7.RP Ratios & Proportional Relationships
7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems
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7.RP.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. -
7.RP.2Recognize and represent proportional relationships between quantities. -
7.RP.2aDecide 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. -
7.RP.2bIdentify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. -
7.RP.2cRepresent proportional relationships by equations. -
7.RP.2dExplain 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. -
7.RP.3Use proportional relationships to solve multistep ratio and percent problems.
7.NS The Number System
7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers
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7.NS.1Apply 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. -
7.NS.1aDescribe situations in which opposite quantities combine to make 0. -
7.NS.1bUnderstand 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. -
7.NS.1cUnderstand 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. -
7.NS.1dApply properties of operations as strategies to add and subtract rational numbers. -
7.NS.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. -
7.NS.2aUnderstand 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. -
7.NS.2bUnderstand 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. -
7.NS.2cApply properties of operations as strategies to multiply and divide rational numbers. -
7.NS.2dConvert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. -
7.NS.3Solve real-world and mathematical problems involving the four operations with rational numbers.
7.EE Expressions & Equations
7.EE.A Use properties of operations to generate equivalent expressions
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7.EE.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. -
7.EE.2Understand 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.
7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations
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7.EE.3Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, 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. -
7.EE.4Use 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. -
7.EE.4aSolve 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. -
7.EE.4bSolve 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.
7.G Geometry
7.G.A Draw, construct, and describe geometrical figures and describe the relationships between them
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7.G.1Solve 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. -
7.G.2Draw (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. -
7.G.3Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
7.G.B Solve real-life and mathematical problems involving angle measure, area, surface area, and volume
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7.G.4Know the formulas for the area and circumference of a circle and use them to solve problems. -
7.G.5Use 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. -
7.G.6Solve 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.
7.SP Statistics & Probability
7.SP.A Use random sampling to draw inferences about a population
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7.SP.1Understand 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. -
7.SP.2Use 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.
7.SP.B Draw informal comparative inferences about two populations
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7.SP.3Informally 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. -
7.SP.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
7.SP.C Investigate chance processes and develop, use, and evaluate probability models
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7.SP.5Understand 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. -
7.SP.6Approximate 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. -
7.SP.7Develop 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. -
7.SP.7aDevelop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. -
7.SP.7bDevelop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. -
7.SP.8Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. -
7.SP.8aUnderstand 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. -
7.SP.8bRepresent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. -
7.SP.8cDesign and use a simulation to generate frequencies for compound events.