Organization: McGraw-Hill Product Name: Illustrative Math Course 2 2020 Product Version: 1.3 Source: IMS Online Validator Profile: t1.3.0 Identifier: tcc_v1p3 Timestamp: Tuesday, April 27, 2021 01:36 PM EDT Status: VALID! Conformant: true ----- VALID! ----- Resource Validation Results The document is valid. ----- VALID! ----- Schema Location Results Schema locations are valid. ----- VALID! ----- Schema Validation Results The document is valid. ----- VALID! ----- Schematron Validation Results The document is valid. Curriculum Standards: CCSS.Math.Practice.MP6 Attend to precision. - A647016E-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.5.NBT.A.3 Read, write, and compare decimals to thousandths. - 1DB4070A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.NS.A.2.c Apply properties of operations as strategies to multiply and divide rational numbers. - 1ED3352A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.G.B.5 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. - 1EF04980-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.G.A.1 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. - 1EE9F0EE-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. - 1CB15556-7053-11DF-8EBF-BE719DFF4B22 SP.M.7.26.c Design and use a simulation to generate frequencies for compound events. (e.g., Use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?) - D0C08368-C91D-11E5-B405-3A383C6237C7 CCSS.Math.Content.7.NS.A.2.a 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 (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. - 1ED0C7D6-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.8b 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., “rolling double sixes”), identify the outcomes in the sample space which compose the event. - 48CE5968-D9B4-11E2-BCA8-F989D51F4EFC CCSS.Math.Content.7.SP.C.8.a 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. - 1F11763C-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. - 1EFE4E72-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. - 1EDE4C8A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. - 1EFA6C26-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.A.1 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. - 1EF5932C-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. - 4851FD46-D9B4-11E2-BCA8-F989D51F4EFC CCSS.Math.Content.7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. - 1ECF626A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations. - 1EDCE3A4-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.EE.B.4.a Solve word problems leading to equations of the form 𝘱𝘱𝘹 + 𝘱𝘹𝘲 = 𝘱𝘹𝘲𝘳 and 𝘱𝘹𝘲𝘳𝘱(𝘱𝘹𝘲𝘳𝘱𝘹 + 𝘱𝘹𝘲𝘳𝘱𝘹𝘲) = 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳, where 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱, 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲, and 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳 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. - 1EE190CA-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.7.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. - 1F094F8E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.2.MD.A Measure and estimate lengths in standard units. - 1C256E10-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. - 1E1E82CE-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.EE.A Use properties of operations to generate equivalent expressions. - 1ED7DB02-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.NS.A.1.b Understand 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱 + 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲 as the number located a distance |𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲| from 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱, in the positive or negative direction depending on whether 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲 is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. - 1ECBB426-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.RP.A.2.c Represent proportional relationships by equations. - 1EBD422E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. - 1EEB2176-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.EE.B.4 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. - 1EE09E22-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning. - A6497ED0-6F89-11DF-BAEE-EA329DFF4B22 SP.M.7.21 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. (e.g., The mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.) - 6E2B4DDC-C91D-11E5-B319-3B383C6237C7 CCSS.Math.Content.7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. - 1EECC468-7053-11DF-8EBF-BE719DFF4B22 SP.M.7.24 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. (e.g., 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.) - 8D6BC38E-C91D-11E5-9AFD-49383C6237C7 CCSS.Math.Content.7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems. - 1EB29FEA-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.RP.A.2.d Explain what a point (𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹, 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳) where 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳 is the unit rate. - 1EC08E02-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C Investigate chance processes and develop, use, and evaluate probability models. - 1F018E7A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. - 1F0453C6-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.NS.A.1.c Understand subtraction of rational numbers as adding the additive inverse, 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱 – 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲 = 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱 + (–𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲). 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. - 1ECD20F4-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm. - 1E3EC138-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.RP.A.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. - 1EBB74C6-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.5.G.A Graph points on the coordinate plane to solve real-world and mathematical problems. - 1E01A78A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.NS.A.1 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. - 1EC7A304-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. - 1E3FE838-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. - 1E28AC4A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. - 1ED58500-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.5.NF.B.5 Interpret multiplication as scaling (resizing), by: - 1DD7837E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers. - 1E629B3A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.8.c Design and use a simulation to generate frequencies for compound events. - 1F14547E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.5 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. - 1F02DA28-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems. - 47BD948A-D9B4-11E2-BCA8-F989D51F4EFC CCSS.Math.Content.5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. - 1DB21288-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.A.2 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. - 1EF69826-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.RP.A.