Combining Simple Shapes
Compose simple shapes to form larger shapes (e.g. two triangles make a rectangle)
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Teaching Table · Reviewed guide
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
Full guide and materials
- Two identical large paper right triangles prepared before the child joins
- One outline card of a rectangle or square the triangles should fill
- Step 1. Show the two triangles and the rectangle outline.
- Step 2. Model joining the long edges so the triangles make one rectangle.
- Step 3. Have your child take the triangles apart and recombine them to fill the outline.
- Step 4. Ask what larger shape the two triangles made.
- Quick check. Success means your child independently joins the two triangles into the larger rectangle/square and can point to the starting triangles and the combined shape.
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.”
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
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
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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 5–6
Standards