# Using Benchmark Fractions to Compare Fractions

Ever hear groans when you start a fraction unit? I sure have. And I totally get it. Fractions can be hard! But with the right strategies and resources, they’re much easier for kids to understand. When teaching elementary students to compare fractions, one of my favorite strategies to use is benchmark fractions.

## What Are Benchmark Fractions?

So first, what are we talking about? Benchmark fractions are common fractions that we compare other fractions to. They are simple fractions that students are familiar with. They’re helpful to use when comparing and ordering fractions that are harder to visualize, like 8/11, because they can help us estimate. For that reason, they’re also useful when teaching students how to estimate sums and differences of fractions.

Generally speaking, benchmark fractions are 0, 1/2, and 1. These are the numbers I’ve used with 4th grade students. With 5th graders, I might use 0, 1/4, 1/2, 3/4, and 1.

## Why Teach Benchmark Fractions?

Let’s pretend we need to compare 2/12 and 6/7.

It looks tricky at first, right? If we solve this problem the long way, we have to calculate the lowest common denominator, multiply both fractions so they have the same denominator, and then compare them.

It’s much faster and easier if we instead compare these fractions using the benchmarks of 0, 1/2, and 1.

By using these familiar and simpler fractions, students have an easier time doing the computation we’re asking them to do. This strategy helps them develop their fraction number sense and mental math skills.

## Benchmark Fractions Activities

A simple way to kick off a lesson on benchmark fractions is to show students a picture like the one below and ask questions like, “Which donut is approximately half-eaten? Which donut is nearly whole, and which one is almost gone?” This example helps students see that we actually use benchmarks in real life!

To start, I recommend modeling problems using a number line and manipulatives like fraction circles and fraction tiles. These visuals help to make benchmark fractions more concrete as you’re introducing this skill.

I like to begin by comparing fractions to 0 and 1. This is a little easier for students. For example, I might show fractions like 1/9 and 10/12 and ask students whether they’re closer to 0 or to 1.

After some practice, we can tackle comparing fractions to one half, again using number lines and manipulatives.

After students have this down, we can move to comparing fractions to each other by comparing both of them to the benchmarks.

When comparing 4/10 and 6/7, students can use the benchmarks of 1/2 and 1. Since 1 is larger than 1/2, students can estimate that 6/7 is larger than 4/10.

### Benchmark Fractions with Mental Math

The next step is to try this strategy without visual aids. You’ll want to have already taught equivalent fractions before starting this.

It’s fairly easy for students to compare fractions to 0 and 1 by comparing the numerator to the denominator. Comparing fractions to 1/2 requires a little more mental math. I ask students to look at the denominator of the fraction and determine what fraction (using that denominator) would be equivalent to 1/2. A simple way to do this is to just divide the denominator by 2.

For example, let’s use the fraction 4/10. 5/10 is equivalent to 1/2. So if we have a fraction with 10 as the denominator, we know that 5/10 is exactly half. When we compare 4/10 to 5/10, we see it’s only 1/10 away. It’s much closer to 5/10, or 1/2, than it is to 0 or 1.

Students definitely need repeated practice with this! It’s harder with odd-numbered denominators, so I recommend starting with even denominators of 12 or less.

In our earlier example of 3/11 and 6/7, 3/11 is closer to 0 and 6/7 is closer to 1. 0 <1, so we know that 3/11 < 6/7. If you choose to also use 1/4 and 3/4 as benchmarks, that can help students reach a more specific answer.

### Benchmark Fraction Resources

A sorting activity is a great way to assess if students are grasping this skill.

Be sure to grab these free benchmark fractions worksheets and anchor chart!

I hope this post helps you see why benchmark fractions are a great strategy for comparing and ordering fractions! If you want to save time, you can grab my benchmark fractions bundle. Be sure to let me know what other strategies you use to teach this lesson!

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