### Cubes

Investigate the number of faces you can see when you arrange three cubes in different ways.

### I'm Eight

Find a great variety of ways of asking questions which make 8.

### Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

# Dotty Six

## Dotty Six

You need a partner, a $1$-$6$ dice and a grid like this;

Take turns to throw the dice and draw that number of dots in one of the boxes on the grid.

Put all of your dots in one of the boxes. You can't split them up and you can't have more than six dots in a box.

When a box is full, you could put a tick in the corner like this:

Keep going until there are three ticks in a row or column or diagonal. The winner is the person who puts the last tick.

Now, can you change the game to make your own version?

### Why play this game?

The game as introduced is intended for KS1 children who are just beginning to become confident with small numbers. However there are many variations, some suggested below, that make it suitable for older children. As with many of the NRICH games, consolidation of basic number facts is combined with an element of strategic thinking.

### Possible approach

With very small children you may wish to play the game with a small group first before encouraging them to play in pairs.

If you have access to a projector and screen, you may wish to use the PowerPoint animation with older children. If that is not possible, choose a child or another adult to play the game with you somewhere where everyone can see what's going on. The children watch in silence, having been prompted to watch closely to see if they can work out what the rules of the game are. You may need to show the animation more than once. You can find some Dotty Six grids here as a Word or a pdf file for recording the results of the game.

Take suggestions about what the rules may be, perhaps recording them centrally once everyone has agreed. They are:

• take turns to throw the dice and put the dots into a box
• you can put your dots anywhere but you can't have more than six dots in any one box
• you have to put all your dots in one box
• you win if you finish the line, row or diagonal of complete boxes
• if you can't go you miss a turn.

When everyone has played a few times, you can change the game:

• by making the total different ($10$, $12$, $15$, $20$)
• by giving different dice (with only even numbers, only odds, dice to $10$ etc)
• by making the grid bigger ($4$ by $4$)

You may also like to read the article Developing the Classroom Culture: Using the Dotty Six Activity as a Springboard for Investigation which suggests focusing on the game in a staff meetingto support the development of classroom culture across the school.

### Key questions

Where will you put your dots? Why?

How do you know where to put your dots?

How many more do you need to win?

### Possible support

Small children can use multilink or counters, or Numicon, on a large grid (available as a Word document or pdf), rather than recording with dots on a small one. They could begin with six counters in each box and take away the number thrown on the dice.

### Possible extension

This is a great game for children to use their creativity and to work at a level at which they feel comfortable. The sophistication of their recording will change with their confidence.

Provide a range of dice including blank ones. They could:

• change the total in each box
• make the winner the first to complete a whole row that adds to a certain total (e.g. $20$)
• change the shape of the grid (triangles rather than squares perhaps)
• use a different sort of number - fractions, decimals, percentages ...
• change the rules completely.
Encourage them to write the rules out for someone else to follow. Perhaps they could submit them to NRICH!