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.
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.
Check learner readiness directly; prerequisite lesson availability is not evidence of attainment.
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Explain equivalence using identical wholes and aligned points, rather than just a numerical rule.
Explain equivalence using identical wholes and aligned points, rather than just a numerical rule.
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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
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 openAsk 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