The pattern
Units and parts
Cut one amount into equal shares. One number tells you what a share is worth.
Cut one amount into equal slices, and let a stated number fix what one slice is worth. Every other slice is worth the same, because they were cut equal. It is the plainest bar model there is, one whole cut up, with a single number pinning the size of a slice. Nothing is transferred and nothing changes hands.
How to spot it
A single amount is split by a ratio, a fraction or a percentage. One extra number gives you the leftover, the difference, or the value of one share.
Common mistake
Children match the given number to the wrong number of shares, using the whole bar when the number covers only the leftover or the difference between two people's shares.
125 worked solutions
Standard
- A bicycle's price — the percentage increase A bicycle shop increased the price of a bicycle from $650 to $780. What is the percentage increase?
- A sunflower — the percentage increase The height of a sunflower increased from 80 cm to 92 cm over a month. What is the percentage increase?
- add in columns Use a written addition algorithm to calculate 46 + 35.
- add in columns Use a written addition algorithm to calculate 38 + 27.
- add like fractions Calculate 2/7 + 3/7.
- add like fractions Calculate 1/8 + 5/8.
- add several single-digit numbers Calculate 6 + 2 + 7.
- add several single-digit numbers Calculate 3 + 5 + 4.
- add within 100 Calculate 46 + 35 within 100.
- add within 100 Calculate 38 + 27 within 100.
- Alice, Bob and Carol — sharing money in ratio Alice, Bob, and Carol share a sum of money in the ratio 2 : 3 : 7. Carol's share is $168 more than Alice's share. Find the total s…
- Ayesha's book — pages left over the weekend Ayesha read 5/8 of a book over the weekend. She had 51 pages left to read. How many pages does the book have in total?
- Ben, Mei, and Farid share a cash prize in the ratio 3 : 5 : 8. Farid's share is $60 more than Ben's share. Find the total prize money.
- calculate mentally Calculate 63 + 4 mentally.
- calculate mentally Calculate 42 + 5 mentally.
- calculate mentally Calculate 13 + 5 mentally.
- calculate mentally Calculate 8 + 7 mentally.
- calculate mentally Calculate 57 + 30 mentally.
- calculate mentally Calculate 34 + 20 mentally.
- Class trip savings — four classmates Four classmates saved money for a class trip. Liam saved $15 less than Sara. Priya saved twice as much as Sara. Tom saved $9 less …
- compare centimetre lengths Which is longer: 8 cm or 12 cm?
- compare centimetre lengths Which is longer: 15 cm or 9 cm?
- compare like fractions Arrange 3/8 and 7/8 from least to greatest.
- compare like fractions Arrange 2/5 and 4/5 from least to greatest.
- compare numbers Complete 34 __ 43 with < or >.
- compare numbers Complete 57 __ 52 with < or >.
- compare sizes of sets One set has 8 counters and another has 11. Which set has more?
- compare sizes of sets One set has 13 counters and another has 9. Which set has more?
- compare unit fractions Which is greater: 1/4 or 1/8?
- compare unit fractions Which is greater: 1/3 or 1/6?
- Concert tickets — four classes Four classes sold tickets to the school concert. Class 6B sold 10 fewer tickets than Class 6A. Class 6C sold twice as many tickets…
- connect addition with subtraction Use 8 + 6 = 14 to complete 14 − 8 = __.
- connect addition with subtraction Use 7 + 5 = 12 to complete 12 − 7 = __.
- count cents to one dollar A purse contains 85 cents. Write the amount using the cent symbol.
- count cents to one dollar A purse contains 65 cents. Write the amount using the cent symbol.
- count objects There are 12 counters. How many counters are there?
- count objects There are 8 counters. How many counters are there?
- count whole dollars There are 75 one-dollar notes. How many dollars is that?
- count whole dollars There are 42 one-dollar notes. How many dollars is that?
- Cupcakes at four stalls — Stall D's share Four stalls at a charity bake sale sold cupcakes. Stall B sold 6 fewer cupcakes than Stall A. Stall C sold 3 times as many cupcake…
- distinguish a.m. and p.m. Is 8:00 in the morning a.m. or p.m.?
- distinguish a.m. and p.m. Is 7:00 in the evening a.m. or p.m.?
- draw a segment Draw a straight segment 6 cm long.
- draw a segment Draw a straight segment 10 cm long.
