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?

Cover the Camel

Stage: 1 Challenge Level:

Why do this problem?

This problem is a lovely context in which children can develop their ability to visualise. In this challenge, the visualisation is required in two ways. Firstly, children must plan ahead so as not to leave impossible spaces and, secondly, they must try to turn each piece in their mind's eye to decide which is needed for a particular gap.

If you would like children to work on this problem practically, you can print out these photocopiable sheets. The image of the camel is on the first sheet and the ten pieces to fit into it on the second sheet.

Key questions

Where might be a good place to start?

Is there anywhere else you can put a piece straight-away?

If you put that piece there, will you be able to fit another one in easily?

Have you tried turning the piece round?

Have you tried turning the piece over so it's the other way up?

Have you got any spaces that you can't fill?

Have you counted the number of squares in the gap?

Possible extension

Learners could make their own designs on squared paper using these shapes or try this similar problem, Tessellate the Triominoes.

Possible support

Sometimes the most surprising children have difficulties with this type of visual problem.

Suggest working on it practically using this copy of the problem which has the camel picture on the first sheet and the ten pieces to fit into it on the second sheet. It might help to print out the second sheet on coloured paper which will emphasise the spaces.

Addition & subtraction. Visualising. Practical Activity. Compound transformations. Combinations. Investigations. Tangram. Working systematically. Games. Interactivities.

You may also like