The bar can be a valuable representation to enable children to represent problems in such a way that the mathematical structure is exposed.

This enables pupils to ‘see’ the problem clearly and to then recognise the strategy they need to solve the problem. The appendix contains sets of problems for each key stage for you to try with the pupils you work with.

Appendix

These problems have been tried and tested in a school for the year groups specified; however you may wish to use them more flexibly for different aged children than that specified.

Year 1 Problems

1. Ebony has 5p and Daniel has 8p. How much do they have altogether?

2. A lolly costs 6p. Amrit paid with a 10p coin. How much change does he get?

3. Michael says that 16 + 5 = 21. Is he correct?

4. I think of a number. I subtract 5. The answer is 4. What was my number?

5. How many gloves are there altogether in 6 pairs of gloves?

6. Twelve people are split into two groups. How any are in each group?

7. Mrs Morton puts five 5p coins into her purse. How much is in her purse altogether?

Year 2 Problems

1. Dylan has 37 coloured pencils and he buys 30 more. How many does he have now?

2. Janie has 40 beads. She loses 25 of them. How many does she have left?

3. What is the difference between seventy six and thirty five?

4. I think of a number. I subtract 5. The answer is 4. What was my number?

5. Last week Ellie got £1.00 pocket money. She spent half of it. How much has she got left?

6. A tub contains 24 coins. Saj takes 5 coins. Joss takes 10 coins. How many coins are left in the tub?

7. Amelia writes the calculation below as a multiplication calculation? What might she write?
3 + 3 + 3 + 3 + 3 = 15

8. Mr Siddique shares £18 equally between his three sons. How much does each son get?

9. Charlotte-May had to find a 14 of a number. Her answer was 4. What number did she start with?

10. Danny cuts his pizza into 8 equal slices. He eats 34 of the pizza and gives the rest to his dog, Gruff. How many pieces does Danny eat?

Year 3 Problems

1. There are 334 children at Springfield School and 75 at Holy Trinity Nursery. How many children are there altogether?

2. Gemma collected 293 badges but she gave 45 of them to her friend, Rebecca. How many badges did she have left?

3. Aiden has seven marbles and Harvey has fifteen. They decide to share them equally between them. How many do they get each?

4. Seven people each put five pens into a pot. Carmen then takes out fifteen pens. How many pens are left?

5. If you spend 61p at the corner shop, how much change do you get from £1.00?

6. If five apples cost fifty pence, how much would two apples cost?

7. Emma buys seven markers for 30p each. How much change does she get from £3.00?

8. A bookcase in the library holds 5 shelves with 46 books on each shelf. How many books are there in the bookcase altogether?

9. How many 5p stickers can Alexis buy with his 55p pocket money?

10. Which is the larger amount, one third of £60 or one quarter of £88?

11. A computer game is £24 in the sale. This is one quarter off its original price. How much did it cost before the sale?

Year 4 Problems

1. Martin has saved £6.78 and spends £4.69. How much does he have left?

2. Sally has 40 football cards. She gives 25 of them away. How many does she give away?

3. Sally has 30 football cards. She gives 25 of them to her friend. How many does she have left?

4. 8 children each download 59 songs to play on their iPod. How many songs do they have altogether?

5. Calculate how many fives there are in 85?

6. At the dressmakers, Debbie buys buttons weighing 3 grams each. If she has 81 grams of buttons, how many buttons does she buy?

7. Kelly buys four fifths of the shop’s oranges. If the shop had 20 oranges, how many does she have?

Year 5 Problems

1. Every day for 4 days Helen scored 7.5 in a test. On the fifth day she scored 8. What was her total score?

2. I cut 60 cm from 3.3m of string and shared the rest between 3 friends. How much string did they get each?

3. How many jugs with a capacity of 250ml could you fill with 10 litres of water?

4. All the children in the school are going on a residential trip to the outdoor activity centre. They will be divided into 6 equal groups If there are 246 children in the school how many will be in each group?

5. Robert calculated 25% of 600. What answer does he get?

6. Sam calculated 40% of 120. What answer does he get?

7. Rita worked out that 16 of a number was 12. What was the number she started with?

Year 6 Problems

1. Three quarters of a number is 54. What is the number?

2. Which is more; 59 of 252 or 47 of 238?

3. There are 36 packets of biscuits. One half are chocolate, a ninth are digestive and a third are wafer biscuits. The rest are ginger nuts. How many biscuits are ginger nuts?

4. There is 20% off in a sale. How much would a track suit cost, if the normal price was £44.50?

5. There is 20% off in a sale. The reduced price of the jeans is £36. What was the original price?

6. At a dance there are 4 girls to every 3 boys. There are 63 children altogether? How many girls are there?

7. Seven in every nine packets of crisps in a box are salt and vinegar. The rest are plain. There are 63 packets of salt and vinegar crisps. How many packets of plain crisps are there?

Key Stage 3 Problems

1. Ralph posts 40 letters, some of which are first class, and some of which are second class.
He posts four times as many second class letters as first.
How many of each class of letter does he post? (This question appeared on a GCSE higher tier paper.)

2. A computer game was reduced in a sale by 20% and it now costs £55 What was the original cost?

3. A computer game was reduced in a sale by 30% and it now costs £77. What was the original cost?

4. Sally had a bag of marbles. She gave one-third of them to Rebecca, and then one quarter of the remaining marbles to John. Sally then had 24 marbles left in the bag. How many marbles were in the bag to start with?

5. Peter is playing Space Explorer on his computer. He finished 13 of the levels last week and 25 of the remaining levels this week. He has 12 more levels to complete. How many levels does Space Explorer have?

6. Sam bakes a variety of biscuits. 13 are peanut, 12 are raisin, the remaining 12 were oat. How many biscuits are baked?

7. Tom spent 30% of his pocket money and put away 45% into his savings. He was left with £2.50. How much pocket money did he receive?

8. Two numbers are in the ratio 4:5. They both sum to 135. Identify both numbers.

9. Two numbers are in the ratio 6:7. They both sum to 169. Identify both numbers.

10. A herbal skin treatment uses yoghurt and honey in the ratio 5 : 3. How much yoghurt is needed to mix with 130 g of yoghurt?

27 June 2014 12:45 I have always been an advocate of "draw it" to make sense of problems and we use the FDP R % P approaches. Good to see you spreading the word.

I do have reservations about the first +/- image with the total amount bar over the two parts below. Tried it out with some KS2 support groups and they found it confusing as opposed to just a bar split into 2 parts. Any thoughts? Experience of using it with ks1?

15 May 2014 14:28 I have been increasingly using these ideas with my post-16 resit GCSE / Functional Maths students, since introduced to them by Fiona Allen.

Extremely useful, especially for my very quick thinking Yr 6 children.