Cubes

How many faces can you see when you arrange these three cubes in different ways?

Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Balance of Halves

Age 7 to 11 Challenge Level:
We've had one way of doing it using a weight on the $\frac{1}{2}$ peg. How could you balance 7 using $1\frac{1}{2}$? Can you carry on going along the balance like this trying the "half numbers" in turn?

How will you make a note of what you have done?

How will you know that you have got all the different ways?