Wearing a hole in your pocket
Imagine a world where we only had 1p coins. In order to be able to make every amount from 1p to 10p, we'd have to carry 10 coins in our pockets...
To lighten the load, we could choose to have coins of two different denominations.
Charlie wants to have 1p and 2p coins.
Alison would prefer 1p and 4p coins.
What is the minimum number of coins each person would need to carry to make sure they can make every amount from 1p to 10p?
Click below to check your answers:
** image of bags with:
1p, 1p, 2p, 2p, 2p, 2p (6coins)
1p, 2p, 2p, 2p, 2p, 2p (6coins)
1p, 1p, 1p, 4p, 4p (5 coins)**
Try some other coin values and work out the minimum number of coins that would be needed to make every amount from 1p to 10p.
Which coin denominations would you choose so that you can carry as few coins as possible?
What other interesting mathematical questions can you think of to explore next?
We have thought of some possibilities:
What if you wanted to make all the values from 1p to £2? Or 1p to £3? Or...
Which two denominations would you choose if you wanted to make every value from 1p to Np?
What if you could choose 3 denominations? Or 4? Or...
To lighten the load, we could choose to have coins of two different denominations.
Charlie wants to have 1p and 2p coins.
Alison would prefer 1p and 4p coins.
What is the minimum number of coins each person would need to carry to make sure they can make every amount from 1p to 10p?
Click below to check your answers:
** image of bags with:
1p, 1p, 2p, 2p, 2p, 2p (6coins)
1p, 2p, 2p, 2p, 2p, 2p (6coins)
1p, 1p, 1p, 4p, 4p (5 coins)**
Try some other coin values and work out the minimum number of coins that would be needed to make every amount from 1p to 10p.
Which coin denominations would you choose so that you can carry as few coins as possible?
Imagine you now need to carry coins that will allow you to make all amounts from 1p to £1 ( £1 = 100p).
Which two denominations would you choose so that you can carry as few coins as possible?
Which two denominations would you choose so that you can carry as few coins as possible?
What other interesting mathematical questions can you think of to explore next?
We have thought of some possibilities:
What if you wanted to make all the values from 1p to £2? Or 1p to £3? Or...
Which two denominations would you choose if you wanted to make every value from 1p to Np?
What if you could choose 3 denominations? Or 4? Or...
We'd love you to share the questions you've come up with. Tell us also how you got started and any conclusions you have arrived at.
Send us your thoughts; we'll be publishing a selection.
Send us your thoughts; we'll be publishing a selection.
While out shopping for snacks, Matt has an idea about coins.
He decided to text Emmy about it...
https://www.youtube.com/watch?v=J8VBkeSpXNI&feature=youtu.be&hd=1
Can you answer Matt's question?
Click below to check your answers:
For Matt's currency, you'd need to carry at least 6 coins: (there are two ways to do this)
or
For Emmy's currency, you'd only need 5 coins:
Image
or
Image
For Emmy's currency, you'd only need 5 coins:
Image
Try some other coin values and work out the minimum number of coins that would be needed to make every amount from 1p to 10p.
Which coin denominations would you choose for your own currency so that you can carry as few coins as possible?
Imagine you now need to carry coins that will allow you to make all amounts from 1p to £1 ( £1 = 100p).
Which two denominations would you choose for your own currency so that you can carry as few coins as possible?
Which two denominations would you choose for your own currency so that you can carry as few coins as possible?
What other interesting mathematical questions can you think of to explore next?
Matt and Emmy have thought of some possibilities:
What if you wanted to make all the values from 1p to £2? Or 1p to £3? Or...
Which two denominations would you choose if you wanted to make every value from 1p to Np?
What if you could choose 3 denominations? Or 4? Or...
We'd love you to share the questions you've come up with. Tell us also how you got started and any conclusions you have arrived at.
Send us your thoughts; we'll be publishing a selection.
Send us your thoughts; we'll be publishing a selection.