# Shut the box

An old game with lots of arithmetic!

## Problem

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.

Can you explain your strategy?

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.

## Getting Started

Which cards *could* you turn down using the numbers you've rolled?

If you've got several choices, how will you decide what to do?

## Student Solutions

There is no particular solution to this game.

Some people have tried other rules;

$1$. You can choose to turn over the numbers you've rolled, or add them together, or subtract one from the other. For example, if you were to roll a $5$ and $4$ you could choose to turn the $4$ and the $5$ over OR you could choose to add or subtract so that you could turn either the $9$ or the $1$ over.

$2$. When you came to a stop because you were unable to turn over new numbers, then those two dice numbers pass to the next player who can use them rather than rolling the dice again.

$3$. You can choose to turn over any set of cards that has the same total as the dice numbers you have thrown. For example, if you throw a 4 and 5, you could choose to turn over:

$4 & 5$ or $9$ or $1 & 8$ or $2 & 7$ or $3 & 6$ or $1 & 2 & 6$ or $1 & 3 & 5$ or $2 & 3 & 4$

$4$. You could multiply the two numbers on the dice together and then turn over any set of numbers which has that total. For example, if you throw 4 and 5, as well as the above, you could also choose to turn over:

$8 & 12$ or $9 & 11$ or $4 & 6 & 10$ or $1 & 2 & 3 & 4 & 10$, etc.

So, try these different versions of the game and different ways of scoring, and tell us what you think works best and why.

## Teachers' Resources

**Why do this game?**

### Possible approach

### 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.