Lesson 6

As in previous lessons, students represent a product of fractions with a diagram. This diagram represents the product $\frac{3}{6} \times \frac{4}{5}$. The diagram shows $\frac{3}{6}$ of $\frac{4}{5}$ of the square so that’s $\frac{3}{6}  \times \frac{4}{5}$. The number of shaded pieces is $3 \times 4$, the product of the numerators. The number of pieces in the whole square is $6 \times 5$, the product of the denominators. So the value of the product can also be written as $\frac{3 \times 4}{6 \times 5}$. In the first activity, students relate expressions to the area in diagrams like this and then they use this structure to find products of non-unit fractions in the second activity.