Using coins. Part one: Gobstopper

This week we will be focusing on a couple of problems using coins.

Money is a great way to allow your child to develop a deeper understanding of the number system up to 10 and also gives them some practical skills that will support shopping.

It may be helpful with this problem to have a collection of real or pretend 1p, 2p and 5p coins for your child to use as prompts. In order to protect your family from the coronavirus, you should wash them first with hot soapy water and a disinfectant if they have recently been in use at a shop. Children should be encouraged to touch and feel the coins. Look at the difference between the two sides of the same coin. Look at the relative size of the coins – ask some fundamental questions such as:

Why is a 2p coin bigger than a 5p coin? Is the 2p coin worth more than a 5p coin? Why is the 5p coin not 5 times the size of the 1p coin? What is the difference between a silver and a copper coin?

Setting a play shop can help children look at some common misconceptions about money

To deepen understanding about coins, it is fun to set up a play shop in your home. You can put anything into your ‘shop’ that your child values: toys, food, decorations, cutlery, plates - even jewelry.

Your child may be unsure of the value of the different coins. It is useful to make piles of coins with equal values and set up a play shop at home. The easiest coin to start playing with is the 1p as children are confident working in units of 1.

Many children believe that five 1p coins are worth a lot more than one 5p coin, so it is fun to make a pile of 1p coins and swap them for the same value in 5p coins.

Using 2p and 5p coins gives your child a good chance to count in 2s and 5s and is the start of their thinking about number in terms of multiplication rather than addition.

In this problem your child is being asked to think about 3 things at once:

How many different ways can they create 6? What coins do we have in the English coin system? Creating a systematic way to record their answers to this problem is an important part of

developing as a mathematician. This is because by using a systematic approach a child learns to spot when they have used all possible combinations and have not either missed out a solution or doubled up. This challenge also gives your child the chance to think in detail about how to present their answers – could they use a table to record?

At the outset of working together:

We want to encourage your child to develop their own recording system. Exploring the difference between having the 6 at the start of the written number sentence or at the end would add to the richness of the discussion you have together.

Either 6p = 1p + 1p + 1p + 1p + 1p + 1p

Or 1p + 1p + 1p + 1p + 1p + 1p = 6p

Possible questions to support your child in the trickier areas

1) Are these two solutions the same or different?

5p + 1p = 6p

1p + 5p = 6p

2) We already know that 3 + 3 = 6 – but would this work in this problem? Why not?

3) You’ve given me 8 different ways to make 6p but the question says there are only 5. Which ones do you need to remove from your solutions? Why do these ones need to be removed?

4) How do you know that you have all the possible ways to pay 6p?

To create a deeper challenge:

5) If we had a 3p or a 4p coin would it mean you had more ways to make 6p?

6) Why do you think we don’t have a 3p or a 4p?

7) Can you estimate how many more ways there would be if the gobstopper cost 7p?

8) How do you know you are correct about the number of different ways for 7p?

9) Is there a difference between the number of ways to make 7p because it is a bigger number or because it is an odd number?

10) What about if the gobstopper cost 8p?