Lesson objective: Add rational numbers using the idea of distance and direction.

This lesson helps to build procedural skill with adding rational numbers, including both positive and negative numbers written as fractions or decimals. The number line is used here because it supports students in thinking about the sign of a number indicating direction, and that there are two numbers a given distance from the first addend. This work develops students' understanding that we can think of adding with any rational numbers in the same way we think about adding positive rational numbers, by combining lengths.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they use the structure of addition that they know from working with positive numbers and the structure of the number line to practice representing sums of integers.

**Key vocabulary:**

- integers
- rational numbers

**Special materials needed:**

- blank number lines (optional)