Mathematics K–6 · Years 3–4

Tangram: seven pieces, one square

Measurement and space

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

Composite shapes are built from familiar shapes, and the seven tangram pieces are fractions of one square, so every shape made from all seven pieces has the same area as the square.

What you need

1 square of card 16 cm by 16 cm per learner
scissors and a ruler
full-size outline cards: a cat, a house, a boat and a rectangle, each made from all seven pieces
1 cm grid paper

How to do it

Cut the square along one diagonal. Fold one half in half and cut along the fold to make the two large triangles.
On the other half, fold the right-angled corner to the middle of the long side and cut along the fold to make the medium triangle. Cut the remaining trapezium in half across its parallel sides, then cut one part into the square and a small triangle and the other into the parallelogram and a small triangle.
Show that the two small triangles cover the square piece exactly, then the medium triangle, then the parallelogram.
Show that the two small triangles and the medium triangle together cover one large triangle.
Name each piece as a fraction of the whole square, then make each outline card using all seven pieces.
Choose an object in the room (a door, a window, a bookshelf) and draw it on grid paper as a combination of rectangles, triangles and circles.

What you should see

The square piece, the medium triangle and the parallelogram are each covered exactly by the two small triangles, so all three are 1/8 of the square and each small triangle is 1/16. Two small triangles and the medium triangle cover a large triangle, so each large triangle is 1/4. From a 16 cm square the areas are 64 cm² for each large triangle, 32 cm² for the medium triangle, the square and the parallelogram, and 16 cm² for each small triangle, adding to 256 cm². Every outline made from all seven pieces, including the rectangle, has an area of 256 cm², though the outlines have very different perimeters.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

The parallelogram looks longer, so it has more area than the square piece.
Rearranging the pieces into a new outline changes the total area.

Safety card

Low riskLearners carry it out

Hazards

scissors

Controls

cut seated at a table and pass scissors handle first

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA2-2DS-02 MAO-WM-01
Australian Curriculum v9AC9M4SP01

Sources

The pages the author read to write this activity.

All Concept Studio activities