### Three Squares

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

### 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?

# Shut the Box

## Shut the Box

Here is a game that uses two dice and cards with the numbers 1 to 12 on them. The aim of the game is to turn over all the cards. You can turn over the cards that match the numbers on the dice.

To play the game, start with the numbers showing on all the cards.

The first player rolls the two dice.
They can turn over the cards which are the same as the numbers rolled.
For example, if a 4 and 5 are rolled, they would turn over the 4 and 5 cards. If a double is thrown, the player's turn ends. They can roll the dice again until they can't turn over any more cards. The cards that are left showing are then added and that is their score.

The dice are then passed to the next player who turns the cards the right way up again and then rolls the dice in the same way as player one. They now can keep on rolling dice as long as each time they can turn over some new cards. Remember that if a double is thrown, the player's turn ends. When the player can't turn over any more cards, those that are left are added together and that is the player's score.

The winner is the person with the lower score.

What is good about the game? What is not so good? Why?
How could you alter the rules to make it better?

It can be played with just one turn each or each player can have a number of turns that you decide at the beginning of the game.
Here .doc pdf are some cards which you could print out and cut up to play the game.

### Why do this game?

This game can give pupils the opportunity to use their number knowledge and it can be adapted to stretch even the highest attainers. In its simplest form it can be accessed by anyone in the class who is able to connect the number of spots on a die to the numeral that represents it. Altering the rules will give the children opportunities to explore ideas about what makes a "good" game and to develop winning strategies to play their games.

### Possible approach

Start with the basic rules and play the game as a class, or perhaps one half of the class against the other, perhaps using large dice. You could use 'real'  pdf larger cards fixed to an ordinary board with Blu Tack, or you could simply have the numbers written on the board and cross them out.

After playing a few times, encourage the children to be critical of the game. The game offers opportunities for you to identify the children's understanding of the meanings of numbers to 6 and linking their iconic representation on dice with their numeral.

Pairs of children could then test out the different versions of the game with the aim of explaining why they thought it was good or not so good. This could then lead into a whole-class discussion about features of 'good' mathematical games in general. Invite the learners to suggest what else could be changed in the game. Identifying the variables in this way (for example, number of players, type of dice, number of cards etc) is a useful skill which children can apply again and again. Pairs could test their own version to see whether they have made a good game.

### Key questions

These questions have been phrased in ways that will help the teacher to identify the children's prior knowledge about both the number concepts involved in playing the game and the strategies and mathematical thinking needed to win.

#### Number concepts

How many spots can you see on the two dice?
Which cards will you turn over?
Can you tell me about why you chose to turn those numbers over?

#### Strategies, problem solving and reasoning

What is good about the game? What is not so good? Why? How could you alter the rules to make it better?
Which cards could you turn over? Which would be best? Why?
What else could we change about the game?

### Possible extension

By giving learners the chance to invent their own rules, children can take responsibility for their own mathematics and demonstrate their potential. You can use twelve numbered cards instead of six and add, subtract or multiply the scores on the two dice together to find the number to turn over. It may be worth considering changing the rule which ends the turn when  double is thrown.

### Possible support

Most children will find it manageable to use numbers 1 to 6 to start with. Do let them go on to explore their own games, they may well surprise you!