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### Number and algebra

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# Double Your Popcorn, Double Your Pleasure

**Use paper that is 20cm by 30cm and sticky tape. Don't forget a ruler to draw the lines. Striped paper is a big help to you for measuring and for cutting straight.**

Aimee thought that was a bargain! "We only need one medium sized bag and we can all share that", she said.**What was Aimee thinking?**

Plan this out first to make sure you have enough paper for your bag.

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### The Big Cheese

### Making Boxes

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Age 7 to 11

Challenge Level

I went to the cinema with some friends last week and we decided to buy some bags of popcorn for during the movie.

My friend, Aimee, asked about the prices.

"Three for the small, five for the medium size and the large size is seven", the popcorn server replied quickly.

"Does the medium bag have twice as much in as the small size?" Aimee asked her. "Of course it does!" said the server, "The bag is double the size. See, it's taller, it's wider and it's deeper."

We estimated that the size of the small bag was 20cm by 10cm by 5cm.

I wonder if you can figure out which size belongs to which side.

You could start by building a model of the small bag.

Aimee thought that was a bargain! "We only need one medium sized bag and we can all share that", she said.

You could construct a model of the medium sized bag to help you explain.

Plan this out first to make sure you have enough paper for your bag.

We wondered what size the large bag would be. The popcorn server told us, "Why, the large size is double the size of the medium bag, of course".

"Do you mean each side is two times bigger?" asked Aimee.

"Naturally!" said the server.

Do you think she is correct?

How big would the large size bag be?

If the small bag contains one serving of popcorn, how many serving would the large bag contain?

Do you think the popcorn server was correct when she said that each bag was double the smaller size?

What do you think she should have said to better explain?

I wonder if a drum container that was 20 cm high and 10 cm across the base (the diameter) would hold more or less than the bag of popcorn.

Perhaps you could find out?

This problem is also available in French: Double Ton Popcorn, Augmente Ton Plaisir!

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?