Section	Teacher-facing learning goals
Interpreting Negative Numbers	Lesson 1 Interpret signed numbers in the contexts of temperature and elevation. Order rational numbers, and justify (orally) the comparisons. Plot points on a vertical or horizontal number line to represent rational numbers.
Adding and Subtracting Rational Numbers	Lesson 2 Determine the final temperature given the starting temperature and the change in temperature, and explain (orally and using other representations) the solution method. Explain (orally) how to create a number line diagram that represents adding signed numbers. Write an addition equation to represent a situation involving a temperature increase or decrease. Lesson 3 Comprehend the term “opposite” (in spoken and written language) refers to numbers with the same magnitude but different signs. Create and interpret equations and diagrams that represent adding signed numbers in the context of elevation. Generalize (orally) a method for determining the sum of two signed numbers. Lesson 4 Apply addition of signed numbers to calculate an account balance after a deposit or withdrawal, and explain (orally and using other representations) the solution method. Explain (orally and in writing) how signed numbers can be used to represent situations involving money, including deposits or withdrawals, and assets or debts. Write an equation with an unknown addend to represent a situation where the amount of change is unknown. Lesson 5 Generalize (orally and in writing) that subtracting a number results in the same value as adding the additive inverse. Interpret a number line diagram that represents subtracting signed numbers as adding with an unknown addend. Use a number line diagram to find the difference of signed numbers, and explain (orally) the reasoning. Lesson 6 Compare and contrast (orally) subtraction expressions that have the same numbers in the opposite order. Recognize that the “difference” of two numbers can be positive or negative, depending on the order they are listed, while the “distance” between two numbers is always positive. Subtract signed numbers, and explain (orally) the reasoning. Lesson 7 Apply addition and subtraction of signed numbers to solve problems in an unfamiliar context, and explain (orally and in writing) the solution method. Interpret signed numbers used to represent gains or losses in an unfamiliar context.
Multiplying and Dividing Rational Numbers	Lesson 8 Explain (orally and in writing) how signed numbers can be used to represent positions and speeds in opposite directions. Generalize (orally) that the product of a negative number and a positive number is negative. Write a multiplication equation to represent a situation involving constant speed with direction. Lesson 9 Generalize (orally) that the product of two negative numbers is positive. Interpret signed numbers used to represent elapsed time before or after a chosen reference point. Use patterns to find the product of signed numbers, and explain (orally and using other representations) the reasoning. Lesson 10 - Optional Identify multiplication expressions that are equal, and justify (orally) that they are equal. Multiply rational numbers, including multiplication expressions with three factors, and explain (orally and in writing) the reasoning. Lesson 11 Apply multiplication and division of signed numbers to solve problems involving constant speed with direction, and explain (orally) the reasoning. Generalize (orally) a method for determining the quotient of two signed numbers. Generate a division equation that represents the same relationship as a given multiplication equation with signed numbers. Lesson 12 Apply operations with signed numbers to solve problems involving constant rates, and explain (orally) the solution method. Explain (orally and in writing) how signed numbers can be used to represent situations involving constant rates. Write an equation of the form \(y=\text-kx\) to represent a situation that involves descending at a constant rate.
Four Operations with Rational Numbers	Lesson 13 Evaluate an expression for given values of the variable, including negative values, and compare (orally) the resulting values of the expression. Generalize (orally) about the relationship between additive inverses and about the relationship between multiplicative inverses. Identify numerical expressions that are equal, and justify (orally) that they are equal. Lesson 14 Apply operations with rational numbers to solve problems involving repeated gains or losses, and present (orally, in writing, and using other representations) the solution method.
Solving Equations When There Are Negative Numbers	Lesson 15 Explain (orally and in writing) how to solve an equation of the form \(x+p=q\) or \(px=q\), where \(p\), \(q\), and \(x\) are rational numbers. Generalize (orally) the usefulness of additive inverses and multiplicative inverses for solving equations of the form \(x+p=q\) or \(px=q\). Generate an equation of the form \(x+p=q\) or \(px=q\) to represent a situation involving rational numbers. Lesson 16 Coordinate (orally and in writing) verbal descriptions, equations, and diagrams that represent the same situation involving an unknown amount in the context of temperature or elevation. Write equations of the form \(x+p=q\) or \(px=q\) to represent and solve a problem in an unfamiliar context, and present the solution method (using words and other representations).
Let's Put it to Work	Lesson 17 Apply operations with rational numbers to calculate a stock’s new value, change in value, or change expressed as a signed percentage of the previous value. Compare (orally and in writing) changes in the value of different stocks, including the dollar amount and the percentage of the previous value. Interpret (orally) tables that represent the values of different stocks in the stock market.

7.5 Rational Number Arithmetic