\nthings, such as some algebraic expressions, as single objects or as being composed of several objects. For\nexample, they can see 5 - 3(x - y)2 as 5 minus a positive number times a square and use that to realize that\nits value cannot be more than 5 for any real numbers x and y.","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2024-07-30T17:33:47+00:00"},{"identifier":"e1778f8d-c8a0-4b75-90d1-ea102fb41e72","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItems/e1778f8d-c8a0-4b75-90d1-ea102fb41e72","fullStatement":"Look for and express regularity in repeated reasoning","CFItemType":"Standard","CFItemTypeURI":{"title":"Standard","identifier":"743c37b9-9a66-4e4e-ba6a-1eca60778834","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItemTypes/743c37b9-9a66-4e4e-ba6a-1eca60778834"},"humanCodingScheme":"MP8","notes":"Mathematically proficient students notice if calculations are repeated, and look both for general methods\nand for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating\nthe same calculations over and over again, and conclude they have a repeating decimal. By paying attention\nto the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope\n3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way\nterms cancel when expanding (x - 1)(x + 1), (x - 1)(x2 + x + 1), and (x - 1)(x3 + x2 + x + 1) might lead them to\nthe general formula for the sum of a geometric series. As they work to solve a problem, mathematically\nproficient students maintain oversight of the process, while attending to the details. They continually\nevaluate the reasonableness of their intermediate results.","language":"en","educationLevel":["KG","01","02","03","04","05","06","07","08","09","10","11","12"],"lastChangeDateTime":"2024-07-30T17:33:53+00:00"}],"CFAssociations":[{"identifier":"e4e40885-5bbf-41c0-bbd1-d6db9e6198d4","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFAssociations/e4e40885-5bbf-41c0-bbd1-d6db9e6198d4","lastChangeDateTime":"2024-07-30T01:21:43+00:00","sequenceNumber":2,"originNodeURI":{"title":"Standards for Math Content","identifier":"80de3bbe-2954-473e-b933-d81c916f89eb","uri":"https://satchel.commongoodlt.com/ims/case/v1p0/CFItems/80de3bbe-2954-473e-b933-d81c916f89eb"},"associationType":"isChildOf","destinationNodeURI":{"title":"Oregon Mathematics Standards 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