Equivalent fractions on a number line

MathematicsFractionsAges 8–9

Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams

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Teaching Table

Set out your lesson

Explain equivalence using identical wholes and aligned points, rather than just a numerical rule.

Activity

Ask the learner to locate 1/2 on an unmarked 0–1 line and describe two equal intervals. If not yet secure, practise unit fractions and equal partitioning first. Hard prerequisite lesson-source availability is checked separately; availability is not learner readiness.

Policy

Check learner readiness directly; prerequisite lesson availability is not evidence of attainment.

Instructions

No printer is required: screen, pencil and scrap paper suffice. All contexts are fictional, not observations or recommendations. Do not cook, cut rope, buy ingredients, handle food or collect personal data. Optional counters can be drawn marks. Adult reads Setup and Show, then uses the supplied Together page; keep adult keys separate. Set aside all worked pages before Try. Use more scrap paper for drawings or explanations.

Teaching Procedure

Invite the learner to identify the whole and unit, select a representation, attempt the task, then explain and check. Use Together prompts in order. If an error persists, return to the prerequisite skill rather than giving more unsupported practice.

Record actual responses, access mode and assistance; never invent observations or infer mastery.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.

Teaching limits and safe use

These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.

This is a bounded practice opportunity, not mastery or a claim of fluency across all values. Fictional scenarios are not real measurements or learner observations. Canonical age ranges are preserved, not proof of developmental fit. Oral, scribed and supported work must be recorded as such.

Record actual responses, access mode and assistance; never invent observations or infer mastery.

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Explain equivalence using identical wholes and aligned points, rather than just a numerical rule.

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Learning resources

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Check understanding

Use fraction strips to show 1/2 = 2/4 = 3/6
Verify on a number line that 2/3 and 4/6 land on the same point
Identify at least three fractions equivalent to 1/2 using diagrams

“If your child sees that 2/4 and 1/2 land on the exact same point on a number line, can they explain in their own words why those two fractions are equal?”

Curriculum record

Type: Representational
Subject: Mathematics
Domain: Fractions
Age range: Ages 8–9