Comparing Fractions

Overview

In this final lesson of the five-part unit, students demonstrate their understanding of equal parts, fraction notation and comparison. They apply visual models and reasoning to compare halves, thirds and quarters when the wholes are identical.

Learning intentions

• WALT compare halves, thirds and quarters when the wholes are the same.
• WALT use fraction diagrams, words and symbols to show comparisons.
• WALT explain equal parts, equivalent fractions and why equal wholes matter.
• WALT demonstrate our understanding independently.

Success criteria

• I can compare fractions of the same whole using a diagram or reasoning.
• I can use more than, less than or equal to, and the symbols >, < and =.
• I can explain comparisons such as 2/3 > 1/3, 3/4 > 1/4 and 1/2 = 2/4.
• I can accurately name, write and represent fractions.

Curriculum links

• Te Mātaiaho Mathematics and Statistics — Number: rational numbers.
• Equal parts and the meaning of the numerator and denominator.
• Unit and non-unit fractions, including halves, thirds and quarters.
• Equivalent fractions and direct comparison of fractions with the same whole.

Lesson structure (60 minutes)

1. 0–8 min · Warm-up: Which is greater? Teacher displays two identical rectangles divided into different equal parts using the comparison warm-up slides and draws examples such as 1/2 and 1/4, or 1/3 and 2/3. Students silently decide which fraction is greater, show a response with their fingers or mini-whiteboards, then explain their reasoning to a partner. Reinforce that the wholes must be the same and that the denominator tells how many equal parts the whole has.

2. 8–18 min · Model the thinking. Teacher models 2/3 > 1/3, 3/4 > 1/4 and 1/2 = 2/4 with identical whole templates, connecting the shaded parts to the notation. Students help complete the comparison sentences and identify the numerator, denominator, equal parts and whole. Ask: “What stays the same in the first comparison?” and “How can two different fraction names represent the same amount?”

3. 18–30 min · Pair comparison sort. Teacher gives each pair the fraction cards and identical whole templates, then introduces the sort instructions on the card-sort instruction slide. Students sort 1/2, 1/3, 2/3, 1/4, 2/4 and 3/4 by comparison, placing cards on matching models and recording at least four true comparison statements. Students must check that each whole is the same before deciding. Circulate and observe whether students partition accurately, use comparison language and justify their choices. They may use the fraction wall and strip cards to check their reasoning.

4. 30–38 min · Group justification challenge. Teacher forms two groups of four and displays prompts from the explain-and-challenge slides. Each group selects two comparisons, such as 1/3 < 2/3 or 1/2 = 2/4, and prepares a diagram and spoken explanation. Groups take turns presenting; the other group agrees, disagrees or asks for clarification, giving a reason. Prompt students to use complete sentences: “___ is greater than ___ because…” and “The wholes are equal, so…”

5. 38–55 min · Individual final assessment. Teacher explains that students will work independently and distributes the Comparing Fractions assessment sheet. While five students begin, conference individually with one student at a time, rotating so all eight students receive a brief conference. Students complete:

• Draw and label 1/2, 1/3 and 3/4.
• Write and explain 1/2 = 2/4.
• Compare 1/3 and 2/3, 1/4 and 3/4, and 1/2 and 1/4 using symbols and words.
• Explain why equal wholes matter. During conferences, ask prompts such as “Show me how you know” and “What does the denominator tell us?” Record whether the student responds independently, with a prompt or with significant support. Other students complete the quiet drawing and explanation tasks on the assessment sheet while waiting.

6. 55–60 min · Plenary and reflection. Teacher revisits the final prompts on the reflection slide and asks students to share one comparison and one important idea about equal wholes. Students complete or orally share: “Today I can compare fractions because…” Collect assessment sheets and note any student requiring a follow-up lesson or additional practice.

Resources

• the Comparing Fractions teaching deck
• the Comparing Fractions assessment sheet
• the fraction wall and strip cards
• Fraction cards: 1/2, 1/3, 2/3, 1/4, 2/4, 3/4
• Identical whole templates
• Mini-whiteboards or scrap paper
• Pencils, coloured pencils and erasers
• Teacher observation and conference record

Assessment

• During the warm-up and pair sort, check accurate partitioning, fraction vocabulary, notation and the understanding that comparisons require equal wholes.
• During group explanations and conferences, record how independently students justify comparisons and explain equivalence.
• Use the final assessment as evidence of accurate equal partitions, correct notation and vocabulary, equivalence, and direct comparison of fractions with the same whole.

Differentiation

• Read assessment questions aloud and clarify vocabulary without giving the mathematical answer.
• Provide identical whole templates, fraction walls and coloured pencils so students can show conceptual understanding visually.
• Accept drawings and oral explanations where writing or notation is a barrier; separate assessment of fraction understanding from handwriting and symbol formation.
• Allow additional time, a scribe or a quiet working space where appropriate. Use sentence starters such as “I know ___ is greater because…” for students needing language support, including English language learners.
• For students ready for greater challenge, ask them to order 1/4, 1/3, 1/2, 2/3 and 3/4, then justify the order using equal-whole reasoning.