Splitting shapes into equal parts (age 7+)
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
Share and support
Teaching Table
Set out your lesson
Make equal-area shares and explain why shape alone does not determine fairness.
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.
Keep the two adult-only cards off the learner screen. Have a pencil and scrap paper if useful; oral pointing/typing/AAC can replace handwriting unless spelling or composition is the target. No printing, cutting, account or purchase is required.
Open Show first, read the explanation together, and pause to check the central idea. Then do Guided Try together.
For Try, close earlier models and the adult keys unless the task explicitly supplies a reference. Record any hints, read-aloud help or model reopening; do not call supported work independent.
Use only the active learner card. Keep the private key closed until an attempt is recorded. Stop or take a break on request; practical claims stay not observed unless actually done.
Use on screen; read aloud or recreate a tactile model only with declared support. No printer or purchased kit.
Never display adult keys or dictation spellings with a learner task; no family financial, identity or conflict disclosure.
Never display adult keys or dictation spellings with a learner task; no family financial, identity or conflict disclosure.
Use the complete materials on screen or print only the current sheet. Keep adult guidance out of learner view. Retain an earlier model only when the current step supplies it as context.
Teaching limits and safe use
These are finite task opportunities, not proof of mastery. Record what was attempted and what support was used.
Supported circle construction. A rectangle made of three squares depends on its dimensions; this does not hold for every rectangle.
These bounded examples do not establish independent performance in other situations. Record the support used.
Never display adult keys or dictation spellings with a learner task; no family financial, identity or conflict disclosure.
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
Reviewed external links that reinforce this concept. They do not replace Gakuva’s teaching approach.
No reviewed resources for this concept yet.
The teaching approach above still stands. Curated practice links will appear here as the shelf fills.
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 7–8
Standards