Money Bags
A Y4 maths group from Cabot Primary School, Bristol (Iman, Andrea-Marie, Sakariya and Aisha) worked on this problem together.
First of all, we found 15 play coins and a painting tray to help us think about the investigation and find a solution to the maths problem.
Secondly, we decided that we definitely needed to have one bag with 1p in it (or we would not be able to pay for something that cost 1p!), so we put 1p in one of the pots.
Then we thought about which numbers could make all of the other prices up to 15p. We realised that if we also had a bag with 2p in it, we could make 2p and 3p (1p + 2p), so we put 2p in our second pot. We tried 3p in the third pot and this gave us more prices:
1p (1p)
2p (2p)
3p (3p)
4p (3p + 1p)
5p (3p + 2p)
6p (3p + 2p + 1p)
...but we couldn’t make 7p.
So we tried again, this time with 4p in the third pot. We could then make all of the prices up to 7p.
1p (1p)
2p (2p)
3p (2p + 1p)
4p (4p)
5p (4p + 1p)
6p (4p + 2p)
7p (4p + 2p + 1p).
We only had one empty pot left, so we put all of the rest of the coins into it – there were 8 of them. We then found that you could make all of the other numbers:
8p (8p)
9p (8p + 1p)
10p (8p+ 2p)
11p (8p + 2p + 1p)
12p (8p + 4p)
13p (8p + 4p + 1p)
14p (8p + 4p + 2p)
15p (8p + 4p + 2p +1p)
So we knew we had found the solution! We tried all the possibilities and didn’t give up because Cabot Primary children are resilient!
PS Our paint tray actually has six pots in it. We can see a pattern building up and are now going to think about how to investigate the maximum number of prices we can make if we use all six pots.