### 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?

# Fencing Lambs

## Fencing Lambs

Some of you reading this live in different continents and know about other animals but I've chosen sheep since they are pretty common across many parts of the world. The young lamb

has a piece of land which it likes but the shepherd is concerned at night time that wild animals may come and attack, and the sheep also needs protection at those times from cold weather. So the thoughtful shepherd used bales of straw:

He arranges these bales of straw around lambs, sometimes one, sometimes two ... sometimes 10 lambs together.

You can see by the area of dark green just how much space each lamb needs. You can also see how the bales are arranged so that the corners are strong and deep around the lamb.

It would not be so good to have them like this

Here are some examples of how it could be done for 1, 2 and 3 lambs.

If you are doing this in school you may find that a teacher has some useful blocks to help. Ask about Cuisenaire blocks that are differently coloured according to how long they are and you could use a white block to stand for a lamb and a RED [2] for a bale of straw. You could also use multilink blocks as a help.

There are also some graphical computer programs that may help, isometric grids are probably better than square ones on this occasion.

Remember these particular rules:-

1. Each lamb must have an area of ground the same as shown above.
2. When you have quite a few lambs they should be next to each other, because they like the company!
3. You should use as few bales as possible each time and these bales are 2 by 1 by 1 in lengths.

Any other rules that you might wonder about are up to you to decide about.

When you send in your results make sure that you tell us what the rules are that you have made extra to my rules.

It will be interesting to see how you put your results together for 1, 2, 3, 4, 5, 6, 7, 8, 9 and10 lambs.

Well Good luck!

Once you've done a set of solutions for 1 ... 10 lambs then have a go at altering the rules, saying "I wonder what would happen if . . . ?"

Here are some possible questions:-

• "I wonder what would happen if the lambs had an illness and had to be separate from each other, how would this affect the number of bales used?"
• "I wonder what would happen if the bales were 3 by 1 by 1?"
• "What happens if I just investigate using 5 lambs but arrange their areas differently?"

### Why do this problem?

This particular activity is a good one to start with if you are not used to carrying out open activities. The children usually enjoy it providing that the introduction is carried out in a way that captivates them! It also provides an easy situation for pupils to start altering the rules for further investigations.

### Possible approach

Show the cuboids and the spaces for the lambs with some suitable resources rather than relying on the pictures, for example Cuisenaire rods or mutlilink cubes joined together.

### Key questions

How are you checking that you've got the young lamb safely protected?

### Possible extension

Encourage pupils to ask and pursue their own questions.

After trying this problem, pupils might like to have a go at Fencing.

### Possible support

Some children may need help with recording their work, for example using a drawing program on the computer.