### Homes

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

### Number Squares

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

### I'm Eight

Find a great variety of ways of asking questions which make 8.

# Starfish Spotting

## Starfish Spotting

I can see 28 'arms' on the beach.

How many children could there be?
How many starfish could there be?

### Why do this problem?

This problem is an engaging context in which to practise counting, repeated addition and recognition/recall of multiples of 2 and 5. It provides an opportunity for children to invent their own ways of recording their thinking and to share these with the whole group.

### Possible approach

Give children chance to consider the task completely on their own for a few minutes - display it on the screen so they also have the visual image of the starfish, and read out the challenge.  Try to insist that there is no talking for these first few minutes so everyone really does have time to think about what they would do to start the problem. You might like to have mini whiteboards available so that learners can jot down their ideas.

Then invite learners to turn to a partner and share their thoughts.  It might be that they have questions too, so after a little while, bring everyone together. Ask for pairs to suggest ways of beginning the task, or to share questions which they have not been able to answer.  Look to other members of the class to provide comments, rather than doing this yourself.

Allow time for pairs to work together to find a solution.  You may wish to post the following on the board as prompts:
• Can you find a solution?
• Can you find another solution?
• Can you find all the solutions? How do you know you've got them all?
In the plenary, you could draw out different ways of approaching the task that you have noticed e.g. by trying a random number of children and starfish, then adapting to get 28 arms; listing multiples of 2 and 5; working in a systematic way such as starting with all children; noticing that if the total number of arms is even then there must be an even number of starfish (or none at all) etc. (This is by no means an exhaustive list and children will find ways that surprise you!)

### Key questions

What could you try first?
How many have you got altogether?
How many more do you need to make 28?
How many fewer do you need to make 28?
How will you remember what you have found out so far?

### Possible extension

The problem Noah offers a great extension to this problem. It allows learners to be creative with their choice of animal and there are may more possible solutions.

### Possible support

All children might benefit from having some sort of equipment to represent the arms e.g. straws, matchsticks...