Division with remainders

MathematicsMultiplication & DivisionAges 9–10

Solve multi-step word problems using the four operations with whole numbers, including interpreting remainders in context; represent with equations using a letter for the unknown; check with estimation

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Teaching Table

Set out your lesson

Choose operations, represent an unknown and interpret leftovers according to the question, not a rounding rule.

Activity

Before starting, ask for 3 × 14 and 45 ÷ 6 with remainder and a reason for each step. Check that the learner distinguishes equal sharing from number of groups. This short probe is activity readiness, not proof of every directed prerequisite.

If Not Ready

Pause the fresh check. Revisit the named prerequisite or repeat the Show with smaller steps; record supported practice rather than an independent result. Authored predecessor existence never proves this learner is ready.

Allow about 25 minutes with a break. Open one learner stage at a time; supply spare paper and pencil if wanted. No physical counters are required. Keep adult keys separate. For the model, point to the supplied bus-seat picture; no bus toy or printer is needed.

Use paper or the supplied screen materials in a comfortable place. No special equipment or purchase is needed. Stop or take a break when wanted.

Record the learner’s actual words or work, task ID and any help. Do not prefill success. Allow oral, pointing or written responses as appropriate; oral independent reasoning is not automatically supported. Copied/scribed text is not independent composition or handwriting. No name, account, upload or real family record is required.

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.

Finite task opportunities, not learner mastery or universal canonical coverage.
Use the supplied materials on screen or print one current sheet; physical printing can vary.
Record the actual response and assistance; completing a task does not establish mastery.

Use paper or the supplied screen materials in a comfortable place. No special equipment or purchase is needed. Stop or take a break when wanted.

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Entire curriculum

1590 concepts · 8 subjects

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Teaching approaches

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Selected Default Gakuva

Choose operations, represent an unknown and interpret leftovers according to the question, not a rounding rule.

Family records and proof options

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Learning resources

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Check understanding

52 children go on a trip in minibuses holding 9 each — how many minibuses are needed? (interpret remainder)
A shop sells packs of 6 pencils for £1.50 each — how much do 5 packs cost?
Represent a two-step problem with an equation using n for the unknown

“If your child reads 'a school buys 7 boxes of 24 pens and shares them equally between 8 classes', can they work through all the steps and decide sensibly what to do with any remainder?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Multiplication & Division
Age range: Ages 9–10