MathematicsFractionsAges 10–11

Dividing unit fractions and whole numbers

Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations

Lesson

Set out your lesson

Distinguish sharing a fractional amount from counting fractional-sized servings, with a clear whole unit.

Before teaching

Use this short check, then start teaching.

Activity

Use mt_ifPDOYvUqm and mt_1PAWhRhpdg first. Ask whether the quotient names an amount per person or a number of servings. No food is needed.

Policy

Check learner readiness directly; prerequisite availability is not attainment.

Printer, credit, and teaching notes

Check learner readiness directly; prerequisite availability is not attainment.

Materials

Pencil and plain paper, or this screen and an oral explanation. No purchases, food, scissors, weighing or real journey needed.

Procedure

Choose one short sitting or stop after Together and return later. Read the model aloud, invite the learner to try, then put Show and Together aside for Try. Keep adult keys closed and out of view.

Access

No printer: show only the active learner sheet; copy the supplied grid/table or draw on plain paper. An adult may read exact prompts or scribe the learner’s own words without adding a method; record that support. Oral work is mathematical evidence, not handwriting evidence.

Privacy

Use fictional quantities. No names, addresses, body measurements, accounts, family records or purchases are required. A learner can pause or decline a context.

Teaching Procedure

Ask what stays the same, which unit is being counted, and what operation fits. Let the learner explain before helping. If stuck, return to the worked model, then retry; record the help rather than calling it independent.

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 do not establish general mastery. Exact canonical examples are rehearsal when previously modeled. No timed testing or forced personal disclosure.

Use fictional quantities. No names, addresses, body measurements, accounts, family records or purchases are required. A learner can pause or decline a context.

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

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Teaching approaches

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Distinguish sharing a fractional amount from counting fractional-sized servings, with a clear whole unit.

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

Dividing by One-Half

Open practice(new tab)

Before you open · source notes

Dividing by one-half supports unit-fraction and whole-number division. Not every mixed-number division.

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

Before you open

Ask how many halves are in a whole number and show why.

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. “Dividing by One-Half.” 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

Solve: '3 people share 1/2 lb of chocolate equally — how much each?' (1/6 lb)
Solve: 'How many 1/3-cup servings in 2 cups of raisins?' (6 servings)
Create a story context for a given unit-fraction division expression

“If your child has half a pizza to share equally among 3 people, can they work out what fraction of the whole pizza each person gets — and explain the steps they took?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Fractions
Age range: Ages 10–11

Standards

ccss-math:5.NF.7.c