MathematicsMultiplication & DivisionAges 9–13

Division with remainders

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

Lesson

Set out your lesson

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

Before teaching

Use this short check, then start teaching.

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.

Printer, credit, and teaching notes

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 the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view.

Next: Show

Adult extras

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.

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.

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Entire curriculum

1858 concepts · 9 subjects

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Teaching approaches

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

Family records and proof options

Keep a record of your learning

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

View learner plans ($12/mo per learner) See sample family archive

Learning resources

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

Illustrative Mathematics · Practice link — not the full lesson

Dan’s Division Strategy

Open practice(new tab)

Before you open · source notes

Dan’s division strategy supports division thinking with leftovers. Not every decimal quotient drill.

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

Before you open

Ask the learner to explain a division result and what is left over.

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. “Dan’s Division Strategy.” 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

52 children go on a trip in minibuses holding 9 each — how many minibuses are needed? (interpret the remainder, including a calculator display such as 5.777… meaning 6 minibuses)
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 9–13

Standards

acara-v9:AC9M4N08acara-v9:AC9M5N07acara-v9:AC9M5N09ccss-math:4.OA.3the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G5-B2.1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G6-B2.1the-ontario-curriculum-mathematics-2020:ON-MATH-2020-G7-B2.1uk-nc-2013:Ma5/2.3j