Lesson objective: Multiply a non-unit fraction by a whole number by using arrows on a number line.

This lesson helps to build procedural skill with multiplying non-unit fractions by whole numbers. A number line is used here because it reinforces the understanding that fractions are numbers and because it illustrates that the product will be the same whether the multiplication is represented as sets of the unit fraction or sets of the non-unit fraction. This work develops students' understanding that a multiple of \(\frac ab\) is a multiple of \(\frac1b\): (n x \(\frac ab\)) = \(\frac {n\ \times\ a}b\).

Students engage in Mathematical Practice 4 (model with mathematics) as they use number lines to represent and solve multiplication problems involving a non-unit fraction and a whole number. Students also engage in Mathematical Practice 8 (look for and express regularity in repeated reasoning) as they begin to develop an understanding of the algorithm n ×\(\frac ab\)= \(\frac {n\ \times\ a}b\).

**Key vocabulary:**

- multiple
- non-unit fraction
- unit fraction
- whole number

**Special materials needed:**

- game cards for "Number Line Mind Meld" (see "Additional materials")