### Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

### Three Squares

What is the greatest number of squares you can make by overlapping three squares?

### A City of Towers

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

##### Stage: 1 Challenge Level:

Here are shadows of some 3D shapes.

What could they be?

### Why do this problem?

This problem requires learners to visualise 3D shapes, and therefore consolidates knowledge of their properties. Pupils are also reminded that there is not necessarily one right answer in mathematics!

### Possible approach

It is important for children to have had lots of experience of handling and talking about 3D shapes prior to this activity, and it would be helpful to have lots of 3D shapes to hand.

You could start off the activity by choosing a particular shape and telling children that you're going to shine a torch on it so that you can see its shadow. (Alternatively, hold a shape under the lamp of the overhead projector.) Ask children what shape they think the shadow will be and why. Give them time to talk to a partner before discussing it as a whole class. You could repeat this once more with a different shape (or by shining the torch on a different face of the first shape) so that the group understands what is happening.

Then show them the pictures of the shadows in the problem and ask them to work in pairs or small groups to decide which shapes could make each shadow. You could give each group a torch to test their predictions.

In a plenary, share solutions and draw attention to those where more than one shape is possible. Are the children certain they have all the possibilities?