Area of compound shapes
Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas
Lesson
Set out your lesson
“Area of compound shapes 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
- 20 counters or beans
- Paper and pencil for recording sums
Extra for the adult
Worked example. 7 counters plus 5 counters make 12. Write 7 + 5 = 12.
Optional challenge. For Area of compound shapes, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Area of compound shapes, not mastery.
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Teaching approaches
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1 approach
Area of compound shapes 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: 20 counters or beans; Paper and pencil for recording sums. Adult models 7 + 5 with counters, then writes the sum. Child builds three addition problems with counters and records each sum. Done: three correct sums with counters matching the written numbers. Stop after the fresh check; keep optional challenge for another day.
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Practice this concept
Start practiceArea of compound shapes practice
Practice key ideas from Area of compound shapes.
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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
Three Hidden Rectangles
Before you open · source notes
A rectilinear figure is split into three non-overlapping rectangles to find total area. Supports compound area, not every perimeter task.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk for one way to split the figure into three rectangles and add their areas.
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. “Three Hidden Rectangles.” 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
- Decompose an L-shape into two rectangles, find each area, and add them
- Find the area of a floor plan shaped like a T by splitting into rectangles
- Solve: A room is L-shaped (3m×5m plus 2m×4m) — what is the total area?
“If your child is given an L-shaped room on squared paper, can they split it into two rectangles, find the area of each part, and add them to get the total area?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Measurement
- Age range
- Ages 8–11
Standards