### Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

### Bracelets

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

### Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

# Shapes on the Playground

##### Age 7 to 11Challenge Level

Classmates from Moorfield Junior School, Thomas and Robert , explain their strategy for solving some of the challenges of Shapes on the Playground :

To find the shapes that Sally drew they explain:
"We listed all the numbers that add up to 100 and then starting multiplying them by 4 and 8.
The answer we got gave us the solution, 7 squares and 9 octagons.
We then worked Ben's out the same way.
The answer we got gave us the solution 20 squares, 0 triangles and 0 hexagons!!!"

Why do you think Thomas and Robert multiplied by 4 and 8? Do you agree with their answer for the shapes that Ben drew? The problem told us that, "Ben drew triangles, hexagons and squares".

The pupils from St. Aldhelm's C.E. Combined School agree with the solution for Sally, but for Ben they have some other thoughts. They made tables showing the amount of chalk used for each shape and then by completing the tables they discovered how many of each shape Ben would have drawn if he drew 20 shapes in total.

The answer they arrived at was that Ben drew 10 triangles (30 metres), 5 squares (20 metres) and 5 hexagons (30 metres). This used 8 sticks of chalk, as each stick drew 10 metres, leaving two unused sticks. Well done St. Aldhelm's! Can you recognise your initials? LM, ED, RD, HS, KT, DF, LH, NT, AND DR.

Mel and Katie from Loretto Junior School also worked out that Ben could have drawn these shapes:

• 17 squares, 2 triangles, and 1 hexagon
• 8 squares, 8 triangles and 4 hexagons

Very well done!