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. - 1E331C2A-7053-11DF-8EBF-BE719DFF4B22 SP.M.7.22 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. (e.g., 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.) - 792D363C-C91D-11E5-B6F6-E1373C6237C7 SP.M.7.25.b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. (e.g., 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?) - A8295D4E-C91D-11E5-8CF9-FC373C6237C7 CCSS.Math.Content.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. - 1DEA1322-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. - 1EC61534-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.NS.A.1.a Describe situations in which opposite quantities combine to make 0. - 1EC910FE-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.5 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. - 4849173A-D9B4-11E2-BCA8-F989D51F4EFC CCSS.Math.Content.6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. - 1E86309A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. - A6430F50-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.7.EE.B.4.b Solve word problems leading to inequalities of the form 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹 + 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲 > 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳 or 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹 + 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲 < 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳, where 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱, 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲, and 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳 are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. - 1EE45C9C-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.8a 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. - 48C96160-D9B4-11E2-BCA8-F989D51F4EFC CCSS.Math.Content.7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. - 1EB42CFC-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. - 1E394C58-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.NS.A.2.d 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. - 1ED49A78-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.B Draw informal comparative inferences about two populations. - 1EF8DA1E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.RP.A.2 Recognize and represent proportional relationships between quantities. - 1EB72628-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. - 1EC1E018-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Practice.MP4 Model with mathematics. - A6446404-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.7.G.B.6 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. - 1EF1A00A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. - 1F07DFD2-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.G.B Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. - 1EEE21BE-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C Investigate chance processes and develop, use, and evaluate probability models. - 47DF4080-D9B4-11E2-BCA8-F989D51F4EFC CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them. - A630F7A2-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.7.NS.A.2.b 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 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱 and 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲 are integers, then –(𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘱/𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘱𝘲) = (–𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘱𝘲𝘱)/𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘱𝘲𝘱𝘲 = 𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘱𝘲𝘱𝘲𝘱/(–𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘲𝘱𝘲𝘹𝘺𝘳𝘳𝘱𝘲𝘱𝘲𝘱𝘹𝘲𝘳𝘱𝘹𝘲𝘳𝘱𝘲𝘳𝘱𝘲𝘱𝘲𝘱𝘲𝘱𝘲). Interpret quotients of rational numbers by describing real-world contexts. - 1ED1FDF4-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. - 1ED93CAE-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Practice.MP7 Look for and make use of structure. - A648672A-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.5.NF.B Apply and extend previous understandings of multiplication and division to multiply and divide fractions. - 1DCE6E38-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.G.A Draw, construct, and describe geometrical figures and describe the relationships between them. - 1EE8951E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.A.1 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. - 48384720-D9B4-11E2-BCA8-F989D51F4EFC CCSS.Math.Content.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. - 1DD2C06E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. - 1DC0E6DC-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.RP.A.3.b Solve unit rate problems including those involving unit pricing and constant speed. - 1E2D1942-7053-11DF-8EBF-BE719DFF4B22 SP.M.7.25.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. (e.g., 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.) - A20C50A6-C91D-11E5-933C-62CB8A248D58 CCSS.Math.Content.7.SP.C.7.b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. - 1F0C8E56-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. - 1D350A5E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.A Use random sampling to draw inferences about a population. - 1EF4393C-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. - 1DC286F4-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.SP.C.8.b 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., “rolling double sixes”), identify the outcomes in the sample space which compose the event. - 1F12C0E6-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.RP.A.2.a 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. - 1EB93512-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Practice.MP5 Use appropriate tools strategically. - A645CA4C-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.6.NS.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. - 1E5C1346-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.RP.A.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. - 1E2AE88E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.5.OA.B Analyze patterns and relationships. - 1DA6C82E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. - 1EDAA90E-7053-11DF-8EBF-BE719DFF4B22 SP.M.7.18 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. (e.g., 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. 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