Fraction number line: An evidence-based math strategy

Comparing fractions can be hard for many elementary students. They often have trouble figuring out if one fraction is greater than, less than, or equal to another fraction.

Students with learning differences like dyscalculia may have an especially hard time with this skill. That’s because they have difficulty with number sense. They often have trouble understanding quantities and comparing two whole numbers. Some students may also wrongly apply their knowledge of comparing whole numbers to comparing fractions. They might think that 1/4 is larger than 1/2 because the whole number 4 is larger than the whole number 2.

A fraction number line can help all students compare fractions, especially students who learn and think differently. It’s just one strategy you can use to provide students with evidence-based math instruction.

Watch: See fraction number lines in action

Download: Printable fraction number line

Read: How to use this strategy

Objective: Students will use a visual model to compare fractions with common and different denominators.

Grade levels (with standards):

• 3 (Common Core Math 3.NF.A.2: Understand a fraction as a number on the number line)

• 4 (Common Core Math 4.NF.A.2: Compare two fractions with different numerators and different denominators)

Best used for instruction with:

• Small groups

• Whole class

• Individuals

How to prepare:

Gather materials. Give each student a copy of the fraction number line download and two colored pencils, crayons, or markers. If you make your own fraction number line, make sure it has a small set of whole numbers (like 0 to 1) and a small set of fractions (like 1/4, 1/2, 3/4) between the whole numbers.

How to teach:

1. Explain that number lines can help to compare fractions. Have students look at their number lines and point to the beginning point, the ending point, and the fractions in between. Talk about how equivalent fractions (such as 1/2 and 2/4) are labeled on the number line.

2. Use the number line to solve a story problem they can relate to. For example: Jacob and Amy are running from one end to the other end of the same soccer field. Jacob ran 1/4 of the field before he stopped. Amy ran 1/2 the field. Who went farther?

3. Explicitly teach how to use the number line to solve the problem. Model how to use one color of a pencil, marker, or crayon to show the distance that Jacob ran, from 0 to 1/4, on the number line. You can label this distance as “J.” Do the same with another color for Amy, from 0 to 1/2, labeling it as “A.”

4. Prompt with follow-up questions. Ask students who ran farther — Jacob or Amy? Then, have students represent the relationship between 1/4 (how far Jacob ran) and 1/2 (how far Amy ran). Challenge students to explain why we need to know it was the same field to say who ran farther.

5. Practice. Give students plenty of opportunities for guided and independent practice comparing fractions in word problems using the fraction number line.

Understand: Why this strategy works

Number lines are important visual models in math. They help students understand the abstract concept of numbers, which is particularly helpful for students with learning and thinking differences like dyscalculia.

Research shows that the ability to tell if a fraction is greater than, less than, or equal to another fraction on a number line is the best predictor of success with fractions. A number line can prevent students from applying knowledge of whole numbers to fractions. That’s because it shows that the denominator represents the number of equal parts into which a whole object or set has been divided.

Relating the number line to real-life word problems can also keep students’ attention and connect new learning to prior knowledge. Those connections can help students better retain new concepts.

Connect: Link school to home

Families can reinforce this strategy at home. Share a family-friendly resource about how to use fraction number lines.

Research behind this strategy

“Intensive intervention for students with mathematics difficulties: Seven principles of effective practice,” from Learning Disability Quarterly

“Mathematical interventions for children with special educational needs: A meta-analysis,” from Remedial and Special Education

“Using evidence-based practices to build mathematics competence related to conceptual, procedural, and declarative knowledge,” from Learning Disabilities Research and Practice

“Inclusive Instruction: Evidence-Based Practices for Students With Learning Disabilities,” by Mary Brownell, Sean Smith, Jean Crockett, and Cynthia Griffin