Adding and Subtracting Integers | Represent addition and subtraction on a horizontal or vertical number line diagram. (7.NS.1)
Model subtraction of rational numbers as adding the additive inverse, 𝑝𝑝−𝑞𝑞=𝑝𝑝+(−𝑞𝑞). (7.NS.1c)
Solve and interpret real-world and mathematical problems involving the four operations with rational numbers. (7.NS.3) |

Multiplying and Dividing Integers | Apply and extend previous understandings of multiplication and division of positive rational numbers to multiply and divide all rational numbers. (7.NS.2)
Solve and interpret real-world and mathematical problems involving the four operations with rational numbers. (7.NS.3) |

Rational Numbers | Apply properties of operations as strategies to multiply and divide rational numbers. (7.NS.2c)
Model subtraction as the distance between two rational numbers on the number line where the distance is the absolute value of their difference. (7.NS.1d)
Model subtraction of rational numbers as adding the additive inverse, 𝑝𝑝−𝑞𝑞=𝑝𝑝+(−𝑞𝑞). (7.NS.1c)
7.NS.2 - Apply and extend previous understandings of multiplication and division of positive rational numbers to multiply and divide all rational numbers.
7.EE.3 - Solve multi-step real-life and mathematical problems with rational numbers. 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. |

Rates and Proportionality | Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (7.RP.1)
Recognize and represent proportional relationships between quantities. (7.RP.2)
Determine whether two quantities are in a proportional relationship. (7.RP.2a) |

Expressions and Equations | Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. (7.EE.1)
Use variables to represent quantities in a real-world or mathematical problem, and construct two-step equations and inequalities to solve problems by reasoning about the quantities. (7.EE.4)
Solve word problems leading to equations of the form 𝑝𝑝𝑝𝑝+𝑞𝑞=𝑟𝑟, and 𝑝𝑝(𝑥𝑥+𝑞𝑞)=𝑟𝑟where p, q, and r are specific rational numbers. Solve equations of these forms fluently (efficiently, accurately, and flexibly). Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. (7.EE.4a) |