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### Number and algebra

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# Pumpkin Pie Problem

$27$ litres of condensed milk

$480$ tablespoons of sugar

$100$ teaspoons of cinnamon

$140$ cups of pumpkin

$2$ eggs

$1 \frac{1}{2}$ teaspoons of cinnamon

$\frac{2}{3}$ of a litre of condensed milk

$15$ tablespoons of sugar

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Age 7 to 11

Challenge Level

Peter, the pumpkin eater, wanted to make two pies for a party. His mother, a professional pie maker, had a recipe for him to use. However, she always made $80$ pies at a time. She used:

$27$ litres of condensed milk

$480$ tablespoons of sugar

$100$ teaspoons of cinnamon

$140$ cups of pumpkin

Peter looked in the cupboard and found:

$4$ cups of pumpkin$2$ eggs

$1 \frac{1}{2}$ teaspoons of cinnamon

$\frac{2}{3}$ of a litre of condensed milk

$15$ tablespoons of sugar

Did Peter have enough ingredients to make two pumpkin pies for the party or did he need to buy more?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?