### Traffic Lights

The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line wins.

### Achi

This game for two players comes from Ghana. However, stones that were marked for this game in the third century AD have been found near Hadrian's Wall in Northern England.

### Yih or Luk Tsut K'i or Three Men's Morris

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.

# Nice or Nasty

## Some Games That May Be Nice or Nasty

Find a partner and a $1-6$ dice, or even a $0-9$ dice if you have one. You could use the dice in Dice and Spinners.

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

Or you can download and print off this scoring sheet.

### Game $1$

Take turns to roll the dice and decide which of your four boxes to fill. Do this four times each until all your boxes are full. Read the four digits as a whole number.

#### 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. You'll probably want to change the scoring system.

### 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.

### 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. Choose a target.

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 $5$

This is 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 downloads

The following printable worksheets may be useful: Nice or Nasty - Instructions Sheet
Nice or Nasty - Scoring Sheet

### Possible approach

These games can be played with 1-6 die but ideally would be played with a decahedral 0-9 dice or spinner. The dice in 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 questions

Why are some cells more significant than others?

### Possible extension

You may wish to move the students on to Dicey Operations .

### Possible support

Start 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.