Coin Multiplication

A crucial element of being numerate is the ability to find multiples of numbers quickly and easily, and to understand how and why what you have done works. Being able to find more challenging multiples by mathematically manipulating the multiple that you have already found shows further core numeracy skills and understanding. Coin Multiplication is a process that children can be skilfully coached in to ensure that they can ‘see’ the deep relationships between numbers and operations… which allows them to find the correct answers! Click here to learn more about How Big Maths Works.

The foundation for any Coin Multiplication is established by taking a given number (usually a 2d number) and then finding the 1st (1p), 2nd (2p), 5th (5p), 10th (10p), 20th (20p), 50th (50p) and 100th (£1) multiples of that number. If the 200th (£2) multiple is included as well, then that is all of the denomination of coins that we use (and that are typically used in most currencies). Children are shown how all of these multiples can be found simply by:

multiplying by 10,
halving and,
doubling.

Step 1

The first of the 5 steps for Coin Multiplication introduces us to a ‘1, 10 Card’ and shows us how to set it out. The 1^st multiple is the number itself and the 10^th multiple is the number itself, but this time made 10 times bigger.

Step 2

The second step extends the ‘1, 10 card’ idea to produce a ‘1, 2, 5, 10 card’. Start with ‘easy’ numbers that lend themselves to getting the correct answers.

Start as before by using the 1^st multiple to find the 10^th multiple
Find the 2^nd multiple by doubling the 1^st multiple
Find the 5^th multiple by halving the 10^th multiple

Well done! This is a completed ‘1, 2, 5, 10’ Coin card. Keep practicing with a 1, 2, 5, 10 (spaces added) card until you can complete quickly (without having to use their fingers) delete before attempting the next step.

Step 3

Now we extend the same ideas to write out a ‘Full Coin Card’. This includes using:
☛ the 2^nd multiple to find the 20^th multiple,
☛ the 5^th multiple to find the 50^th multiple.

Then using:
☛ the 1^st multiple to find the 100^th multiple,
☛ and the 2^nd to find the 200^th multiple.

Once we have written out all these multiples (1^st, 2^nd, 5^th, 10^th, 20^th, 50^th, 100^th and 200^th) then we have a ‘Full Coin Card’! Congratulations! Now, practise with lots of different starting numbers (mainly using 2 digit whole numbers). The challenge is to be able to write a Full Coin Card like this for any 2 digit number in less than 60 seconds! Remember to always fill in the multiples in this order: 1^st, 10^th, 2^nd, 5^th, 20^th, 50^th, 100^th.

By the way…

Always remember to fill in the multiples in this order:

1^st, 10^th, 2^nd, 5^th, 20^th, 50^th, 100^th, and finally the 200^th multiple if you want to include it.

Step 4

Once you can write out a ‘Full Coin Card’ fluently, try adding 2 of the coin multiples together. For example, you can find the 21^stmultiple by adding the 20^th and 1^st multiples together, or find the 52^nd multiple by adding the 50^th and 2^nd multiples together. Try finding different variations of which multiples you can find, and combing this with different starting numbers.

Step 5

At Step 5 we add 3 different coin multiples together. For example, you can find the 121^st multiple by adding the 100^th, 20^th and 1^st multiples together, or find the 252^nd multiple by adding the 200^th, 50^th and 2^nd multiples together.