Comparing Fractions Through a Number Sense Building Lens

Building number sense doesn’t need to be a separate activity in your classroom. Teaching comparing fractions? Let’s boost your student’s number sense in the process!

How can we build number sense? We can build our student’s flexibility with numbers by strengthening their understanding of number relationships including:

  • One More/One less and Two More/Two Less
  • Spatial Relationships
  • Part/Whole Thinking
  • Benchmarks Numbers

Each of the following fraction comparison activities will target and boost one (or more!) of these number relationships for your students.

This is certainly not an exhaustive list of fraction comparison activities but rather a look at a few easy-to-implement activities through the lens of number sense.

Pattern Block Fraction Comparison

In this activity, students choose a comparison card, build the fractions using pattern blocks and then shade in a model before recording a comparison statement.

Why does this activity build number sense?

  • This activity builds your student’s spatial relationships as they gain mental images of a whole, 1/2, and 1/3. Your students see the size of each of these pieces relative to one another
  • This activity promotes the part/whole relationship. If your students are to build 6/6 for example, they see that they need six separate 1/6 pieces to create that fraction. Your students also see that unit fractions can be put together to compose other fractions.

Ordering Fraction Strips

When teaching students to compare fractions it is helpful to start with two main ideas:

  1. Fractions with the same denominator can be compared by looking at the numerators. Since all pieces are the same size, the greater the numerator, the greater the fraction.
  2. Fractions with the same numerator are referring to two fractions with the same number of pieces. Looking at the denominator can tell us which fraction has “bigger” pieces and therefore a greater fraction.

Ordering fraction strips with the same denominator can help students to build number sense that makes the first type of comparison above a breeze!

  • Ordering fraction strips builds spatial relationships as your students gain a mental picture of, for example, 1/3, 2/3 and 3/3.
  • The benchmark numbers relationship is also boosted as students see each of the fraction strips grow relative to the whole.

Drawing Tape Diagrams

When students are comparing fractions that have the same numerator it is critical that they are able to reason about the size of the denominator.

The greater the denominator, the greater number of pieces the whole is broken into and so each share is smaller.

This isn’t necessarily intuitive to students. Up until this point in their schooling, bigger numbers meant a greater amount! Using visuals and asking students to partition a whole into equal parts supports your students in gaining this understanding.

This activity also builds your students number sense around fraction numbers:

  • Building with fraction strips and drawing a tape diagram (and having to partition the whole into equal pieces!) boost your students spatial relationships.
  • When using tape diagrams students can begin to notice the part of the whole that is shaded *as well as* the part of the whole that is not shaded! 4/6 is greater than 4/8 because it is a lot closer to the whole! This idea strengthens both your students benchmark understanding of fractions as well as their understanding of the part/whole relationship.

Related Resources

Looking for activities to support your small groups in understanding fraction comparisons? Check out this unit! It includes everything you need to teach the concept including:

  • Simple to implement ENGAGING lessons
  • Pre and Post Assessment
  • Independent Practice Activities
  • Daily Exit Tickets for Understanding

Units are EASY to prep, EASY to follow and pack a punch in terms of helping your students to understand difficult concepts such as comparing fractions!


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