Multiplying fractions

MathematicsFractionsAges 9–10

Understand a/b as a multiple of 1/b; multiply proper fractions and mixed numbers by whole numbers, supported by visual models (e.g. 3 × 2/5 = 6/5 = 1 1/5)

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Teaching Table

Set out your lesson

Multiply a fraction or mixed number by a whole number using repeated equal quantities and a matching visual model.

Activity

Ask the learner to express 3/5 as three copies of 1/5. If the denominator is treated as a piece count to multiply, revisit unit-fraction sums first. Mixed-number practice may need extra regrouping support. Hard prerequisite lesson-source availability is checked separately; availability is not learner readiness.

Policy

Check learner readiness directly; prerequisite lesson availability is not evidence of attainment.

Instructions

No printer is required: screen, pencil and scrap paper suffice. All contexts are fictional, not observations or recommendations. Do not cook, cut rope, buy ingredients, handle food or collect personal data. Optional counters can be drawn marks. Adult reads Setup and Show, then uses the supplied Together page; keep adult keys separate. Set aside all worked pages before Try. Use more scrap paper for drawings or explanations.

Teaching Procedure

Invite the learner to identify the whole and unit, select a representation, attempt the task, then explain and check. Use Together prompts in order. If an error persists, return to the prerequisite skill rather than giving more unsupported practice.

Record actual responses, access mode and assistance; never invent observations or infer mastery.

Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.

Teaching limits and safe use

These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.

This is a bounded practice opportunity, not mastery or a claim of fluency across all values. Fictional scenarios are not real measurements or learner observations. Canonical age ranges are preserved, not proof of developmental fit. Oral, scribed and supported work must be recorded as such.

Record actual responses, access mode and assistance; never invent observations or infer mastery.

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Multiply a fraction or mixed number by a whole number using repeated equal quantities and a matching visual model.

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Check understanding

Calculate 4 × 3/8 using repeated addition or the rule n × a/b = (n×a)/b
Multiply 2 1/3 × 3 and express as a mixed number
Use a visual model to show why 5 × 1/4 = 5/4

“If a recipe uses 2/3 of a cup of butter and your child wants to make it three times over, can they work out how much butter they need in total?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Fractions
Age range: Ages 9–10