Conjecturing and generalising

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Have a look at this table of how children travel to school. How does it compare with children in your class?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.