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## Ratios and Proportional Relationships

7.RP.1

Comparing Unit Rates

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

7.RP.2.a

Find, Show Proportional Amounts

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.

7.RP.2.b

Find, Show Proportional Amounts

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.2.c

Represent Proportions

Represent proportional relationships by equations.

7.RP.2.d

Represent Proportions

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.

7.RP.3

Ratio, Proportion Word Problems

Use proportional relationships to solve multistep ratio and percent problems.

## The Number System

7.NS.1.a

Describe situations in which opposite quantities combine to make 0.

7.NS.1.b

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. 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.

7.NS.1.c

Subtract Rational Numbers

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.

7.NS.1.d

Subtract Rational Numbers

Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2.a

Multiply Rational Numbers

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.

7.NS.2.b

Division of Rational Numbers

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 -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

7.NS.2.c

Division of Rational Numbers

Apply properties of operations as strategies to multiply and divide rational numbers.

7.NS.2.d

Convert Numbers to Decimals

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.

7.NS.3

Four Operations with Numbers

Solve real-world and mathematical problems involving the four operations with rational numbers.

## Expressions and Equations

7.EE.1

Factor and Expand

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

7.EE.2

Generate Equivalent Expressions

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.

7.EE.3

Multi-Step, Real-World Problems

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.

7.EE.4.a

Solving Equations

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.

7.EE.4.b

Word Problems: Inequalities

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.

## Statistics and Probability

7.SP.1

Inferential Statistics

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.

7.SP.2

Inferential Statistics

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.

7.SP.4

Measures of Central Tendency

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

7.SP.5

Probability of a Chance Event

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.

7.SP.6

Predict and Compare Probability

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.

7.SP.7.a

Predict and Compare Probability

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

7.SP.7.b

Predict and Compare Probability

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

7.SP.8.a

Probabilities of Compound Events

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.

7.SP.8.b

Summarizing Data Sets

Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.