Worked example · Mathematics and Numeracy · Year 3
LNF: Numeracy → Understanding the number system helps us to represent and compare relationships between numbers and quantities → Financial literacy
A secure Year 3 response, annotated so you can see which success criterion each part meets. It is also the answer key. Key figures: order totals Cerys 55p, Osian 80p, Mali £1.05, Dewi £1.35. Change: Rhys 15p, Cerys 45p, Osian 20p, Mali 95p, Dewi 65p. Elin’s order costs £1.10, so she is 10p short. With £1 Gethin can buy 3 Welsh cakes and gets 10p change.
| Least | 1p | 2p | 5p | 10p | 20p | 50p | £1 | £2 | Most |
|---|
(b) The 5p coin is worth more, even though it is smaller.
| Order | Item | Price |
|---|---|---|
| 1st | Apple | 15p |
| 2nd | Cup of lemonade | 25p |
| 3rd | Welsh cake | 30p |
| 4th | Flapjack | 35p |
| 5th | Cupcake | 40p |
| 6th | Slice of bara brith | 45p |
| 7th | Bag of 4 Welsh cakes | £1.10 |
| 8th | Jar of strawberry jam | £1.50 |
| 9th | Whole bara brith loaf | £3.75 |
| Slice of bara brith (45p) | > | Cupcake (40p) |
| Bag of 4 Welsh cakes (£1.10) | < | Jar of strawberry jam (£1.50) |
| Whole bara brith loaf (£3.75) | > | Jar of strawberry jam (£1.50) |
(e) No, Iolo is wrong. The jam is £1.50, which is 150p. The flapjack is 35p. 150p is more than 35p, so the jam costs more. The £ sign means pounds, not pence.
The coins are ordered by value, not by size. Prices in pounds are changed to pence before comparing, so pence and pounds are never mixed up. Evidences criteria 1 and 2.
| Item | Way 1 | Way 2 |
|---|---|---|
| Welsh cake (30p) | 20p + 10p | 10p + 10p + 10p |
| Cup of lemonade (25p) | 20p + 5p | 10p + 10p + 5p |
| Slice of bara brith (45p) | 20p + 20p + 5p | 10p + 10p + 10p + 10p + 5p |
| Bag of 4 Welsh cakes (£1.10) | £1 + 10p | 50p + 50p + 10p |
Way 1 for the bara brith uses fewer coins: 3 coins instead of 5.
Each way adds up exactly to the price. Many other answers are right; check that the coins add up. Evidences criterion 3.
| Customer | Order | Working | Total |
|---|---|---|---|
| Cerys | Welsh cake, cup of lemonade | 30p + 25p = 55p | 55p |
| Osian | Cupcake, apple, cup of lemonade | 40p + 15p = 55p, 55p + 25p = 80p | 80p |
| Mali | Slice of bara brith, 2 Welsh cakes | 45p + 30p + 30p = 105p | £1.05 |
| Dewi | Bag of 4 Welsh cakes, cup of lemonade | 110p + 25p = 135p | £1.35 |
The working is in pence, and totals over 100p are written in pounds with a point: 105p is £1.05, not £1.5. Evidences criterion 4.
(a) Rhys: flapjack 35p, pays 50p.
5p + 10p = 15p. Change = 15p.
(b) Cerys: 55p, pays £1 (100p).
5p + 40p = 45p. Change = 45p.
(c) Osian: 80p, pays £1 (100p).
80p is already a 10, so 1 jump of 20p. Change = 20p.
(d) Mali: £1.05 (105p), pays £2 (200p).
5p + 90p = 95p. Change = 95p.
(e) Dewi: £1.35 (135p), pays £2 (200p).
5p + 60p = 65p. Change = 65p. The pupil jumps to the next 10 first, then to the money paid, and adds the jumps. Evidences criterion 5.
| Change | Coins | Number of coins |
|---|---|---|
| 15p | 10p, 5p | 2 |
| 45p | 20p, 20p, 5p | 3 |
| 20p | 20p | 1 |
| 95p | 50p, 20p, 20p, 5p | 4 |
| 65p | 50p, 10p, 5p | 3 |
Think: Yes, 10p + 10p + 20p + 5p = 45p, so it is the right amount. But Tomos could use 3 coins: 20p, 20p, 5p. The two 10p coins can be swapped for one 20p coin.
The pupil starts with the biggest coin that fits each time and checks that the coins add up to the change. Evidences criterion 6.
(a) 40p + 45p + 25p = 110p = £1.10. £1.10 is more than £1, so Elin does not have enough. She is 10p short. She could swap the bara brith (45p) for a Welsh cake (30p): 40p + 30p + 25p = 95p.
(b) 30p, 60p, 90p. A 4th Welsh cake would make 120p, which is too much. Gethin can buy 3 Welsh cakes for 90p and gets 10p change.
| Item | Price |
|---|---|
| Cup of lemonade | 25p |
| Welsh cake | 30p |
| Flapjack | 35p |
| Total | 90p |
| Change from £1 | 10p |
| Change in the fewest coins | 10p (1 coin) |
The pupil keeps a running total and checks it is not more than £1 before finding the change. Any order of at least 2 items costing £1 or less is right if the total and change are correct. Evidences criteria 4, 5 and 6.
4 single Welsh cakes cost 30p + 30p + 30p + 30p = 120p = £1.20. The bag of 4 costs £1.10. The bag is cheaper and you save 10p.
Seren: 150p + 40p = 190p = £1.90. 190p to 200p is 10p, so her change is 10p.
Aled: two £2 coins make £4 (400p). The loaf is £3.75 (375p). 375p to 380p is 5p, 380p to 400p is 20p, so the change is 25p: 20p and 5p, 2 coins.