Lesson objective: Apply understanding of distance, direction, and locations on the number line to justify sums of integers.

This lesson provides an opportunity for students to apply their knowledge and understanding of the location of signed numbers on the number line to a mathematical situation. Students are asked to make and defend claims or make and test conjectures about distances and direction to find sums of rational numbers.

Key Concept students will use:

- positive and negative directions to understand that the number
*p *+ *q* is a distance from *p* equal to the absolute value of *q*. (For instance, 14 is a distance fo 5 from 9, but 4 is also a distance of 5 from 9, but in the opposite direction.)

Skills students will use:

- locating numbers on the number line
- understanding that distances are determined by a number's distance from 0, and that a particular distance can be identified between other points on the number line
- understanding that addition of rational numbers can be thought of as joining distances

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they create claims and justifications about sums of rational numbers using a number line.

**Key vocabulary: **

- integers
- rational numbers

**Special materials needed:**

- blank number lines (optional)