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MathematicsFractionsAges 10–13

Dividing fractions (unit fractions)

Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result

Lesson

Set out your lesson

Divide a unit fraction by a positive whole number and explain the smaller share using a fixed-whole model.

Before teaching

Use this short check, then start teaching.

Activity

Use mt_4Km38F4L-6 to check fraction-as-division and mt_AabJisinfi to check multiplication back. Ask the learner to distinguish one quarter of a whole from one quarter of an already small piece. Canonical ages are 10–11, not a readiness guarantee. These activity checks are inferred; source availability is not 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

Use the supplied screen sheets or print only the active sheet. A pencil and scrap paper are enough; no printer, purchase, cutting, cooking, food handling or personal disclosure is required. Read Show first, then use Together with support. Put Show and adult keys aside before Try. Stories are fictional; no activity is evidence until the learner actually attempts it. Allow drawing, pointing, oral explanation or adult scribing; record the support actually used. Scribed mathematics is not independent handwriting. Pause or return to a prerequisite when needed, without treating uncertainty as failure.

Teach The Idea

Keep the original whole fixed. Splitting one b-th into n equal shares makes each share one of b × n equal parts of the whole. So dividing 1/b by n gives 1/(b × n). This lesson uses positive whole-number divisors; never divide by zero. When n is greater than one the result is smaller than the starting unit fraction.

Teaching Procedure

Read the Show model aloud while tracing the relevant unit. In Together, invite an attempt before giving the private hint. Ask the learner to explain why the operation fits. For Try, remove worked material and let the learner choose a representation. Discuss mistakes after recording the attempt, then retry another day if useful.

Models And Materials

Supplied fixed-unit models make partition size, equal sharing or square-area units visible. Learner diagrams are blank scaffolds or stated givens, not worked answers. Screen or paper drawing serves the purpose; no digital interactive is needed.

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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Selected Default Gakuva

Divide a unit fraction by a positive whole number and explain the smaller share using a fixed-whole model.

Divide a unit fraction by a positive whole number and explain the smaller share using a fixed-whole model.

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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

How many servings of oatmeal?

Open practice (new tab)
Before you open · source notes

An oatmeal servings story supports dividing with unit fractions. Not every decimal division.

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

Before you open

Ask how many servings fit and write the division equation.

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. “How many servings of oatmeal?.” 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

  • Compute (1/3) ÷ 4 = 1/12 and explain using a visual model of splitting 1/3 into 4 equal parts
  • Create a story context for (1/6) ÷ 3 and solve it
  • Verify (1/3) ÷ 4 = 1/12 by showing (1/12) × 4 = 1/3
“If your child has 1/3 of a bag of rice and splits it into 4 equal portions, can they work out what fraction of the whole bag each portion is — and explain why the answer is smaller than 1/3?”

Curriculum record

Type
Conceptual
Subject
Mathematics
Domain
Fractions
Age range
Ages 10–13

Standards

ccss-math:5.NF.7ccss-math:5.NF.7.athe-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-B2.8uk-nc-2013:Ma6/2.3e