MathematicsFractionsAges 8–11

Equivalent fractions (age 8+)

Generate simple equivalent fractions and explain why they are equivalent using visual fraction models

Lesson

Set out your lesson

Generate and simplify equivalent fractions by repartitioning the same whole.

Before teaching

Use this short check, then start teaching.

Activity

On equal-length bars, ask why one half and two quarters cover the same length. If the learner counts shaded pieces without considering piece size, revisit equivalent fractions on a number line (mt_Ep7TDFuYUa). This activity check is inferred, not a change to canonical edges. Source availability is not learner mastery.

Policy

Check learner readiness directly; prerequisite availability is not attainment.

Printer, credit, and teaching notes

Check learner readiness directly; prerequisite availability is not attainment.

Instructions

Screen or supplied sheets, pencil and scrap paper are sufficient; no printer, cutting or purchase is required. Read Setup and Show first; use Together with help, then put worked pages, matching cards and adult keys aside for Try. All story quantities are fictional: no cooking, eating, cutting, buying or collection of personal data. Draw any needed counters; no small objects are required. Read text aloud or let the learner point, draw or explain orally. Adult scribing is supported mathematical work, not independent handwriting. Record any hints actually used; never invent a response.

Teaching Procedure

Read the worked model aloud. Ask the learner to identify the whole and equal-part unit. In Together, let them attempt before offering the listed hint. Ask why a method preserves value. If the readiness skill is uncertain, pause and return to the named prerequisite; do not drill unsupported errors. Use fresh Try contexts without the key; after the attempt compare the method as well as the answer.

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

Next: Show

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Teaching approaches

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1 approach

Selected Default Gakuva

Generate and simplify equivalent fractions by repartitioning the same whole.

Family records and proof options

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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

Jon and Charlie's Run

Open practice(new tab)

Before you open · source notes

Two run distances look different but may be equivalent fractions. Use it for equivalence, not every unlike-denominator sum.

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

Before you open

Ask whether 3/6 and 1/2 name the same distance and show why with a picture.

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 2026-11-12 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. “Jon and Charlie's Run.” 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

Given 1/3, generate 2/6 as equivalent and show with area model
Simplify 4/8 to 1/2 and justify with a fraction strip
Complete equivalence chains: 1/4 = ?/8 = ?/12

“If your child is shown a fraction bar split into 3 parts with 1 shaded (= 1/3), can they draw an equivalent bar with 6 parts that shows exactly the same amount shaded?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Fractions
Age range: Ages 8–11

Standards

acara-v9:AC9M4N03ccss-math:3.NF.3.bthe-ontario-curriculum-mathematics-2020:ON-MATH-2020-G5-B1.3