http://nrich.maths.org/6605&part=noteNice and NastyGame | Teachers' Notes | Printable page |Stage: 2 and 3 Challenge Level: 

There are nasty versions of this game but we'll start with the nice ones...

Find a partner and a 1-6 dice, or preferably a 0-9 dice if you have one.

Interactive Spinners or Dice and Spinners can be used to simulate dice.

Each of you draw a set of four boxes like this:

Alternatively you can download and print off this pre-made scoring sheet.

Game 1

Take turns to throw the dice and decide which of your four cells to fill.

Do this four times each until all your cells are full.

Whoever has the larger four-digit number wins.

There are two possible scoring systems:

A point for a win. The first person to reach 10 wins the game Work out the difference between the two four-digit numbers after each

round.The winner keeps this score. First to 10000 wins.Now for some variations...

Game 2

Whoever makes the smaller four digit number wins.

Adapt the scoring to suit.

Game 3

Set a target to aim for. Then throw the dice four times each and work out how far each of you is from the target number. Whoever is the closer wins.

There are two possible scoring systems: A point for a win. The first person to reach 10 wins the game Work out the difference between the two four-digit numbers and the target

number after each round. Keep a running total. First to 10000 loses.Possible targets: 5000, 3500, 2222, ...Game 4

This game introduces a decimal point. The decimal point will take up one of the cells so this time the dice only needs to be thrown three times by each player.

The winner is the one closer to the target.Possible targets: 35, 3.1, 24, 2.6, 10, ....

Two possible versions: each player decides in advance where they want to put the decimal point

before taking turns to throw the dice

each player throws the dice three times and then decides where to place the digits and the decimal point.Again, two different scoring systems are possible.

Game 5

The nasty version!!Play any of the games above. This time you can choose to keep your number and put it in one of your cells, or give it to your partner and tell them which cell to put it in. You might lose a friend this way!! It's really important to take turns to start each round if this game is going to be fair.

This becomes even nastier when you play the games above with more than two people.

Game 6

A cooperative game rather than a competitive one - for three or more people.

Choose any of the games above. Decide in advance which of you will get the closest to the target, who will be second closest, third, fourth etc. Now work together to decide in whose cells the numbers should be placed, and where.

Why play these games?These games are thought provoking and very engaging. They encourage discussion of place value and strategic mathematical thinking.

Resource downloadsInstructions sheet

Scoring sheet

Possible approachThese games can be played with 1-6 die but ideally would be played with a decahedral 0-9 dice or spinner. Interactive Spinners or Dice and Spinners can be used to simulate dice.

Ask the students to each draw a set of four boxes. Throw the dice and ask them to place the number in any of the boxes. Do this three more times. Then ask who has the largest four digit number. What would you have done differently if you knew in advance you were trying to make the biggest number?

Play the game again several times drawing out strategies that the students use.

Working in pairs, set the students off on playing game 1.

When appropriate, move onto the other games clarifying the targets and scoring system for each.

Key questionsWhy are some cells more significant than others?

Possible extensionYou may wish to move the students on to Dicey Operations .

Possible supportStart with two, then three boxes, before moving onto four. Choose the easiest scoring system or allow calculators for scoring the more difficult version. Allow pairs of students to play against other pairs, so that they can support each other.

The first article in this series discussed what is meant by 'mathematical games', and the possible benefits of using them as part of a teaching programme. This article looks at some different types of games and the sort of mathematical thinking they can develop. 

One way of classifying games is by their format, that is; the equipment used and the sort of actions the players are involved in. Some of the following classification has been drawn from two articles by Gough (1999). Examples have been provided by referring to well-known games, 'hotlinks' to games that have been published on the Primary Website, or a brief description of a game. Some thoughts on the nature of mathematics involved are also given. 

Game FormatsRaces 

These games involve racing pieces around or across a board to a finishing point,

like Ludo. Other games might be a race against time. 

Some race games depend on rote learnt skills, like basic counting or reciting number facts, and therefore have limited mathematical value. Such games also tend to have little interaction between players, or interdependence between 'turns' and therefore require little or no strategy development. However, race games can be deliberately designed to focus on particular mathematical skills, such as the probability game and the arithmetic game given below. 

Tricky Track

Place counters on the squares numbered 2 to 12. Roll two dice and add to decide which player moves forward one square. The game should be played several times and discussion about the fairness of the game encouraged.

Fast FiguringUsing the number cards from an ordinary pack, deal out five cards to each player. Turn up one more card to reveal the 'target number'. Players race to use their five cards and any of the four operations (+, -, x, / ) to form a statement that results in the target number. The first player to do so wins a point. If, after 3 minutes, no one can find a solution, the players show their hands for checking, then cards are shuffled and play continues.

Board Games

Moving round a board to build to build towards a goal, like Monopoly. Whilst there is some mathematical value in these games, they are perhaps most useful in the classroom when adapted to include problems and puzzles, which when solved, give some advantage to the player (or players).Spatial Strategy GamesSpatial Strategy: This might involve moving pieces around a board strategically, usually to capture or block an opponent, like Chess and Draughts (see Mini Draughts below). See Jumping Reindeer , Two Stones , and Roundabout . 

Mini DraughtsDraughts can be difficult for young children to learn. A reduction in the size of the game grid and the number of pieces can provide the challenge and interest of 'real' draughts without the overwhelming number of possibilities for moves.

Spatial strategy games involve placing pieces to make a pattern or seize territory, like Noughts and Crosses or Connect Four. See Line of Four , Endless Noughts and Crosses , Sprouts . 

Numerical Strategy Games 

This usually involves removing pieces to achieve a goal, like Nim or Mancala, See Last Biscuit ,Squayles , Slippery Snail . 

Magic 15

This is a game for two players. Begin with the numbers 1 to 9. Players take turns to select a number, with each number used only once. The winner is the first player to have exactly three numbers that total 15. (There's a link to magic squares).

As suggested in the title, to be successful at strategy games, players need to

analyse the 'moves' and patterns of moves that lead to winning. This is where the underlying mathematics is discovered! Once the patterns have been found and practised, the games lose their appeal, but can be revived through variations and extensions. 

Card Games 

Using a pack of cards: taking tricks, building sets, emptying one's hand, like Rummy, Fish or Old Maid. These can be further adapted to create more mathematical games (see January's article). 

Arithmetical Games 

These games might use cards (like ONO'99), dice (like Number Boggle) or targets (like Darts) to deliver the numbers that are then calculated in some way according to a set of rules. The games usually involve an element of chance, which adds more interest. 

Roll Six

Players roll six dice and use five of the numbers together with any of the four operations to make the sixth number. Points are scored for successful equations.

See also Stop or Dare 

Matching Games 

Using a set of tiles, matching ends or making patterns, like Dominoes and the less known number game Triominoes. Memory (under its many other names) involves turning a set of pairs of cards face down and trying to locate the pairs turning only two cards face-up at a time. 

This type of game is very useful for practise and consolidation of basic number skills, particularly with very young children, but usually involves little strategy or player interaction. 

Mystery Games 

Guess My Number and Twenty Questions type games can stimulate quite a lot of mathematical thinking and strategy development. 

Teachers, take advantage of the fact that children will happily play and enjoy mathematical games that they wouldn't normally choose to play at home! 

ReferencesCar, J. (1999) Primary Mathematics Masterclasses. Mathematics in School, January 1999.

Gough, J. (1999). Arithmetics Games: Very equable? Australian Primary Mathematics Classroom. Vol.4 No. 3

Gough, J. (1999). Strategy Board Games and Spatial Thinking. Australian Primary Mathematics Classroom . Vol 4. No.4