### Three Squares

What is the greatest number of squares you can make by overlapping three squares?

### 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?

# Two Dice

## Two Dice

Here are two dice.

If you add up the dots on the top you'd get $7$ !

Roll the dice. Add the numbers that are on the top.
What other totals could you get if you roll the dice again?

You will need two dice to play this game. The children can count the total number of spots on the dice or add them together using number facts they already know.
Record the results and explore the different totals that you can get.
Help them to find all the possible combinations.

        Photograph acknowledgement.

http://imgisland.com/wallpapers/3D/red_dice.jpg



### Why do this problem?

This activity provides a valuable experience for younger pupils to explore some simple additions while finding all possibilities.

### What children need to know to play this game

The children need to be able to roll two dice and identify their score.

### Possible approach

Using a dice with dots on, encourage discussion as to what numbers are represented by the faces of the dice before introducing the challenge itself.

You could support the children to collect their totals on the board. Ask them how they should be arranged and see if they can suggest a systematic way of recording their results. For example, they might start with all the totals that use a $1$. In this way, you can ask the class to talk about the patterns they notice and this will help to reveal any combinations that are missing.

### Key questions

These questions have been phrased in ways that will help you to identify the children's prior knowledge about both the number concepts involved and the strategies and mathematical thinking needed to solve the problem.
Can you make a bigger/smaller total?
What is the highest total you could make?
What is the lowest total you could make?
If one dice shows $6$, what could the other dice be showing?
How will you know when you've found all the totals?

### Possible extension

You could make use of more dice and/or dice with different numbers of faces. Alternatively, consider finding the difference between the two numbers or the product of the two numbers.

### Possible support

Children who struggle with addition may count the dots to help them but encourage them to articulate the number sentence once they have done so. This will help them to build the visualisations of the numbers as dotty dice patterns which will support their learning of number bonds.