Comparing Fractions Visually

Overview

This 60-minute lesson is designed for Year 4 students in New Zealand to develop understanding and skills related to comparing and ordering fractions with the same numerator or the same denominator. Using hands-on activities and visual aids such as fraction walls, number lines, and paper strips, students will explore the relationship between numerators, denominators, and fraction size. This lesson aligns with the New Zealand Curriculum Refresh for Mathematics and incorporates key learning objectives and achievement standards to strengthen number sense and reasoning around fractions.

Curriculum Links

Learning Area: Mathematics and Statistics

Strand: Number and Algebra

Achievement Objective:

Number and Algebra - Understand multiplication and division of whole numbers and fractions to solve problems (Number and Algebra Level 3)
Recognise and represent fractions (including unit and non-unit fractions) and relate them to division and to decimal fractions
Compare and order common fractions

Key Competencies:

Thinking: Developing understanding of fraction size and relationships between numerators and denominators
Using Language, Symbols and Text: Reading and representing fractions using visual models and number lines
Managing Self: Working independently and managing time on tasks
Participating and Contributing: Sharing thinking and reasoning with peers during collaborative activities

Learning Objectives

By the end of this lesson, students will be able to:

Understand how the size of fractions is affected by numerators and denominators.
Compare fractions that have the same numerator or the same denominator, using visual models.
Order a set of fractions from smallest to largest (and vice versa) using hands-on materials and explanation.
Explain their reasoning using appropriate mathematical language and visual aids.

Lesson Outline

Time Allocation and Activities

Time	Activity	Teacher Actions	Student Actions
0–10 min	Introduction & Discussion	Introduce fractions; discuss numerators and denominators; use simple fractions on board (e.g. 1/4, 2/4, 3/4, 1/3, 1/5)	Recall prior knowledge, listen, ask questions
10–25 min	Activity 1: Using Fraction Walls	Model fractions on fraction walls, demonstrate comparing same numerator and same denominator fractions	Use fraction walls to compare pairs of fractions and record observations
25–40 min	Activity 2: Number Line Comparisons	Draw fraction number lines; model placing fractions; explain ordering fractions on number lines	Place paper strips on number lines; order fractions and discuss placement
40–55 min	Activity 3: Paper Strip Ordering Task	Distribute paper strips representing fractions; guide grouping and ordering tasks in pairs or small groups	Collaborate to order sets of fractions; explain reasoning to peers
55–60 min	Assessment & Reflection	Provide comparison pairs and sets of fractions for written or verbal explanation; summarise learning points	Complete comparison and ordering tasks; reflect on learning

Detailed Activities

Introduction & Discussion (0-10 mins)

Begin with review: What do the numerator and denominator represent? Use simple fractions like 1/2, 1/3, 1/4 to activate prior knowledge.
Discuss how fractions with the same numerator but different denominators compare (e.g., 1/2 vs 1/4).
Discuss how fractions with the same denominator but different numerators compare (e.g., 1/4 vs 3/4).
Confirm students understand the concept of “greater than” and “less than” in the context of fractions.

Activity 1: Using Fraction Walls (10-25 mins)

Use fraction walls as a tactile visual aid—show walls divided into equal parts labelled with fractions.
Compare two fractions with the same numerator: e.g., 2/5 and 2/8. Ask which is larger and discuss why (larger denominator means smaller pieces).
Compare two fractions with the same denominator: e.g., 3/6 and 5/6. Ask which is larger and explain because numerators differ.
Students use fraction walls to compare pairs of fractions themselves.
Facilitate discussion on what they notice about numerators and denominators.

Activity 2: Number Line Comparisons (25-40 mins)

Draw a large number line from 0 to 1 on the board.
Model placing fractions on the number line: e.g., placing 1/4, 2/4, 3/4.
Focus on fractions with the same numerator and then with the same denominator.
Students receive paper strips representing different fractions; place these strips on an individual or group number line.
Encourage students to observe and explain ordering based on position on the number line.

Activity 3: Paper Strip Ordering Task (40-55 mins)

Provide sets of paper strips representing fractions with same numerator and same denominator but different sizes.
In pairs or small groups, students order their fraction strips from smallest to largest and explain their thinking.
Circulate and support reasoning development by asking guiding questions:
“If these have the same numerator, which piece looks smaller or bigger?”
“What changes when the denominators are different?”
Encourage students to use fraction walls or number lines as reference to confirm their answers.

Assessment & Reflection (55-60 mins)

Give students two short tasks:

Compare two given fractions (e.g., 3/5 and 3/7) and explain which is larger and why.
Order a small set of fractions (e.g., 1/6, 1/3, 1/4) from smallest to largest with reasoning.

Ask students to share their explanations verbally or in writing.
Summarise the key points of the lesson: role of numerator and denominator in fraction size, visual aids support understanding.

Resources Needed

Fraction walls (classroom sets or displayed on smartboard)
Large classroom number line (0 to 1)
Paper strips cut into fractions (e.g., halves, thirds, quarters, fifths, sixths) for hands-on use
Whiteboard and markers
Student worksheets for assessment tasks

Differentiation

For students needing extra support:
Use physical fraction pieces for tactile exploration.
Pair with a buddy for discussion and support.
For students needing extension:
Challenge to compare fractions with different numerators and denominators; discuss equivalencies.
Introduce simple fraction addition by combining strips.

Reflection and Next Steps

Reflect on student understanding of fraction comparisons based on assessment outcomes and class discussion.
Plan further lessons to build on fraction equivalence and addition/subtraction with fractions.
Consider developing digital fraction wall activities for interactive learning at home.

This lesson plan leverages concrete visual aids and active student participation to develop strong conceptual understanding of fractions aligned with the New Zealand Curriculum Refresh standards for Year 4 mathematics. It emphasises key competencies and mathematical language to support deeper learning.

Teaching Instructions