In the last post, I gave an overview of using math tools to model fractions for comparisons. Here we’ll dive deeper into examples and how to support third graders as they develop their understanding of fractions through comparisons.

## Comparing Fractions With the Same Denominator

Start out with different fractions that have the same denominator. Since each whole is divided into the same number of parts, each part is equal.

**Sixths are all the same size, so the more sixths you have, the larger the fraction. **Pattern blocks easily show how 5/6 is larger than 2/6.

Number lines are also great to compare fractions. Take this example comparing 3/8 and 7/8.

**Students will be able to see that 7/8 is closer to 1 whole, and therefore the larger of the two fractions.**

## Comparing Fractions With the Same Numerator

Students should be comfortable partitioning shapes into equal shares. When they do this, they start to develop an understanding that **more parts means smaller pieces**. This is helpful for students to compare unit fractions (fractions with 1 as the numerator).

In this example, you can see how you can use pattern blocks to show 1/2 is larger than 1/3.

When using number lines with students, either use the same number line to compare fractions, or make sure to **mark 0 and 1 at the same distance if using two separate number lines so the comparisons are accurate.**

Ask students to come up with a rule for comparing fractions with the same numerator. **When two different fractions have the same numerator, the fraction with the smaller denominator is larger. **

## Reminder: Comparisons Only Work if the Whole is the Same

As students are developing their understanding of fractions, it’s essential to remind them that **comparisons are only valid when using the same whole.** Students can visualize half of a small pizza compared to half of an extra large pizza.

This tri-fold offers students another way to explore how fractional pieces change size as the size of the whole changes.

Students can clearly see that where they mark 1/2 changes depending on the length of the number line.