- Farmland — coconut, rice and fallow land A farmer owns 40 hectares of land. He plants coconut trees on 25% of the land and rice on 45% of the land. The rest is left fallow…
- Flour stock — cakes first, then bread A baker used 30 kg of flour to bake cakes. This was 2/5 of his total flour stock. After baking the cakes, he used 1/3 of the remai…
- Four boys' money — Peter's share Four boys received a sum of money. Mike received $10 less than Nate. Owen received twice as much money as Nate. Peter received $6 …
- Four volunteers collected recyclable cans for a school drive. Aiden collected 15 fewer cans than Mei. Farah collected 4 times as many cans as Mei. Devi collected 20 fewer cans than Farah. Alto…
- Four workshops used paint to decorate murals for a festival. Workshop P used 6 litres less than Workshop Q. Workshop R used twice as much paint as Workshop Q. Workshop S used 3 litres less th…
- identify tens and ones How many tens and ones are in 57?
- identify tens and ones How many tens and ones are in 34?
- interpret cm A pencil is 8 centimetres long. Write the length using the abbreviation cm.
- interpret cm A pencil is 12 centimetres long. Write the length using the abbreviation cm.
- interpret h and min Write 2 hours 30 minutes using h and min.
- interpret h and min Write 1 hour 45 minutes using h and min.
- interpret operation and equality symbols Complete 8 __ 6 = 14 with + or −.
- interpret operation and equality symbols Complete 9 __ 5 = 14 with + or −.
- Jane's book — two fifths spent Jane spent 2/5 of her money on a book. She had $24 left. How much money did she have at first?
- John's salary — rent, food and savings John's salary is $3,200. He spends 40% on rent, 25% on food, and saves the rest. How much does he save each month?
- Kayaking race — Ben and Farah Ben and Farah took part in a kayaking race. Ben paddled at a constant speed of 24 km/h. Both of them did not change their speed th…
- Laptop price — the percentage increase The price of a laptop increased from $1,200 to $1,380. What is the percentage increase?
- Library books — fiction, non-fiction and reference A library has 1,800 books. 30% of the books are fiction and 45% are non-fiction. The rest are reference books. How many reference …
- Marcus's savings — the new game Marcus spent 3/8 of his savings on a new game. He had $35 left. How much money did he have at first?
- measure a segment The shown segment starts at 0 cm and ends at 8 cm. How long is it?
- measure a segment The shown segment starts at 0 cm and ends at 12 cm. How long is it?
- measure length in centimetres A ribbon measures 8 centimetres. State its measured length.
- measure length in centimetres A ribbon measures 12 centimetres. State its measured length.
- Mrs Kumar's bonus — shopping, charity, savings Mrs Kumar received a bonus of $3,600. She spent 30% of it on shopping and 15% on charity donations, and saved the rest. How much d…
- multiply within 40 Calculate 8 × 5. The answer is within 40.
- multiply within 40 Calculate 6 × 4. The answer is within 40.
- multiply within 40 Write 2 + 2 + 2 + 2 + 2 using the multiplication symbol, then calculate.
- multiply within 40 Write 3 + 3 + 3 + 3 using the multiplication symbol, then calculate.
- Noodle stalls — Uma's bowls Four stalls sold bowls of noodles at a food fair. Rosli's stall sold 8 fewer bowls than Siti's stall. Tarik's stall sold twice as …
- order numbers Arrange 57, 50 and 65 from least to greatest.
- order numbers Arrange 34, 29 and 41 from least to greatest.
- Pie chart — 25% chose Science A pie chart shows that 25% of students chose Science as their favourite subject. If 60 students chose Science, how many students w…
- Priya's renovation budget — paint then tiles Priya spent $24 on paint for her renovation budget. This was 3/10 of her total budget. After buying the paint, she spent 1/4 of th…
- PSLE 2023 — Three paint tins Gopal had 3 identical tins of paint that were filled to the brim. He poured 760 ml out of each tin. The total amount of paint left…
- Raj, Wei Ling, and Siti packed oranges in the ratio 4 : 6 : 11. Siti packed 140 more oranges than Raj. How many oranges did the three of them pack altogether?
- read a clock in five-minute intervals The shown analogue clock is above a school library door. What time does it display?
- read a clock in five-minute intervals The shown analogue clock is in a kitchen. What time does it display?
- read a numeral Write 57 in words.
- read a numeral Write 34 in words.
- read and represent a fraction Read the fraction represented by 3 shaded parts out of 8 equal parts.
- read and represent a fraction Read the fraction represented by 2 shaded parts out of 5 equal parts.
- recognise a fraction of a whole One whole is divided into 8 equal parts and 3 are shaded. What fraction of the whole is shaded?
