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.

• Grade 3
• Mathematics
• 4 activities
• 20 min–40 min

Learning Objectives

1. Compare visual models to identify equivalent fractions.
2. Explain why two fractions with different numerators and denominators can represent the same value.
3. Design a visual model to demonstrate the equivalence of simple fractions, such as 1/2 and 2/4.
4. Justify how to find equivalent fractions using multiplication or division of the numerator and denominator by the same number.
5. Create pairs of equivalent fractions using visual models and numerical methods.

Jigsaw

⏱ 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.

Prepare & details

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.

Setup: Flexible seating for regrouping

Materials: Expert group reading packets, Note-taking template, Summary graphic organizer

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Jigsaw

⏱ 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.

Prepare & details

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

Setup: Flexible seating for regrouping

Materials: Expert group reading packets, Note-taking template, Summary graphic organizer

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Jigsaw

⏱ 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.

Prepare & details

Justify how we can find equivalent fractions without drawing pictures.

Setup: Flexible seating for regrouping

Materials: Expert group reading packets, Note-taking template, Summary graphic organizer

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Jigsaw

⏱ 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.

Prepare & details

Explain why two different fractions can represent the same amount.

Setup: Flexible seating for regrouping

Materials: Expert group reading packets, Note-taking template, Summary graphic organizer

• Understand
• Analyze
• Evaluate
• Relationship Skills
• Self-Management

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Shape Partition Challenge, provide pre-drawn shapes divided into halves, fourths, or eighths. Ask students to shade 1/2 on one shape and 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 in two sentences.

Exit Ticket

During Fraction Folding, give each student a card with the fraction 1/3. Ask them to draw an equivalent fraction on a folded paper strip and write the new fraction. Then, ask them to explain how they know the fractions are equivalent in one sentence.

Discussion Prompt

During Number Line Parade, pose the question: 'If you have a pizza cut into 6 equal slices and another cut into 12 equal slices, how many slices from the 12-slice pizza would equal 3 slices from the 6-slice pizza?' Ask students to use drawings or fraction strips to justify their answers and connect it to equivalent fractions.

Extensions & Scaffolding

• Challenge students to find three equivalent fractions for 3/4 and create a visual proof for each, using the most creative partition they can imagine.
• For students who struggle, provide fraction strips pre-labeled with halves, fourths, and eighths so they can focus on matching rather than drawing.
• Deeper exploration: Ask students to explain why multiplying the numerator and denominator by the same number always produces an equivalent fraction, using their visual models as evidence.

Key Vocabulary

Equivalent Fractions	Fractions that represent the same portion of a whole, even though they have different numerators and denominators.
Numerator	The top number in a fraction, which tells how many parts of the whole are being considered.
Denominator	The bottom number in a fraction, which tells how many equal parts the whole is divided into.
Fraction Bar	The line separating the numerator and the denominator, indicating division.
Partition	To divide a whole into equal parts or pieces.