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Make a cube out of straws and have a go at this practical challenge.


Reasoning about the number of matches needed to build squares that share their sides.

Little Boxes

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World of Tan 7 - Golden Goose

Age 7 to 11
Challenge Level

Why do this problem?

This problem is an engaging context in which pupils can consolidate their knowledge of the properties of squares, triangles and parallelograms. By attempting this activity, children will be putting into practise their visualising skills, making guesses about where the different shapes might go before trying out their ideas. When combining the shapes to make the tangram, pupils will use their understanding of translations, reflections and rotations to decide how to transform each shape. There are also links between tangrams and fractions, and children can be encouraged to work out what fraction of the whole square is represented by each smaller shape.

Possible approach

Read this story with the whole class and look at the tangram as a group. Ask pupils to suggest where a shape might go. What transformation would be needed to move the shape into that position?

When pupils are solving the tangram, they would benefit from working in pairs with a tablet or a printed copy of the shapes to cut out and move around. Working together will lead to rich discussions about the possible options for where each shape can go. When the children have solved the tangram, they can have a go at the extra activities.

At the end of the lesson, bring all of the pupils together and model the solution on the whiteboard. How does each shape need to be transformed? What fraction of the whole picture is each shape?

Key questions

What could you put with this piece to make a square?
Are all of the pieces different?
What's the smallest square you can make?
What has to go in that space? How do you know?

Possible extension

Pupils could have a go at other tangrams in the 'World of Tan' series. Some children might like to create their own tangram from the same pieces, or make their own tangram pieces by cutting up a square.

Possible support

Some children might need encouragement to experiment and 'have a go'. Using the printable tangram pieces will help all pupils try out their ideas.