Mathematical Mastery: Exploring Patterns and Logic · 4th Year (TY)

Active learning ideas

Equivalent Fractions

Equivalent fractions are a visual and kinesthetic concept, and active learning helps students build concrete understanding. When students manipulate materials and interact with different representations, they move beyond rote memorization to grasp the underlying proportional reasoning.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Fractions

• 30–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Gallery Walk
• 45 min · Pairs

Fraction Wall Construction Challenge

Students work in pairs to construct a large fraction wall using coloured paper strips. They must label each strip accurately and then use their wall to identify and record at least three sets of equivalent fractions, explaining their reasoning.

Justify why multiplying the numerator and denominator by the same number does not change the fraction's value.

Facilitation Tip

During the Fraction Wall Construction Challenge, circulate to ensure pairs are accurately comparing the lengths of their paper strips to confirm equivalence.

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

Activity 02

• Gallery Walk
• 30 min · Small Groups

Equivalent Fraction Match-Up

Prepare cards with various fractions and visual representations (e.g., shaded shapes, fraction bars). Students work in small groups to match equivalent fractions, justifying each match using their understanding of proportions.

Explain how to use a fraction wall to prove two fractions are equal.

Facilitation Tip

During the Equivalent Fraction Match-Up, observe students' strategies for matching; are they relying on visual cues, or can they articulate the numerical relationship?

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

Activity 03

• Gallery Walk
• 35 min · Individual

Simplification Station

Provide students with a set of fractions (e.g., 6/8, 9/12, 10/15). Individually, they use diagrams or fraction walls to find the simplest equivalent form for each, then share their strategies with a partner.

Assess when it is more helpful to use a simplified fraction rather than a large one.

Facilitation Tip

During the Simplification Station, check that students are systematically dividing both the numerator and denominator by common factors, not just guessing.

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

A few notes on teaching this unit

Focus on the multiplicative relationship between equivalent fractions, rather than just additive. Use visual aids consistently to demonstrate that multiplying or dividing the numerator and denominator by the same non-zero number results in an equivalent fraction. Avoid simply presenting rules without visual reinforcement.

Students will be able to articulate that equivalent fractions represent the same part of a whole, even with different numbers. They will confidently generate equivalent fractions and explain their reasoning using visual models or multiplication/division strategies.

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Watch Out for These Misconceptions

• During the Fraction Wall Construction Challenge, watch for students who try to make equivalent fractions by adding the same number to the numerator and denominator.

  Redirect students by asking them to compare the visual lengths of their constructed fraction strips; show them how adding to both numerator and denominator changes the proportion on their wall, unlike multiplying by the same number.

• During the Equivalent Fraction Match-Up, watch for students who assume a fraction with larger numbers (e.g., 10/20) is always greater than a fraction with smaller numbers (e.g., 1/2).

  Guide students to use the visual representations on the cards to compare 10/20 and 1/2 directly, demonstrating that they cover the same area or length, thereby reinforcing the concept of equivalence despite the number size.

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Methods used in this brief

• Gallery Walk