Fraction Order

Overview

In this lesson, students compare and order fractions by reasoning about size using diagrams, number lines, and equivalence (rather than only calculating). The lesson builds from recognising which fraction is larger to justifying ordering choices with clear mathematical explanations.

Learning intentions

• Students will compare fractions using active reasoning (diagrams/number lines/equivalence).
• Students will order fractions by thinking about what each part represents.
• Students will explain and justify which fraction is larger or smaller using mathematical language.

Success criteria

• I can explain how I know which fraction is larger using a diagram or number line.
• I can use equivalent fractions to compare two fractions with different denominators.
• I can order fractions from smallest to largest and justify my order.
• I can check my answer by reasoning (not only by calculating).

Curriculum links

• Number – fractions (including decimals), Year 4: recognising and showing families of common equivalent fractions.
• Number – fractions (including decimals), Year 4: solve problems involving increasingly harder fractions to calculate quantities (used here in comparison contexts).
• Focus on comparing and ordering fractions using reasoning and representations (UK NC mathematics approach).

Lesson structure (35 minutes)

1. 0–5 min · Engaging hook (reasoning challenge). Teacher displays: “Which is bigger: 2/3 or 3/5? You must justify!” Students think-pair-share using any method (no calculating required). Teacher listens for reasoning ideas (e.g., “thirds are bigger/smaller parts,” “need same denominator,” “use a strip/number line”). Targeted whole-class questions (with think time):

• Bloom—Analyse: “What makes this comparison tricky—what do you notice about the denominators?”
• Bloom—Explain: “If you drew both, what would you expect to see?”
• Bloom—Evaluate: “Which is your strongest reason so far, and why?”

2. 5–12 min · Modelling: compare with active reasoning (prove it). Teacher models “Prove it” using a fraction strip or area model and a number line. Use sentence stems and a timer.

Model example to copy (on board, then students copy): “Compare 2/3 and 3/5.” “I want to compare like-sized wholes, so I make equivalent fractions.” “Common denominator: 15.” “2/3 = 10/15 (because 2×5=10 and 3×5=15).” “3/5 = 9/15 (because 3×3=9 and 5×3=15).” “10/15 is larger than 9/15, so 2/3 > 3/5.” “Therefore, 2/3 is bigger because it represents more parts of the same size.”

Verbal reasoning first (timer): Teacher says, “You have 30 seconds to explain out loud using this stem: ‘I chose a common denominator because…’” Sentence stems (whole class and then pairs):

• “I compared by…”
• “I used equivalent fractions because…”
• “The denominator tells me…”
• “My check is…”

Targeted whole-class questions (layered):

• Bloom—Remember/Understand: “What does the denominator represent in your diagram?”
• Bloom—Apply: “What common denominator would you choose and why?”
• Bloom—Analyse: “How can you be sure the parts are the same size after converting?”
• Bloom—Justify/Evaluate: “What comparison fact would convince someone who disagrees?”

AfL (during modelling): Teacher circulates with a quick checklist: can students verbally use “common denominator/equivalent fractions/parts of the same size” language? Use thumbs for confidence after verbal explanations.

3. 12–18 min · Guided practice: layered ordering (small steps, reasoning emphasis). On board: “Order these from smallest to largest: 1/2, 2/3, 3/4.” Teacher runs a short “Reasoning Sprint”:

• Step A (whole class): choose the smallest between two fractions first (e.g., 1/2 vs 2/3).
• Step B: then decide between the remaining pair. Teacher prompts using Bloom and sentence stems.
• Bloom—Analyse: “Which fraction is closer to 0? How do you know from the parts?”
• Bloom—Create: “Can you propose an ordering method for any set of three fractions?”

AfL: Use “cold-call with scaffolding” — ask one student to explain and the next to critique: “Do you agree with their reason? What would you add?” Teacher marks only reasoning quality (not correctness).

4. 18–28 min · Independent/partner task: gradually increasing complexity. Task sheet (or cards) with 3 questions. Students must show reasoning using at least one representation (strip/area or number line) and an equivalence step.

Q1 (easy): “Compare and write > or <: 3/4 and 5/8. Explain how you know.” Q2 (medium): “Order: 2/5, 1/2, 3/10 from smallest to largest. Explain your strategy.” Q3 (harder): “Which is larger, 4/6 or 5/9? Then place them on a number line between 0 and 1. Explain your reasoning.”

Differentiation support: sentence-starters on task sheet; common denominators bank (e.g., 8, 10, 12, 15, 18). Challenge: students must give two checks (diagram check + equivalence check).

AfL points throughout:

• Teacher uses a “Reasoning Tick”: + if student uses “equivalent fractions/common denominator/like-sized parts.”
• Mid-task verbal check: pause at 6 minutes in; ask one pair to give their explanation verbally (30 seconds) before teacher confirms.

5. 28–35 min · Plenary: Prove it reasoning wrap-up. Teacher presents a “common mistake” statement on board: “2/5 is bigger than 3/10 because 2 is bigger than 3.” Students respond: “Agree or disagree and prove it.”

Layered whole-class questions:

• Bloom—Remember/Understand: “What is wrong with the reasoning?”
• Bloom—Analyse: “How can we compare them correctly without relying on the numerators alone?”
• Bloom—Evaluate: “What would be a convincing justification for a friend?”
• Bloom—Apply: “Convert to a common denominator and state the correct ordering.”

Exit ticket (2 minutes, quick): “Order: 1/3, 2/5, 3/5. Circle your final order and write one sentence: ‘I know because…’” Teacher collects to assess whether students justify using equivalence/representation.

Resources

• Fraction strips or paper folding strips (sets for 30)
• Number line from 0 to 1 (printed A4 for modelling/extra)
• Whiteboard/visualiser for the worked model
• Task sheet with 3 questions and reasoning sentence stems
• Timer (30 seconds verbal reasoning)
• Highlighters or sticky notes for “my strongest reason”
• Common denominator mini-bank cards

Assessment

• During hook: listen for initial reasoning (not just answers).
• During modelling: check verbal use of “common denominator/equivalent fractions/like-sized parts” using thumbs + targeted questioning.
• During guided practice: assess reasoning quality via “agree/disagree” explanations.
• Exit ticket: evaluate whether the student’s justification mentions equivalence or diagram/number line reasoning.

Differentiation

• Support: pre-written sentence stems, fraction strips readily visible, and a common denominator bank.
• Targeted scaffolds for misconceptions:
• “Numerator bigger doesn’t always mean fraction bigger” reminder with a quick strip comparison.
• “Denominators must refer to same-sized parts” prompt before converting.
• Extension (for fast finishers): require a second justification method (number line + equivalence) and a brief explanation of how they checked their ordering.
• EAL/SEN: allow verbal rehearsing before writing; provide “because” stems and word bank (greater than, smaller than, equivalent, common denominator, same size).

Common misconceptions to address (built in)

• Thinking fractions can be compared using numerators only (teacher counters with “prove it” diagram).
• Assuming the larger denominator always means the smaller fraction without checking (teacher models with equivalent fractions).
• Incorrect common denominator use (teacher emphasises “same size parts” and checks conversions on the strip/area model).