### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

# Home City

### Why do this problem?

This problem encourages logical thinking and can also be used to discuss different ways of representing information.

### Possible approach

Some teachers put a question on the board for the children to think about as they arrive in the classroom at the beginning of the day or lesson, and this question could be used in this way.

Give the children a chance to work in pairs. Working in pairs means that children can check the meaning of the language, which is one of the most problematic parts of this question, with a partner. Invite pairs of children who think they have a solution to come and talk about their methods and if possible record it on the board. The sentence that is likely to give the most problem is 'Sheng lives in the city ...' and if no-one has done so, you may want to explore what this actually means taking one example at a time and working through it. If Sheng lives in Manchester then who lives in Toronto? Mohamed. And that would mean ...

Working through each possibility leads to the realisation that there are two possible answers. This is an important lesson.

There are likely to be several different ways of representing the information in pictures/table etc. Some children may have seen logic problems in books and magazines, and this is one visual way of recording the given information:

 Manchester Sydney Toronto Bahrain Mohamed Sheng Tanya Bharat

You could suggest this if none of the children do.

### Key questions

Is there only one solution?
How do you know?
Do you think one way of solving this was better than the others? Why?

### Possible extension

Children could be challenged to make up their own logic table and questions to go with it. To make up questions so that there is only one answer is challenging - probably more so than answering the original question.