Lesson objective: Extend the understanding that there are rules for adding and subtracting rational numbers.

Students bring prior knowledge of adding and subtracting integers from 7.NS.A.1.B. This prior knowledge is extended to adding and subtracting rational numbers as students discover and apply the rules derived from operating with rational numbers. A conceptual challenge students may encounter is understanding the difference between operations and signs (i.e. 9 - (+8) = 1).

The concept is developed through work with number lines and equations, which reveal patterns for how rational numbers relate to each other when operating with addition and subtraction.

This work helps students deepen their understanding of operations because discovering the patterns that lead to the rules stems from the meanings and connections between operations students have previously learned using numbers they know.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they work through equations that reveal patterns while adding and subtracting rational numbers.

**Key vocabulary:**

- integer
- positive
- negative
- rational number
- sign