MathematicsFractionsAges 8–12

Equivalent fractions on a number line

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

Lesson

Set out your lesson

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

Before teaching

Use this short check, then start teaching.

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.

Printer, credit, and teaching notes

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.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view.

Next: Show

Adult extras

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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Teaching approaches

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1 approach

Selected Default Gakuva

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

Family records and proof options

Keep a record of your learning

Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.

View learner plans ($12/mo per learner) See sample family archive

Learning resources

Extra practice links — they do not replace Gakuva’s teaching approach.

Illustrative Mathematics · Practice link — not the full lesson

Explaining Fraction Equivalence with Pictures

Open practice(new tab)

Before you open · source notes

Picture models explain why two fractions name the same amount. Use it for equivalent fractions on diagrams; number-line equivalence still needs separate talk.

Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.

Before you open

Ask the learner to point to the same amount in both pictures and say the two fraction names.

Opening this link does not save learning or assess mastery.

Source, access and review notes

Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-11 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.

Illustrative Mathematics. “Explaining Fraction Equivalence with Pictures.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.

CC BY-NC-SA 4.0 — link only

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 8–12

Standards

acara-v9:AC9M4N03acara-v9:AC9M6N03ccss-math:3.NF.3.athe-ontario-curriculum-mathematics-2020:ON-MATH-2020-G5-B1.3uk-nc-2013:Ma/KS2/Y4/F/1