OC maths: sharing in a ratio with bar models (8 questions)

Quick Answer

To share an amount in a ratio, draw one equal box for each part, work out what one box is worth by dividing the whole amount by the number of boxes, then count the boxes in the share you want. This page from Braintree Coaching Australia has eight original questions for Year 3–4 children preparing for OC mathematical reasoning, two worked models and the value of one box in every solution. It is free, needs no sign-up, and takes about 25 minutes including review.

What does sharing in a ratio mean?

Sharing in a ratio means one person gets more equal parts than another. If Kai gets 1 part and Lena gets 2 parts, Lena gets twice as much as Kai. The parts are always the same size. Only the number of parts differs.

This is skill practice for Year 3–4 children who are comfortable with equal groups and division facts. It is not a copy of official test items, and we do not claim that a question like these will appear on the real test, or that the topic is taught at a given year level. Check what your child's class has covered before you start. The NSW Department of Education's own OC practice tests are the place to see the real format.

How does a bar model show the shares?

Draw one box for every part. Every box is the same size and holds the same amount. Put the boxes for each person on their own row, then count all the boxes. The whole amount divided by that count is the value of one box.

Each drawing below has a table version and a plain sentence under it, so it can be read without seeing the picture.

Model 1: one box each

Share 12 marbles between Ana and Ben. Ana gets 1 box. Ben gets 2 boxes.

Person	Bar (each ▢ is one box)
Ana	▢
Ben	▢ ▢

Text description of the bar drawing: two rows of equal boxes. Ana's row has 1 box and Ben's row has 2 boxes, so there are 3 boxes in all.

1. Count all the boxes: 1 + 2 = 3 boxes.
2. Find the value of one box: 12 ÷ 3 = 4 marbles in one box.
3. Ana has 1 box, so 4 marbles. Ben has 2 boxes, so 2 × 4 = 8 marbles.
4. Check: 4 + 8 = 12.

Model 2: "for every 2 … there are 3 …"

A bag has 20 counters. For every 2 red counters there are 3 blue counters. Draw 2 boxes for red and 3 boxes for blue.

Colour	Bar (each ▢ is one box)
Red	▢ ▢
Blue	▢ ▢ ▢

Text description of the bar drawing: two rows of equal boxes. The red row has 2 boxes and the blue row has 3 boxes, so there are 5 boxes in all.

1. Count all the boxes: 2 + 3 = 5 boxes.
2. Find the value of one box: 20 ÷ 5 = 4 counters in one box.
3. Red is 2 boxes: 2 × 4 = 8 counters. Blue is 3 boxes: 3 × 4 = 12 counters.
4. Check: 8 + 12 = 20.

The eight questions

Work on paper. Draw the boxes yourself each time, even when a drawing is shown. Questions 1 to 3 show the bars, questions 4 to 6 use the words "for every", and questions 7 and 8 use the a:b form.

Stage 1: the bars are drawn

Question 1. Kai and Lena share 18 stickers. Kai gets 1 box and Lena gets 2 boxes. How many stickers does Lena get?

Person	Bar (each ▢ is one box)
Kai	▢
Lena	▢ ▢

Text description of the bar drawing: two rows of equal boxes. Kai's row has 1 box and Lena's row has 2 boxes, so there are 3 boxes in all and the whole bar is worth 18 stickers.

• A. 9
• B. 12
• C. 6
• D. 21

Question 2. Sam and Tia share 20 cards. Sam gets 2 boxes and Tia gets 3 boxes. How many cards does Tia get?

Person	Bar (each ▢ is one box)
Sam	▢ ▢
Tia	▢ ▢ ▢

Text description of the bar drawing: two rows of equal boxes. Sam's row has 2 boxes and Tia's row has 3 boxes, so there are 5 boxes in all and the whole bar is worth 20 cards.

• A. 8
• B. 10
• C. 4
• D. 12

Question 3. Ann and Ben share 24 beads. Ann gets 1 box and Ben gets 3 boxes. How many beads does Ben get?

Person	Bar (each ▢ is one box)
Ann	▢
Ben	▢ ▢ ▢

Text description of the bar drawing: two rows of equal boxes. Ann's row has 1 box and Ben's row has 3 boxes, so there are 4 boxes in all and the whole bar is worth 24 beads.

• A. 18
• B. 6
• C. 8
• D. 28

Stage 2: "for every … there are …"

Question 4. A bag has 30 counters. For every 2 red counters there are 3 blue counters. How many blue counters are in the bag?

• A. 10
• B. 6
• C. 12
• D. 18

Question 5. A class has 45 children. For every 3 girls there are 2 boys. How many girls are in the class?

• A. 15
• B. 27
• C. 18
• D. 50

Question 6. A pet shop has 36 pets. For every 1 cat there are 3 dogs. How many dogs are in the shop?

• A. 40
• B. 9
• C. 27
• D. 12

Stage 3: the a:b form

Question 7. Zoe and Max share 40 stickers in the ratio 3 : 5. Zoe gets the 3 and Max gets the 5. How many stickers does Max get?

• A. 25
• B. 8
• C. 15
• D. 48

Question 8. Two children share some marbles in the ratio 2 : 5. The larger share is 12 marbles more than the smaller share. How many marbles are there altogether?

