Compare fractions

Overview

Students compare fractions by reasoning about size, not by just finding the “bigger number”. They use common denominators, benchmarks (0, 1/2, 1), and equivalent fractions to justify decisions.

Learning intentions

• Students will compare fractions with the same or different denominators using diagrams and equivalent fractions.
• Students will explain why one fraction is larger or smaller using active reasoning.
• Students will use correct fraction language (numerator/denominator, greater than/less than, equivalent).
• Students will check their comparisons for reasonableness.

Success criteria

• I can compare two fractions and write a clear statement (e.g. “3/4 is greater than 2/3”) with a justification.
• I can show my thinking using a model (bar/number line/area) and reference the same-sized parts.
• I can find equivalent fractions when denominators differ and explain why it helps me compare.
• I can explain my choice using a stem and evidence, not a guess.

Curriculum links

• Number — fractions (including decimals): recognise and show families of common equivalent fractions (Year 4).
• Number — fractions (including decimals): solve problems involving increasingly harder fractions to calculate quantities and fractions to divide quantities, including non-unit fractions where the answer is a whole number (reasoning supports comparison tasks).
• Add and subtract fractions with the same denominator is connected, as comparing relies on understanding parts of wholes and equivalent fractions.

Lesson structure (45 minutes)

1. 0–7 min · Hook: “Which is bigger?”

• Teacher shows two fraction cards: 2/3 vs 3/5 (no calculators, no answers yet).
• Teacher asks a high-attention starter: “How can we decide without guessing?”
• Students do Think–Pair–Share: each pair must produce a reason.
• Targeted whole-class questions (answers require explanation):
• “What does the denominator tell us about how many equal parts the whole has?”
• “If we drew both, would they have the same-sized parts? How do you know?”
• “What benchmark could you use (0, 1/2, 1) to estimate which is larger?”

2. 7–18 min · Model: prove it with reasoning (verbal first, then write)

• Teacher models comparing 2/3 and 3/5 using a shared representation.
• Active reasoning template on board:
• Sentence stem A: “I know ___ because the denominator shows ___ equal parts.”
• Sentence stem B: “I compare by making equivalent fractions with the same denominator.”
• Sentence stem C: “Therefore, ___ is greater/less than ___ because ___.”
• Teacher walk-through (timer included):
• 0:30 verbal planning: “Talk to your partner: what denominator could we use that both can reach?”
• 0:40 verbal explaining: teacher elicits student reasoning: “Both can become fifteenths, so 2/3 = 10/15 and 3/5 = 9/15, so 2/3 is larger.”
• 1:00 written proof: students copy the example reasoning (next section) into books.
• AfL during modelling:
• Cold call one student per sentence stem to complete “I know…” and “Therefore…”.
• Quick thumbs check: “Do we agree the parts are the same size now?” (thumbs up/down).

3. 18–30 min · Guided practice: layered whole-class questions

• Teacher sets up 3 comparison prompts, increasing reasoning demands.
• Students work in pairs first, then teacher prompts whole class to justify.
• Prompt 1 (same numerator reasoning): 3/8 vs 3/5
• Q1 (Recall + explain): “Which is bigger and what does equal numerator mean about size here?”
• Q2 (Deeper): “Do you need a common denominator? If you do, why might it help?”
• Prompt 2 (equivalent fractions required): 1/2 vs 3/8
• Q3 (Understand): “Explain why 1/2 is a benchmark. What fraction of the same whole is 3/8?”
• Q4 (Apply): “Show how you could rewrite 3/8 using a denominator that makes comparison easiest.”
• Prompt 3 (non-obvious comparison): 5/6 vs 7/12
• Q5 (Analyse): “Which is closer to 1? How do you know using parts of the whole?”
• Q6 (Evaluate): “If someone says ‘7/12 is bigger because 7>5’, what is wrong with that reasoning?”
• AfL points:
• Use “Reasoning checkpoints”: ask pairs to hold up a mini whiteboard with a fraction statement plus one justification phrase.
• Teacher listens for misconceptions; records common errors on a class board.

4. 30–40 min · Independent task (complexity builds)

• Task: Fraction Compare Cards (increasing challenge)
• Card A: 4/7 vs 5/7 (same denominator)
• Card B: 2/9 vs 1/5 (different denominators; choose a strategy)
• Card C: 3/4 vs 5/6 (equivalent fractions or benchmarks)
• Card D: 7/10 vs 2/3 (reasonability + justify)
• Students must write for each card:
• A comparison sentence
• A model/diagram note (bar or number line idea)
• A written reason using a stem
• AfL during task:
• Teacher uses a short checklist: “Did they justify with evidence?” “Did they reference denominator meaning or equivalent fractions?”
• Give “micro-feedback” to 3–5 groups using sentence-stem nudges.

5. 40–45 min · Plenary: “Which reasoning is strongest?”

• Teacher shows two student-style explanations for 5/6 vs 7/12 (one correct with reasoning; one incorrect).
• Students vote and then justify aloud.
• Plenary questions (layered):
• “What claim is being made in each explanation?”
• “Which evidence is better and why?”
• “What misunderstanding does the weaker explanation show?”
• AfL:
• Exit snapshot: “Write one sentence: the best reason I used today was ___ because ___.”

Resources

• Fraction comparison cards (teacher-made or printable): pairs like above.
• Fraction bar/area models (paper strips or board slides).
• Mini whiteboards + pens.
• Sentence stem strip (for desks).
• Timer (phone/projector).
• Example sheet (printed) for students to copy.

Example to copy (model proof)

Compare 2/3 and 3/5

1. “I notice the denominators are different, so the parts are not the same size yet.”
2. “I can compare by making equivalent fractions with a common denominator.”
3. “For denominator 15: 2/3 = 10/15 and 3/5 = 9/15.”
4. “10/15 is greater than 9/15, so 2/3 is greater than 3/5.” Therefore: 2/3 > 3/5 because both are compared using the same-sized fifteenths.

Assessment

• Formative checks:
• During modelling: student completes stems; teacher listens for correct use of denominator meaning.
• During guided questions: each pair shows a comparison statement plus a reason (not just an answer).
• During independent task: teacher checklist on “evidence + explanation”.
• Exit ticket: one justified comparison sentence.

Differentiation

• Support:
• Provide a desk stem bank and fraction bars with pre-drawn common denominators (e.g., fifteenths/twelveths).
• Offer a “choose your strategy” prompt: “If denominators match → compare numerators; if not → find equivalent fractions.”
• Targeted intervention:
• For pupils stuck, give one guided step: “What common denominator could work here?” then let them complete the rest.
• Extension:
• Ask: “Compare in two different ways (benchmarks AND equivalent fractions). Do you get the same result? Explain.”
• Misconceptions to address explicitly:
• “Bigger numerator always means bigger fraction” (use counterexample and explain role of denominator).
• Confusing numerator and denominator (use denominator = number of equal parts).
• Comparing fractions without ensuring equal-sized parts (emphasise making equivalent fractions or using a common representation).
• Over-reliance on calculation without explanation (require a model-based reason each time).

Common AfL points (where and how)

• After hook: “What strategy are you using?” (teacher records top strategies on board).
• After each guided prompt: thumbs check + one explained response from a student.
• While circulating in task: quick oral check using sentence stems.
• End plenary: choose between two reasonings and justify vote.