Mathematics · Grade 3

Active learning ideas

Equivalent Fractions with Visual Models

Active learning works for equivalent fractions because students need to see, touch, and manipulate visual models to truly grasp that different fraction names can describe the same quantity. Physical actions like folding paper or matching strips build spatial reasoning and memory, which static worksheets cannot. This hands-on approach addresses common misconceptions by letting students test and correct their own thinking through direct comparison.

• Ontario Curriculum Expectations
• 3.NF.A.3.A
• 3.NF.A.3.B

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Numbered Heads Together
• 25 min · Pairs

Pairs: Fraction Folding

Give each pair square paper. Fold to show 1/2, unfold and refold into fourths to shade 2/4. Partners discuss and label why amounts match. Share one model with class.

Explain why two different fractions can represent the same amount.

Facilitation Tip

In the Shape Partition Challenge, provide blank paper and colored pencils so students can iterate on their designs if their initial partitions do not yield equivalent fractions.

What to look for

Provide students with pre-drawn shapes (circles, rectangles) divided into different numbers of equal parts. Ask them to shade 1/2 of one shape, then shade an equivalent amount on another shape divided into fourths or eighths. Have them write the two equivalent fractions and explain why they are the same.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 02

• Numbered Heads Together
• 35 min · Small Groups

Small Groups: Strip Matching Game

Provide precut fraction strips for halves, fourths, thirds, sixths. Groups sort and match equivalents by laying strips side-by-side on a mat. Record pairs on chart paper.

Design a visual model to demonstrate that 1/2 is equivalent to 2/4.

What to look for

Give students a card with the fraction 1/3. Ask them to draw a visual model to show an equivalent fraction and write the new fraction. Then, ask them to explain in one sentence how they know the fractions are equivalent.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 03

• Numbered Heads Together
• 40 min · Whole Class

Whole Class: Number Line Parade

Draw large number lines on floor with tape. Students hold cards for 0, 1/2, 1, 2/4. Walk to mark positions, adjust to show equivalence. Discuss overlaps.

Justify how we can find equivalent fractions without drawing pictures.

What to look for

Pose the question: 'Imagine you have a pizza cut into 6 equal slices and another identical pizza cut into 12 equal slices. If you eat 3 slices from the first pizza, how many slices from the second pizza would be the same amount of pizza?' Facilitate a discussion where students use drawings or fraction strips to justify their answers and connect it to equivalent fractions.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

Activity 04

• Numbered Heads Together
• 20 min · Individual

Individual: Shape Partition Challenge

Students draw rectangles or circles, partition into 2, 4, or 8 parts, shade equivalents like 3/4 = 6/8. Self-check with ruler for equal parts.

Explain why two different fractions can represent the same amount.

What to look for

Provide students with pre-drawn shapes (circles, rectangles) divided into different numbers of equal parts. Ask them to shade 1/2 of one shape, then shade an equivalent amount on another shape divided into fourths or eighths. Have them write the two equivalent fractions and explain why they are the same.

• Remember
• Understand
• Apply
• Relationship Skills
• Self-Management

A few notes on teaching this unit

Teachers should approach equivalent fractions by first prioritizing visual and tactile models over symbolic rules. Students need repeated opportunities to repartition the same whole and observe that the shaded amount remains unchanged. Avoid rushing to algorithms; instead, use students’ observations from activities like Shape Partition Challenge to co-construct the multiplication rule together. Research shows that delaying symbolic practice until after concrete experiences leads to deeper, more flexible understanding.

By the end of these activities, students will confidently explain and demonstrate that fractions are equivalent through multiple representations, using visual models to justify their reasoning. They will also be able to generate equivalent fraction pairs independently and describe the process in clear, everyday language. Look for students comparing shaded areas directly, discussing their observations, and applying their understanding to new fraction pairs.

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Watch Out for These Misconceptions

• During Fraction Folding, watch for students who believe that the larger the numbers in the fraction, the bigger the amount.

  Have students fold a paper strip in half and shade it, then fold it in half again to create fourths. Ask them to compare the shaded halves and fourths side by side to see that the area remains the same despite the different numerals.

• During Strip Matching Game, watch for students who think equivalent fractions must look identical in their drawings.

  Provide several identical strips and have students fold one strip into halves and another into fourths. They should match the shaded areas across strips to see that different partitions can represent the same amount.

• During Shape Partition Challenge, watch for students who rely solely on drawing to find equivalent fractions.

  After students partition and shade a shape, ask them to explain the rule they used to create the equivalent fraction. Transition their focus from drawing to verbalizing the multiplication pattern by having them describe it to a partner.

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Methods used in this brief

• Numbered Heads Together