Area and the distributive property
Use tiling to demonstrate the distributive property: the area of a rectangle with sides a and (b+c) equals a×b + a×c; use area models to represent the distributive property
Lesson
Set out your lesson
“Area and the distributive property means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Paper shapes or a ruler and pencil
- Shape name cards
Extra for the adult
Worked example. A rectangle has four right angles. Naming the property is the check.
Optional challenge. For Area and the distributive property, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Area and the distributive property, not mastery.
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Teaching approaches
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1 approach
Area and the distributive property means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Paper shapes or a ruler and pencil; Shape name cards. Adult traces or shows one shape and names a property (sides/angles). Child identifies three shapes or measures one simple property and records it. Done: three correct shape/property responses. Stop after the fresh check; keep optional challenge for another day.
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Practice this concept
Start practiceArea and the distributive property practice
Practice key ideas from Area and the distributive property.
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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
Introducing the Distributive Property
Before you open · source notes
Arrays of circles are split to show a×(b+c) as a×b + a×c. Use it for the distributive property with area, not every algebra proof.
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 write a number sentence that matches a split array. One array does not prove every distributive case.
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. “Introducing the Distributive Property.” 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
- Tile a 3×(4+2) rectangle and show it decomposes into 3×4 and 3×2
- Use an area model to compute 6×13 as 6×10 + 6×3
- Draw an area model showing 5×(7+3) = 5×7 + 5×3
“If your child wants to work out 6 × 13 by splitting it into 6 × 10 and 6 × 3, can they draw a rectangle divided into two parts to show why that method works?”
Curriculum record
- Type
- Representational
- Subject
- Mathematics
- Domain
- Measurement
- Age range
- Ages 8–13
Standards