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Pizza Portions

My friends and I love pizza. Can you help us share these pizzas equally?


How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?


Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Once Upon a Time

Age 7 to 11
Challenge Level

Once upon a time there were three bears. There was Father Bear, Mother Bear and Baby Bear. But you knew that!

the three bears

Mother Bear was three quarters the size of Father Bear.
Baby Bear was half the size of Father Bear.
And all the things they had were in the same proportions.
This means that Father Bear's chair was twice as big as Baby Bear's chair and Mother Bear's chair came exactly in between.
the bears' chairs

Mother Bear's chair was $60$ cm high. How high were the other two chairs?
The diameter across the top of each Bear's porridge bowl was three times the height.

bears' porridge bowls

Father Bear's bowl was $24$ cm across. What was the diameter of Mother Bear's bowl and the height of Baby Bear's bowl?
A little girl lived with the three Bears. (Her name was Goldilocks - but you knew that too!)
Goldilocks had all the same things as the bears, but hers were all sorts of odd sizes, some nearly as big as Father Bear's, and some almost as small as Baby Bear's!

the bears' and Goldilock's beds

Who did all these beds belong to? You might need to do some measuring!
Father Bear's spoon was $30$ cm long. Goldilocks' spoon was five sixths of that.

the bears' and Goldilock's spoons

What proportion of Goldilocks' spoon was Baby Bear's spoon?