In third grade, students use manipulatives and pictures to show fractions that are equivalent. They are not shown abstract methods to find equivalent fractions, such as multiplying by 2/2. Students are typically successful in third and fourth grades
finding equivalent fractions when they use manipulatives such as fraction circles. However, they sometimes struggle to show their understanding of equivalent fractions when asked to show a pictorial representation. In this lesson, students first find the fraction circle that matches 1/3. They use the fraction piece to cover 1/3 on the circle that shows thirds. They then place the same third on the circle showing sixths. By using the same third, they clearly see that it is 1/3 in the first circle and covers 2/6 in the second circle. The lesson stresses the fact that equivalent fractions cover the same area of the whole. They then show 1/3 on the circle showing ninths. Although it is hard to see in the photos, these fraction circles are slightly translucent. The students can make out how many sections are covered on each circle. It is then simply up to them to interpret the fractions that are covered. They discover that
1/3 = 2/6 = 3/9
This example shows that 1/4 = 2/8 = 3/12
The students can use the same sheet to find fractions equivalent to 2/3 and to 3/4:
Indictors:
6.3.2.1 identify equivalent fractions using
models and pictures.
6.4.1.3 recognize and name equivalent
fractions.
