Lesson objective: Apply and extend understanding of adding and subtracting with integers to the set of rational numbers.

This lesson provides an opportunity for students to apply their knowledge and understanding of adding and subtracting integers to the full set of rational numbers. Students are asked to use number lines and the idea of distance and direction to write equivalent expressions to add and subtract.

Key Concept students will use:

- Using distance and direction on the number line, we can understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q).

Skills students will use:

- The sign of a number indicates its direction from 0 (Grade 6, Unit 6)
- Using a number line to represent distance and direction, as well as addition and subtraction of integers
- Writing equivalent expressions (Grade 6, Unit 8)

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they make and defend claims about extending what they know about adding and subtracing integers to the more general set of rational numbers.

**Key vocabulary: **

- integers
- rational numbers

**Special materials needed:**

- Blank number lines (optional)