Partitioning shapes into equal shares
Partition circles and rectangles into two, three, or four equal shares; describe shares as halves, thirds, and fourths; recognise that equal shares of identical wholes need not have the same shape
Lesson
Set out your lesson
Make equal-area shares and explain why shape alone does not determine fairness.
Before teaching
Use this short check, then start teaching.
Inferred, not a taxonomy edge: learner can access the supplied prompt with agreed support and can explain or mark a response. If earlier skills are unfamiliar, use the prerequisite topic for teaching; an authored prerequisite is not proof this learner is ready.
Share and support
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Make equal-area shares and explain why shape alone does not determine fairness.
Make equal-area shares and explain why shape alone does not determine fairness.
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.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Representing Half of a Rectangle
Before you open · source notes
Show half of a rectangle in more than one way. Equal shares can look different; this does not claim thirds or fourths.
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 to shade half two different ways and explain why both are equal shares of the same whole.
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 2026-11-11 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. “Representing Half of a Rectangle.” 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
- Partition a circle into 3 equal parts and label each 'a third'
- Partition a rectangle into 4 equal shares in more than one way
- Explain that two different-looking shares can still be equal in size
“If you cut a rectangle into thirds in two different ways (three strips vs three squares), can your child recognise that both give equal thirds — even though the pieces look different?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Fractions
- Age range
- Ages 6–10
Standards