### Grouping Goodies

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

### Odd Tic Tac

An odd version of tic tac toe

### Break it Up!

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

# What Number?

## What Number?

I am less than 25.

My ones digit is twice my tens digit.

My digits add up to an even number.

What am I?

### Why do this problem?

This is a quick problem suitable for starting a lesson and requiring no resources. It can usefully be made into a longer activity by focussing discussion on the possible problem-solving strategies and evaluating them.

### Possible approach

Offer the children time to work in pairs and record their thinking on large pieces of paper. Pin them up centrally and encourage the children to look for similarities and differences in the way the problem has been solved. Do they think one way is better than the others, and if so why?

You could make it a more structured discussion by writing the three pieces of information (less than $25$, ones double tens, add to even number) on three pieces of paper and ordering them differently, in each case writing down the possible numbers from the first piece of information and eliminating those that don't fit the second and the third. Do the children think one order was better than the others?

### Key questions

What do you know?
Can you make a list?

### Possible extension

Children can make up similar questions for each other. Can they use three digits? Can they be sure there is only one answer to their question?

### Possible support

Working in pairs to record thought processes can be very threatening for children who find such questions difficult. You could instead perhaps give them cards with numbers up to $25$ and they could remove the ones that didn't fit the other two conditions.