Lesson objective: Divide negative and positive numbers by representing problems on the number line.

From 7.NS.A.2a, students bring prior knowledge of representing multiplication with negative numbers on the number line. This prior knowledge is extended to dividing with negative numbers as students rewrite division equations as multiplication equations. A conceptual challenge students may encounter is understanding that the "rules" for multiplying with negatives are not simply arbitrary facts to memorize but they follow naturally from their understanding of the number line.

Work with the number line helps students deepen their understanding of operations because they will be able to discover the patterns or "rules" for dividing with negative numbers (i.e., a positive number divided by a negative number equals a negative quotient, a negative number divided by a positive number equals a negative quotient, and a negative number divided by a negative number equals a positive quotient).

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they extend their knowledge of the number line to include dividing with positive and negative numbers and notice patterns in their work.

**Key vocabulary:**

- opposite
- dividend
- divisor
- quotient

**Special materials needed:**