Comparing Fractions

Fraction comparison has very little to do with looking for tricks in the numbers and everything to do with being able to look at a fraction and reason about the size based on the numerator and denominator. The collection of activities listed below are designed to support your students in developing their number sense and understanding of fractions.

The 5 examples listed are certainly not an exhaustive list of tools and lessons that could be used to teach this skill.

They are rather a sample progression from hands-on to abstract thinking!

Which step represents your students’ current level of understanding?

Introduce your students to stories where they can see what happens to the size of a piece as a fraction changes.

For example, start with a whole candy bar. Ask two students to share the bar. What fraction of the whole candy bar is each student holding?

Next, ask two more students to join into the demonstration. Break the candy bar so it is now in 4 equal pieces. What fraction of the whole candy bar is each student holding now? What happened to the size of their pieces?

Alter the story problem by putting pieces back together in order to compare fractions with unlike numerators. If one student is holding 2/4 of the candy bar, how does the size of their share compare to the students holding only 1/4?

Allow your students to explore with pattern blocks. Given the hexagon as a whole, ask your students:

Did you find any shapes that equaled ½ of the hexagon? Did you find any shapes that equaled 1/3 of the hexagon? Did you find any shapes that equaled 1/6 of the hexagon? You could also ask these questions by saying, what fraction are each of the green triangles that made up a hexagon?

“Which of the pieces is largest? Which of the pieces is smallest? How is 1/6 smaller than 1/3? 6 is a big number? Why is the 1/6 piece smaller than the others?”  A number of your students are likely struggling with this exact though so having a conversation about how the 6 means we have a lot of pieces… a lot of small pieces… will help these students to move towards understanding.

Use fraction bars to prompt a conversation about fractions with the same numerator.

Try this:

To begin the activity, ask students which is more, ¼ or 1/8.

After students answer, show them a set of ¼ fraction bars above a set of 1/8 fraction bars. Ask students if the fraction bars confirm their thinking. How do they know the ¼ pieces are larger than the 1/8 pieces?

Next, ask students “Which would be more, ¾ or 3/8?” Leave the fraction bars on the table for the students to reference in their answer. Look for or model language that reinforces the idea that ¼ size pieces are larger than 1/8 size pieces so three ¼ size pieces are all more than three 1/8 size pieces.

Continue to posing questions comparing fractions with the same numerator but unlike denominators and asking students to share their reasoning by looking at and moving the fraction bars.

This activity is a fun hands-on exploration of fractions with the same denominator.

Begin by giving students strips of paper and asking them to fold the strips into fourths.

Assign some students to shade 1/4 of the fraction strip, some students to shade 2/4, some students to shade 3/4 and some students to shade 4/4 of the strip.

Ask your students to walk around the room comparing their strip with their classmates strips.

Next, remove the visual models and ask your students to report their findings and to compare ¼ with 4/4. Which is the greater amount? How do they know? Ask your students if they can come up with a “rule” that might help them compare fractions whenever the denominator is the same.

Repeat the activity with fractions with a variety of denominators.

Provide your students with a story context and ask them to solve first by reasoning mentally and then by using a variety of tools (pattern blocks, fraction bars, paper strips, tape diagrams, etc.) to confirm and model their thinking.

An example of a comparison story might include:

Ben shared a medium pizza equally with 3 other boys. Rachel and her friend Teagan shared a medium pizza equally as well. Who ate larger pieces of pizza, the boys or the girls?