### Two Dice

Find all the numbers that can be made by adding the dots on two dice.

### Biscuit Decorations

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

### Writing Digits

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

# The Tall Tower

## The Tall Tower

You have been imprisoned at the top of the Tall Tower by the Wicked Magician!

You can get out by climbing down the ladders. As you come down you collect useful spells.

You can go down the ladders and through the doorways into the adjoining room but you cannot go into the same room twice, nor climb up the ladders.

The numbers in the rooms show how many spells there are in each one.

Which way should you go to collect the most spells?

And which way to collect as few as possible?

Can you find a route that collects exactly $35$ spells?

### Why do this problem?

This problem allows children to do addition and subtraction, and compare numbers in an interesting and challenging setting. They will be encouraged to develop skills linked with reasoning about numbers while engaging with the problem. It is a good opportunity to talk about working through combinations systematically and ways of recording this.

### Possible approach

This sheet might be useful for both working on the problem and recording. The numbers in each of the rooms will have to be put in by children themselves.

### Key questions

Can you go through all the numbers?
Which is the best number to leave out?
How any spells do you collect going that way?
Would it help to record the routes you take so that you do not repeat yourself?
Can you find a route that collects more/less spells?
Is that route exactly $35$ spells?

### Possible extension

Children could find how many different ways there are to go down the tower or put in different/harder numbers on this sheet. Alternatively they could try Getting the Balance.

### Possible support

Suggest using simpler numbers such as only one and two on this sheet. Counters representing the spells could be used on the sheet or a rough picture of the problem.