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MathematicsFractionsAges 10–12

Dividing by Fractions

Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend

Lesson

Set out your lesson

Interpret whole-number division by a unit fraction as counting equal small portions.

Before teaching

Use this short check, then start teaching.

Activity

Use mt_AabJisinfi to check fraction multiplication. Equal-sharing language from mt_4Km38F4L-6 can help, but distinguish counting small portions from sharing into a given number of groups. 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

Ask how many portions of the named size fit into the total. Each whole contains b portions of size 1/b, so q wholes contain q × b portions. Multiplication checks the original amount. A positive whole divided by a proper unit fraction gives a larger numerical count, not a larger physical quantity. Dividing zero or dividing by one does not give a larger result.

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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Family records and proof options

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

Learning resources

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

PhET Interactive Simulations · Practice link — not the full lesson

Fraction Matcher

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

Fraction Matcher supports hands-on exploration for Dividing by Fractions. Not every lab worksheet.

Free interactive page, no sign-in required for the tested path.

Before you open

Ask the learner what they changed in the sim or page and what they observed.

Opening this link does not save learning or assess mastery.

Source, access and review notes

Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.

PhET Interactive Simulations. “Fraction Matcher.” External page; Gakuva does not copy, host, embed, or redistribute materials.

Unknown — link only

Check understanding

  • Compute 4 ÷ (1/5) = 20 and explain: 'How many fifths fit in 4 wholes?'
  • Create a story context for 6 ÷ (1/4) and solve it
  • Verify 4 ÷ (1/5) = 20 by showing 20 × (1/5) = 4
“If you have 4 metres of ribbon and each bow needs 1/5 of a metre, can your child work out how many bows you can make — and explain why the answer is bigger than 4?”

Curriculum record

Type
Conceptual
Subject
Mathematics
Domain
Fractions
Age range
Ages 10–12

Standards

ccss-math:5.NF.7ccss-math:5.NF.7.bthe-ontario-curriculum-mathematics-2020:ON-MATH-2020-G5-B2.8the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G6-B2.10