• A. 4
• B. 19
• C. 28
• D. 84

How is each one worked with boxes?

Check one question at a time. For each wrong answer, find the option your child chose and read why it is tempting.

Question 1 answer: B, 12

There are 1 + 2 = 3 boxes. One box is 18 ÷ 3 = 6 stickers. Lena has 2 boxes: 2 × 6 = 12. Option A (9) divides 18 by 2, one share instead of all 3 boxes. Option C (6) is the value of one box, not Lena's share. Option D (21) adds the 3 boxes to 18.

Question 2 answer: D, 12

There are 2 + 3 = 5 boxes. One box is 20 ÷ 5 = 4 cards. Tia has 3 boxes: 3 × 4 = 12. Option A (8) is Sam's share, which is the two shares swapped. Option B (10) divides 20 by 2, one share. Option C (4) is the value of one box.

Question 3 answer: A, 18

There are 1 + 3 = 4 boxes. One box is 24 ÷ 4 = 6 beads. Ben has 3 boxes: 3 × 6 = 18. Option B (6) is the value of one box, which is also Ann's share. Option C (8) divides 24 by 3, one share. Option D (28) adds the 4 boxes to 24.

Question 4 answer: D, 18

Draw 2 boxes for red and 3 boxes for blue: 5 boxes. One box is 30 ÷ 5 = 6 counters. Blue is 3 boxes: 3 × 6 = 18. Option A (10) divides 30 by 3, one share. Option B (6) is the value of one box. Option C (12) is the red counters, the shares swapped.

Question 5 answer: B, 27

Draw 3 boxes for girls and 2 boxes for boys: 5 boxes. One box is 45 ÷ 5 = 9 children. Girls are 3 boxes: 3 × 9 = 27. Option A (15) divides 45 by 3, one share. Option C (18) is the boys, the shares swapped. Option D (50) adds the 5 boxes to 45.

Question 6 answer: C, 27

Draw 1 box for cats and 3 boxes for dogs: 4 boxes. One box is 36 ÷ 4 = 9 pets. Dogs are 3 boxes: 3 × 9 = 27. Option A (40) adds the 4 boxes to 36. Option B (9) is the value of one box, which is also the number of cats. Option D (12) divides 36 by 3, one share.

Question 7 answer: A, 25

The ratio 3 : 5 means 3 boxes for Zoe and 5 boxes for Max: 8 boxes. One box is 40 ÷ 8 = 5 stickers. Max has 5 boxes: 5 × 5 = 25. Zoe has 3 × 5 = 15 and 15 + 25 = 40. Option B (8) divides 40 by 5, one share. Option C (15) is Zoe's share, the shares swapped. Option D (48) adds the 8 boxes to 40.

Question 8 answer: C, 28

The ratio 2 : 5 means 2 boxes and 5 boxes. The larger share is 5 − 2 = 3 boxes more than the smaller share, and those 3 boxes are worth 12 marbles. One box is 12 ÷ 3 = 4 marbles. There are 2 + 5 = 7 boxes altogether: 7 × 4 = 28. Check: the shares are 8 and 20, and 20 − 8 = 12. Option A (4) is the value of one box. Option B (19) adds the 7 boxes to 12. Option D (84) multiplies the difference by 7, as if 12 were one box.

What mistakes should we look for?

Tally which kind of error came up. Each one needs a different fix.

Pattern	Seen in	What to practise next
Divided by one share instead of all the boxes	Questions 1, 2, 3, 4, 5, 6, 7	Count every box first and say the total out loud
Gave the value of one box as the answer	Questions 1, 2, 3, 4, 6, 8	Underline what the question asks for before dividing
Swapped the two shares	Questions 2, 4, 5, 7	Label each row with a name before drawing boxes
Added the number of boxes to the amount	Questions 1, 3, 5, 6, 7, 8	Ask "does one box hold the whole amount plus more?"

Can my child draw the bars for a new problem?

Share 30 stickers between two children in the ratio 2 : 3 and draw the bars.

Self-check: there should be 2 boxes in one row and 3 boxes in the other, so 5 boxes in all. One box is 30 ÷ 5 = 6 stickers. The shares are 12 and 18, and 12 + 18 = 30. If your child drew 5 boxes in each row, go back to Model 2.

What should we do after this set?

• If two or more answers showed the same pattern in the table, repeat only those questions tomorrow with new numbers. Do not sit a full test yet.
• If the a:b questions were unfamiliar, leave them for later and practise the "for every" wording instead.
• For mixed OC practice with worked solutions, open the OC practice tests guide.
• For full papers to sit under time, see the OC past papers page.
• The free mock tests need a free classroom account. Create one only when your child is ready for a timed sitting.

Sources and review

Official source: NSW Department of Education, Opportunity Class practice tests, for the real test format. This page makes no claim about which topics appear on the test.

Where the questions came from: all eight questions and both models are original Braintree Coaching Australia material written for this page. None is taken from an official or third-party paper.

Author: James Rush, content writer, Braintree Coaching Australia.

Answer check: draft. A second solver (an AI model, not a teacher) recomputed every answer on 2026-10-15. A named teacher review, including whether ratio notation suits Year 3–4, has not yet been recorded for this set. If you find an error, please tell us.

Last updated: 2026-10-15.