### Worms

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

### Buzzy Bee

Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?

### Fair Exchange

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

# Sweetie Box

##### Age 5 to 11Challenge Level

We were sent lots of different ideas about this challenge, so thank you to everybody who sent a solution in.

Saif from Pierrepont Gamston Primary School in England said:

We know that Bryony has more sweets than Max because if they have the same amount of sweets in each box Bryony would still have the 3 extra sweets on top of her box so she will have more.

Well done Saif - can we say anything about how many more sweets Bryony will have compared to Max?

Owen from Stoke Bishop Primary School in England thought about how many sweets Max and Bryony could have in total:

If it's an even number in the box it is doubled, add 3 gets an odd number. But an odd number doubled is an even number, if you add 3 you also get an odd number. So Max and Bryony have an odd number of sweets total but we don't know if they each have an odd or an even number.

Thank you for those ideas, Owen - it's always interesting to think about whether numbers might be odd or even.

Hugh from Dame Bradbury's in England thought about the numbers of sweets in terms of percentages:

If Max had ten sweets and 100%. Bryony would have 13 sweets and 130%.

Well done Hugh! Think about what would happen if Max had a hundred sweets in his box instead - will the percentages still be 100% and 130%?

Nate from Pierrepont Gamston Primary School represented the number of sweets in a box with algebra:

Bryony will always have three more sweets than Max. If we say the number of sweets inside their boxes is X, then Max will have X and Bryony will have X+3.

Thank you for that idea, Nate. When we don't know one of the numbers in a question, it's sometimes helpful to use a picture or a letter to represent that number.

Some children used estimation to work out how many sweets might be in each box. Sara and Kate from University of Chicago Laboratory Schools in the USA sent in this explanation:

Bryony has 3 more candies than Max because they have the same amount of candies in their boxes and Bryony has 3 extra candies on top.

The box seems to hold about 24 candies because the box is 1 inch tall and 1.5 inches wide (when it appears on-screen), the candies are 1/4 inch by 1/4 inch. Therefore 6 candies can fit across and there can be 4 stacks of 6, and 4 times 6 is 24. This is all assuming that the box only consists of the (type of) candies on top and that they are all the same size.

Max has 24 candies because of the thinking shown above and Bryony has 27 candies because 24 plus 3 is 27.

Thank you for that clear explanation, Sara and Kate. Have a look at the pictures they've used to represent the boxes of sweets. Can you see why they think there might be 24 sweets in each box?

Lots of other children from the University of Chicago Laboratory Schools also sent in their ideas about how to estimate the number of sweets in each box. Emma, Saidie and Ellie noticed that the box is actually 3D, and they pointed out that there might be more layers of sweets behind the front layer. How could this change the number of sweets in Sara and Kate's estimation in the picture above?

If you have any other ideas about how many sweets Max and Bryony might have, we'd love to hear from you. Please email us with your ideas.