MathematicsFractionsAges 8–12

Fractions of amounts (harder)

Solve problems involving increasingly harder fractions to calculate quantities, including non-unit fractions where the answer is a whole number

Lesson

Set out your lesson

Find non-unit fractions of whole-number quantities by identifying one equal share and then combining selected shares.

Before teaching

Use this short check, then start teaching.

Activity

Ask for 1/4 of 12 and how the equal groups were made. If equal grouping is insecure, revisit fractions of discrete sets before non-unit fractions. 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.

Printer, credit, and teaching notes

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.

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.

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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Teaching approaches

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Selected Default Gakuva

Find non-unit fractions of whole-number quantities by identifying one equal share and then combining selected shares.

Family records and proof options

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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

How Much Pie?

Open practice(new tab)

Before you open · source notes

A pie-sharing story supports harder fractions of amounts. Not every percent tip calculation.

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 find a fractional amount of the pie and say what the whole is.

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. “How Much Pie?.” 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

Find 3/5 of 20
Calculate 2/3 of 18 and explain the two-step process (divide then multiply)
Solve: A bag has 24 sweets, 3/8 are red — how many red sweets?

“If 3/4 of a class of 28 pupils brought their homework in, can your child work out exactly how many pupils that is?”

Curriculum record

Type: Procedural
Subject: Mathematics
Domain: Fractions
Age range: Ages 8–12

Standards

acara-v9:AC9M6N07uk-nc-2013:Ma/KS2/Y4/F/3

Curriculum