Composing Shapes
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) to create composite shapes, and compose new shapes from the composite shape
Lesson
Set out your lesson
Join and separate flat shapes, explaining the pieces rather than just naming the outline.
Before teaching
Can discuss the supplied example in an accessible mode; adapt directions without supplying the target answer.
Check the learner can follow the model with support before moving on. Source prerequisite ordering is not learner mastery; return to prerequisite work when needed.
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Teaching approaches
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1 approach
Join and separate flat shapes, explaining the pieces rather than just naming the outline.
Join and separate flat shapes, explaining the pieces rather than just naming the outline.
Family records and proof options
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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
Make Your Own Puzzle
Before you open · source notes
Learners cut and reassemble a square into a puzzle of composite shapes. Use it for composing shapes, not every tangram story.
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 put the pieces back into the original square and name two shapes used.
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. “Make Your Own Puzzle.” 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
- Combine two triangles to form a rectangle or larger triangle
- Put together half-circles and quarter-circles to form circles or new shapes
- Decompose a composite shape and describe which simpler shapes make it up
“Can your child use flat shapes like triangles and rectangles to fit together and make a new larger shape — like a puzzle?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 6–10
Standards