- recognise a fraction of a whole One whole is divided into 5 equal parts and 2 are shaded. What fraction of the whole is shaded?
- recognise one-hour and half-hour durations How many minutes are in one hour?
- recognise one-hour and half-hour durations How many minutes are in half an hour?
- Rectangle — length to width ratio 5 : 2 The ratio of the length to the width of a rectangle is 5 : 2. The perimeter is 84 cm. Find the area of the rectangle.
- represent a number Represent 57 using tens and ones.
- represent a number Represent 34 using tens and ones.
- Ribbon — cut into three in the ratio 2 : 3 : 5 A ribbon was cut into three pieces in the ratio 2 : 3 : 5. The longest piece was 40 cm. How long was the ribbon?
- Ribbon — wrapping a gift Mei used 2/7 of a ribbon to wrap a gift. She had 45 cm of ribbon left. What was the length of the ribbon at first?
- Roller-skating race — Kai and Mia Kai and Mia took part in a roller-skating race. Kai skated at a constant speed of 18 km/h. Both skaters kept the same speed throug…
- School enrolment — the percentage increase A school's enrollment increased from 240 students to 300 students over one year. What is the percentage increase?
- Sticker collection — four friends Four friends collected stickers over the summer. Ana collected 8 fewer stickers than Ben. Cara collected twice as many stickers as…
- subtract in columns Use a written subtraction algorithm to calculate 85 − 37.
- subtract in columns Use a written subtraction algorithm to calculate 72 − 28.
- subtract like fractions Calculate 7/8 − 3/8.
- subtract like fractions Calculate 6/7 − 2/7.
- subtract within 100 Calculate 85 − 37 within 100.
- subtract within 100 Calculate 72 − 28 within 100.
- Three consecutive even numbers — summing to 162 The sum of three consecutive even numbers is 162. What are the three numbers?
- Three ropes — 3 : 4 : 9 A red rope, a blue rope, and a green rope are cut so their lengths are in the ratio 3 : 4 : 9. The green rope is 30 m longer than …
- understand addition 8 objects are joined with 6 objects. How many altogether?
- understand addition 7 objects are joined with 5 objects. How many altogether?
- understand division 15 objects are shared equally among 5 groups. How many are in each group?
- understand division 12 objects are shared equally among 3 groups. How many are in each group?
- understand division 18 objects are shared equally among 3 groups. How many are in each group?
- understand division 16 objects are shared equally among 4 groups. How many are in each group?
- understand equal-group multiplication There are 5 equal groups of 2. How many altogether?
- understand equal-group multiplication There are 4 equal groups of 3. How many altogether?
- understand subtraction 7 are taken away from 16. How many remain?
- understand subtraction 5 are taken away from 13. How many remain?
- use ordinal words and symbols Write the ordinal word for 8th.
- use ordinal words and symbols Write the ordinal word for 4th.
- Water tank — from three-quarters full to half A tank was 3/4 full. After removing 15 litres, it was 1/2 full. What is the capacity of the tank?
- write a numeral Write “thirty-four” in numerals.
- write a numeral Write “fifty-seven” in numerals.
Challenging
- A bakery bakes two kinds of loaves for its morning batch. ⅜ of the loaves are wholemeal and the rest are white. ⅙ of the wholemeal loaves are raisin loaves. In the whole batch, ¼ of the lo…
- Amusement park Q16 — Amusement park
- Apples and pears — red and green A fruit stall sold apples and pears, each available in red and green varieties. In total, 800 pieces of fruit were sold. There wer…
- PSLE 2024 — Devi eric haziq Devi, Eric and Haziq had a total of $1560 at first. Devi donated 1/4 of her money, Eric donated 2/7 of his money and Haziq donated…
- Two groups on a learning journey — the girls Pupils in a school are put into two groups for a learning journey. ⅖ of the pupils are in Group A and the rest are in Group B. ¼ o…
8 more that use it
Filed under a different pattern, but this one is part of the working.
- Shirt — $85 after a 15% discount Filed under Working backwards
- PSLE 2025 — Zach jacket Filed under Working backwards
- A dress and a handbag — Mei's savings Filed under Branching
- Jacket — sold at a profit Filed under Working backwards
- An antique vase — the cost price Filed under Working backwards
- Ahmad's savings — books, then a game Filed under Branching
- Bicycle shop — sold at a profit Filed under Working backwards
- Wedding cake — sold at a profit Filed under Working backwards
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.