Mathematics · 3rd Year

Active learning ideas

Equivalent Fractions (Simple Cases)

Active learning helps students visualize that different fractions can represent the same amount, moving beyond symbols to concrete understanding. Third-year students need to see, touch, and compare fractions to build lasting comprehension of equivalence rather than memorize rules.

• NCCA Curriculum Specifications
• NCCA: Primary - Fractions

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Gallery Walk
• 30 min · Small Groups

Manipulative Matching: Fraction Strips

Provide pre-cut strips for 1/2, 2/4, 1/3, 2/6. Students lay strips side-by-side on a mat to match equivalents by aligning shaded lengths. Groups record pairs and explain matches to the class.

Explain how two different looking fractions can represent the same amount.

Facilitation Tip

During Manipulative Matching, remind students to align fraction strips carefully to see identical lengths for equivalent fractions.

What to look for

Provide students with pre-drawn fraction strips. Ask them to shade 1/3 on one strip and then shade an equivalent fraction on a second, identical strip, labeling both fractions. Observe if they correctly shade 2/6.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Gallery Walk
• 25 min · Pairs

Paper Folding: Equivalent Shares

Each student folds A4 paper into halves, then refolds into quarters. Shade 1/2 and overlay on 2/4 to compare. Pairs swap papers to verify and label equivalents.

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

Facilitation Tip

For Paper Folding, encourage students to fold slowly and press creases sharply to maintain equal partitions.

What to look for

Present students with two different visual models showing 1/2 and 2/4. Ask: 'How do these models show that the fractions are the same amount? What would you tell someone who said 1/2 and 2/4 are different amounts?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 03

• Gallery Walk
• 35 min · Individual

Circle Models: Pizza Slices

Draw circles as pizzas. Divide one into 2 equal parts and shade 1; divide another into 4 and shade 2. Students compare areas, then create models for 1/3 and 2/6. Share justifications in whole class.

Compare different equivalent fractions and justify their equality.

Facilitation Tip

When using Circle Models, have students color the same amount on each pizza slice to reinforce equal portions.

What to look for

Give each student a card with a fraction, for example, 3/4. Ask them to draw a visual model to represent this fraction and then draw a second model showing an equivalent fraction, writing the equivalent fraction below their drawing.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 04

• Gallery Walk
• 40 min · Small Groups

Sorting Relay: Fraction Cards

Prepare cards with visuals of 1/2, 2/4, etc. Teams race to sort equivalents into piles at stations, then verify with strip models. Discuss errors as a group.

Explain how two different looking fractions can represent the same amount.

What to look for

Provide students with pre-drawn fraction strips. Ask them to shade 1/3 on one strip and then shade an equivalent fraction on a second, identical strip, labeling both fractions. Observe if they correctly shade 2/6.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Experienced teachers approach this topic by starting with concrete models before moving to abstract symbols, as research shows this builds stronger foundational understanding. Avoid rushing to numerical rules; instead, let students discover equivalence through hands-on exploration. Emphasize the importance of the whole remaining consistent across all models to prevent misconceptions about fraction size.

By the end of these activities, students should confidently identify and justify equivalent fractions using visual models and manipulatives. They should explain why fractions like 1/2 and 2/4 are equal by comparing shaded areas and describing the whole uniformly.

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Watch Out for These Misconceptions

• During Manipulative Matching, watch for students who believe 2/4 is larger than 1/2 because the numerator 2 is bigger than 1.

  Prompt students to lay the 1/2 and 2/4 fraction strips side by side and observe that they cover the same length. Ask them to measure and compare the shaded parts directly to see the equivalence.

• During Sorting Relay, watch for students who think fractions are equivalent only if numerator and denominator match exactly.

  During the relay, pause to have students explain why a fraction card with 1/2 fits with a card showing 2/4. Ask them to point to the shaded areas in their models to justify the match.

• During Paper Folding, watch for students who believe more parts in the denominator always means a smaller fraction.

  Have students fold paper into halves and then into fourths, shading 1/2 on both. Guide them to compare the shaded areas and see that 1/2 and 2/4 cover the same amount despite different numbers of parts.

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Methods used in this brief

• Gallery Walk