### Roll These Dice

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

### Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

### Taking a Die for a Walk

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

# Six Ten Total

##### Stage: 2 Challenge Level:

Take sixteen dice - six of one colour and ten of another.
Here we use blue and red.

Warm up: check the total of the faces showing is 84 when the dice are arranged as shown:

To play the Six Ten Total challenge:
• all the blue need to have the same number on the top
• all the red need to have the same number on the top
• there always needs to be six of one colour and ten of the other
• the red dice have to use a different number to the blue
• there is always a difference of two between the numbers on the blue and red dice.

#### THE  MAIN CHALLENGE

What are the possible arrangements when you choose your own numbers for the dice using the rules above?
What is the total for each of these arrangements?
Explain what you notice. What else do you notice?

#### TAKING IT FURTHER

Can you prove any of the things you've noticed from the main challenge are always true?
Instead of having a difference of two between the numbers showing on each face of the blue and the red dice, choose a new difference.

Now, what totals can you find? What do you notice?  Explain what you notice.

#### AND NOW

Can you predict - without having to make them - what numbers need to be on the faces that you can see on the blue and the red dice to make a total of 42?
Are there more ways to make a total of 42?