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MathematicsRatio & ProportionAges 11–13

Dividing Quantities by Ratio

Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole

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Dividing Quantities by Ratio means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.

Materials: Paper strips or a folded circle; Pencil and labels (1/2, 1/4). 1. Say the goal of Dividing Quantities by Ratio in plain words once. 2. Adult folds a strip into halves and labels 1/2. 3. Child makes three fair shares (or fraction operations with strips) and names each result. 4. Fresh check: one fresh equal-part or fraction result. Record and stop. Done: three correctly named fraction results. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.

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Dividing Quantities by Ratio practice

Practice key ideas from Dividing Quantities by Ratio.

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Learning resources

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PhET Interactive Simulations · Practice link — not the full lesson

Proportion Playground

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Before you open · source notes

Proportion Playground supports hands-on exploration for Dividing Quantities by Ratio. Not every lab worksheet.

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

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

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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. “Proportion Playground.” External page; Gakuva does not copy, host, embed, or redistribute materials.

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Check understanding

  • Share £60 between two people in the ratio 2:3 by finding the value of one part
  • Express the result of sharing 24 sweets as 10 and 14 in ratio form as 5:7
  • Solve problems involving three-part ratios (e.g. divide 180 in the ratio 1:2:3)
“If £60 is shared between two people in the ratio 2:3, can your child work out how much each person gets?”

Curriculum record

Type
Procedural
Subject
Mathematics
Domain
Ratio & Proportion
Age range
Ages 11–13

Standards

ccss-math:6.RP.3uk-nc-2013:KS3.Maths.Ratio.5