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.

Build a model of the small bag. The template below might help you think about the pieces needed.
The four unnamed sections are the sides.
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.

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?

If you have a bag of unpopped corn, it will help you with the next part of this problem. You must have an adult help if you pop the corn.

Let's try to find out about the popcorn that each bag holds.

Fill the small bag with dry popcorn and weigh the contents.
Keep a record of this amount.

How many times can the bag be filled with the dry corn that you have?

What weight of popcorn do you think will fill the two larger bags?

You could always fill the bags to check your estimates.

Can you do this from the bag of popcorn that you are using?

But what if we use popped corn to fill the small bag ....

You could use ready popped corn. Have an adult help you if you pop dry corn. While you are waiting to heat the corn, try to discover what causes corn to pop.

What is weight of a small bag of popped corn?

Can you find out how many times heavier he unpopped corn is?

How many small bags could you fill with the popped corn?

I wonder if you can fill the two other sized bags with the corn that you have popped?

How many times more popcorn do they hold than the small bag?

Could you fill the medium sized bag more than once? How many times?

What about the large bag, would you be able to fill that more than once?

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 it hold more or less than the bag of popcorn.

Perhaps you could find out?