### Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

### Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

### How Big?

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

# Tray Bake

##### Age 11 to 14Challenge Level
Start from the information given for 12 cakes.

12 cakes cost 65p.
For 24 cakes, double the cost is £1.30.
For 36 cakes, the cost of 12 cakes multiplied by 3 is £1.95.
For 6 cakes, half the cost is not 32.5p, since we no longer have half pence in the UK.  The cost is therefore 33p.

For the ingredients:

 Ingredients 12 cakes 24 cakes 36 cakes 6 cakes 1 cake Caster sugar 130g 260g 390g 65g 10.8g Margarine 130g 260g 390g 65g 10.8g Self raising flour 130g 260g 390g 65g 10.8g Eggs 2 4 6 1 1/3 Baking powder (5ml spoons) 1 2 3 1/2 1/12

To scale the recipe for other numbers of cakes which are not a simple multiple of 12 or 6, you will need to find the cost of 1 cake and the amount of ingredients required for 1 cake.  Then multiply by the number of cakes required, rounding your answers sensibly and remembering that eggs come in whole numbers!  (Professional kitchens weigh the eggs, rather than using whole numbers of eggs.)

If you are using the provided arrows, these facts may help you:
• use x2 (doubling) arrows going from 6 cakes to 12 and from 12 cakes to 24
• use divide by 2 or multiply by 1/2 (halving, same thing as division and multiplication are inverse processes,and 1/2 is the inverse of 2) arrows for 12 cakes to 6 or 24 cakes to 12
• use x 1.5 or x3/2 or half as much again cards going from 24 cakes to 36
• use divide by 1.5 or x2/3 cards going from 36 cards to 24