Fractions of a whole (age 10+)
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers
Lesson
Set out your lesson
Explain a/b as a divided by b, including equal-sharing answers greater than one.
Before teaching
Use this short check, then start teaching.
Check equal sharing and multiplication of a fraction by a whole number using mt_TgHxujL81r. Whole-number division with remainders is helpful but can be represented with drawn wholes; it is not silently added as a hard edge. Canonical ages are 10–11, not a readiness guarantee. These activity checks are inferred; source availability is not mastery.
Check learner readiness directly; prerequisite availability is not attainment.
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Explain a/b as a divided by b, including equal-sharing answers greater than one.
Explain a/b as a divided by b, including equal-sharing answers greater than one.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Sharing Lunches
Before you open · source notes
Sharing Lunches supports fractions of a whole in a sharing context. Not every long-division layout.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner what fraction each person gets and how the whole was shared.
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. “Sharing Lunches.” 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
- Explain that 3/4 means 3 ÷ 4 and verify by showing 3/4 × 4 = 3
- Solve: '9 people share a 50-pound sack equally — how many pounds each?' and express the answer as 5 5/9
- Use a visual model to show that sharing 3 wholes among 4 people gives each person 3/4
“If your child shares 3 pizzas equally among 4 friends, can they work out what fraction each person gets — and explain why 3 ÷ 4 gives the same answer as 3/4?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Fractions
- Age range
- Ages 10–13
Standards