Combining Simple Shapes
Compose simple shapes to form larger shapes (e.g. two triangles make a rectangle)
Lesson
Set out your lesson
“Small shapes can combine into a bigger shape. Two identical right triangles can join along the long side to make a rectangle. We fit edges like puzzle pieces.”
Bring to the table
- Two identical large paper right triangles prepared before the child joins
- One outline card of a rectangle or square the triangles should fill
Extra for the adult
Worked example. Long edge to long edge turns two right triangles into one rectangle. If the outline is square and the triangles fit, the larger shape is a square, which is a special rectangle.
Optional challenge. Try a second arrangement: can the same two triangles make a larger triangle as well as a rectangle?
What to notice. Save a photo of the combined shape or a parent note: “two triangles made a rectangle.”
Share and support
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Teaching approaches
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2 approaches
Small shapes can combine into a bigger shape. Two identical right triangles can join along the long side to make a rectangle. We fit edges like puzzle pieces.
Spend about 10–15 minutes joining two triangles into a rectangle and naming the new shape.
Combine specified smaller shapes to fill a rectangle and hexagon without gaps or overlaps.
Combine specified smaller shapes to fill a rectangle and hexagon without gaps or overlaps.
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
Grandfather Tang's Story
Before you open · source notes
Tangram animals support combining simple shapes. Not every 3-D net folding.
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 build one figure from smaller shapes and name the pieces 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. “Grandfather Tang's Story.” 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
- Join two triangles to make a rectangle or larger triangle
- Use pattern blocks to fill a hexagon outline
- Create a picture or design by combining basic shapes
“Can your child fit smaller shapes together to make bigger ones — like combining two triangles to make a rectangle?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 4–6
Standards