Mathematics · 3rd Year

Active learning ideas

Non-Unit Fractions (e.g., 2/3, 3/4)

Active learning works for non-unit fractions because visual and hands-on experiences help students move beyond abstract symbols to concrete understanding. Students need to see, touch, and discuss fractions to grasp that the denominator defines the size of each share, not the numerator. This physical engagement turns confusing rules into clear, memorable insights.

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

• 15–25 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Formal Debate
• 20 min · Whole Class

Formal Debate: Which Would You Rather?

Present scenarios like 'Would you rather have 1/2 of a giant chocolate bar or 1/10 of the same bar?' Students must choose a side, use fraction tiles to prove their choice, and then debate their reasoning with someone who chose the opposite (if anyone did!).

Explain how 3/4 is related to 1/4.

Facilitation Tip

During the Structured Debate, assign clear roles like 'presenter,' 'questioner,' and 'illustrator' to keep all students engaged.

What to look for

Provide students with pre-drawn fraction bars. Ask them to shade in 3/5 of the bar. Then, ask them to write one sentence explaining how their shaded bar relates to 1/5.

• Analyze
• Evaluate
• Create
• Self-Management
• Decision-Making

Activity 02

• Gallery Walk
• 25 min · Small Groups

Gallery Walk: The Fraction Wall Build

In small groups, students build a large fraction wall on the floor using colored tape or long strips of paper. Once finished, they move around the wall in pairs, identifying which 'bricks' are longer or shorter and recording their findings using < and > symbols.

Construct a model to show 2/3 of a pizza.

Facilitation Tip

For the Gallery Walk, have students label their fraction walls with sticky notes to explain their choices and invite peer feedback.

What to look for

Pose the question: 'How is 5/8 different from 1/8, and how are they related?' Encourage students to use fraction manipulatives or drawings to support their explanations and use the terms numerator and denominator.

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

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Fraction Number Line

Give pairs a set of unit fraction cards (1/2, 1/3, 1/4, 1/10). They must work together to place them on a 0-to-1 number line. They then explain to another pair why 1/10 is closer to zero than 1/2, despite 10 being a 'bigger' number.

Differentiate between a unit fraction and a non-unit fraction.

Facilitation Tip

During the Think-Pair-Share, provide blank number lines on paper for students to fold and mark as they discuss their reasoning.

What to look for

Give each student a card with a non-unit fraction (e.g., 2/4, 3/3, 4/6). Ask them to draw a model representing this fraction and then write the fraction as a sum of unit fractions.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Experienced teachers approach non-unit fractions by prioritizing visual models over symbolic procedures, as research shows this deepens understanding. Avoid rushing to rules like 'bigger denominator means smaller fraction' without context, as this can reinforce misconceptions. Instead, use repeated opportunities for students to compare fractions using fraction circles, bars, and number lines to build intuitive sense-making.

Successful learning looks like students confidently comparing fractions by reasoning about denominators and using terms like numerator and denominator correctly. They should explain their thinking using visual models and articulate why 3/4 is larger than 1/2 without relying on memorized rules. Students should also demonstrate flexibility in representing fractions in multiple ways.

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Watch Out for These Misconceptions

• During the Structured Debate, watch for students who assume 1/2 and 1/4 are equal because they have the same numerator.

  Use the pizza sharing analogy during the debate. Ask, 'If you share a pizza with 2 friends, do you get more or less than if you share it with 4 friends?' Have students model this with fraction circles to see the size difference.

• During the Think-Pair-Share: Fraction Number Line, watch for students who order fractions by numerator size instead of denominator size.

  Have students fold a string number line in half to mark 1/2, then fold it again to mark 1/4. Ask them to place 1/3 by estimating its position relative to these folds to see that 1/3 is not between 1/2 and 1/4.

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Methods used in this brief

• Formal Debate
• Gallery Walk
• Think-Pair-Share