In this section, students make sense of adding and subtracting signed numbers. They begin by considering how changes in temperature and elevation can be represented with tables, number line diagrams, expressions, and equations. Then they use these examples to generalize rules for adding signed numbers. They apply the rules to signed numbers that represent money contexts, including deposits, withdrawals, and...

In this section, students explore ways to represent pairs of numbers that include negative values. They do so by extending the horizontal axis to the left of and the vertical axis below and plotting ordered pairs in all four quadrants of the coordinate plane. They reason about how to appropriately scale and label a set of axes in order to...

Work in this section expands students’ understanding of the number system to include both positive and negative numbers. Students begin by examining situations involving temperature and elevation to understand the need for numbers less than 0. They work with both vertical and horizontal number lines to represent positive and negative values, observing the symmetry present in the number line. Students...

In this section, students solve problems involving the four operations with rational numbers. First, they evaluate algebraic expressions involving signed numbers. They extend their understanding of algebraic notation to include negative numbers, by using “next to” notation (that is, numbers or variables placed next to each other, either with or without parentheses) to represent multiplication and the fraction bar to...

In this section, students make sense of multiplying and dividing signed numbers. They begin by exploring constant velocity. This builds on their previous work with constant speed but uses signed numbers to represent positions and movement in opposite directions from a reference point. Students calculate the resulting position for a given velocity and time. Then they use these examples to...