OC maths: fractions of a quantity with bar models

Quick Answer

To find a fraction of an amount, draw a bar, cut it into equal parts named by the bottom number, and work out what one part is worth first. This page from Braintree Coaching Australia has ten original multi-step problems solved that way, including three that give you a part and ask for the whole. It is free and needs no sign-up. Allow about 25 minutes, including the answers.

Who is this set for?

This set suits a Year 3 or Year 4 child who can name simple fractions such as 1/2, 1/4 and 3/4 and can divide by 2 to 8 with whole-number answers. It is skill practice for mathematical reasoning. It is not a copy of official test items, and we do not say that a question like these will appear on the real test.

The NSW Department of Education describes the Opportunity Class Placement Test as computer-based, with three multiple-choice sections: Reading, Mathematical Reasoning and Thinking Skills. Calculators are not permitted, so every problem here is meant to be worked on paper. The Department's own OC practice tests show the real format. Our problems have four options each so that each wrong option can be tied to one mistake.

If your child is not yet sure where a fraction sits, start with OC fractions on a number line and come back to this set afterwards.

How does a bar model show a fraction of an amount?

In every bar on this page, the whole amount is one long bar. The bottom number of the fraction says how many equal boxes the bar has. The top number says how many of those boxes are shaded. The number written in each box is what one box is worth. Every bar has a one-line text reading above it, so it can be followed without seeing the picture.

Model 1: a fraction of an amount

A bag has 20 beads. 3/5 of them are blue. How many are blue?

1. The bottom number is 5, so draw 5 equal boxes for the 20 beads.
2. One box is 20 ÷ 5 = 4 beads.
3. The top number is 3, so shade 3 boxes: 3 × 4 = 12 beads.

The question asked for a part of the 20, so the answer (12) is smaller than 20.

Model 2: the whole from a part

6 is 2/3 of a number. What is the number?

1. The bottom number is 3, so the bar has 3 equal boxes.
2. The top number is 2, so the 2 shaded boxes together are worth 6.
3. One box is 6 ÷ 2 = 3.
4. The whole bar is 3 boxes: 3 × 3 = 9.

The question asked for the whole, so the answer (9) is bigger than the given 6. The given number goes in the shaded boxes, not in the whole bar.

The questions

Work on paper without a calculator. Draw the bar before you calculate, even when you think you can see the answer. The ten questions are in four groups: three on a fraction of an amount (1–3), three on finding the whole (4–6), two where a second fraction is taken from what is left (7–8) and two that compare fractions of different wholes (9–10).

Question 1. Mei has 24 stickers. She gives 3/4 of them to her class. How many stickers does she give away?

• A. 6
• B. 8
• C. 18
• D. 21

Question 2. A box holds 35 pencils. 2/5 of them are red. How many are red?

• A. 7
• B. 14
• C. 21
• D. 70

Question 3. A path is 30 m long. Tom has painted 5/6 of it. How many metres has he painted?

• A. 5
• B. 6
• C. 35
• D. 25

Question 4. 12 is 3/4 of a ribbon. How long is the whole ribbon?

• A. 16
• B. 4
• C. 9
• D. 12

Question 5. 8 is 2/5 of the marbles in a bag. How many marbles are in the bag?

• A. 4
• B. 12
• C. 20
• D. 40

Question 6. 9 is 3/8 of the stickers in a book. How many stickers are in the book?

• A. 3
• B. 24
• C. 15
• D. 27

Question 7. Mia has 40 stickers. She gives 1/4 of them to her brother. She uses 2/5 of the stickers she has left on a card. How many stickers does she use on the card?

• A. 16
• B. 12
• C. 10
• D. 18

Question 8. A book has 48 pages. Sam reads 1/3 of it on Monday. On Tuesday he reads 3/8 of the pages he had left. How many pages are still unread after Tuesday?

• A. 12
• B. 14
• C. 20
• D. 32

Question 9. Which is more, 1/2 of 18 or 1/3 of 30, and by how many?

• A. 1/2 of 18, by 1
• B. They are equal
• C. 1/3 of 30, by 3
• D. 1/3 of 30, by 1

Question 10. Which is more, 3/5 of 40 or 5/8 of 32, and by how many?

• A. 3/5 of 40, by 24
• B. 5/8 of 32, by 4
• C. 3/5 of 40, by 4
• D. 5/8 of 32, by 20

Answers and bar models

Check one question at a time. Each answer says whether the question wanted the part or the whole, then shows the bar. For a wrong answer, find the option your child chose and read the reason it is tempting. Questions 7 and 8 need two bars, because the second fraction is taken from what is left, not from the start. Questions 9 and 10 show one bar for each amount.

Question 1 answer: C, 18

This asks for a part. Cut the 24 into 4 equal boxes of 6, then take 3 boxes: 3 × 6 = 18. Option A (6) stops at one box. Option B (8) divides by the top number, 24 ÷ 3. Option D (21) takes 3 away from 24 instead of finding 3 boxes.

Question 2 answer: B, 14

This asks for a part. Five equal boxes of 7, and 2 of them are red: 2 × 7 = 14. Option A (7) stops at one box. Option C (21) is the 3 boxes that are not red. Option D (70) multiplies by the top number, 35 × 2.

Question 3 answer: D, 25

This asks for a part. Six equal boxes of 5, and 5 of them are painted: 5 × 5 = 25. Option A (5) stops at one box. Option B (6) divides by the top number, 30 ÷ 5. Option C (35) adds one box to the whole.

Question 4 answer: A, 16

This asks for the whole. The 3 shaded boxes hold 12 together, so one box is 12 ÷ 3 = 4. The whole bar has 4 boxes: 4 × 4 = 16. Option B (4) is one box. Option C (9) takes 3/4 of 12, which treats the given 12 as the whole. Option D (12) gives the part back.

Question 5 answer: C, 20

This asks for the whole. Two boxes hold 8, so one box is 4. The whole bar has 5 boxes: 5 × 4 = 20. Option A (4) is one box. Option B (12) is the 3 unshaded boxes, the other part. Option D (40) multiplies 8 by the bottom number.

Question 6 answer: B, 24

This asks for the whole. Three boxes hold 9, so one box is 3. The whole bar has 8 boxes: 8 × 3 = 24. Option A (3) is one box. Option C (15) is the 5 unshaded boxes, the other part. Option D (27) multiplies 9 by the top number.

Question 7 answer: B, 12

This asks for a part of what is left. Bar 1: 40 in 4 boxes of 10, so she gives away 10 and has 30 left. Bar 2 is a new bar for the 30: 5 boxes of 6, and 2 of them is 12. Option A (16) takes 2/5 of the original 40. Option C (10) is the first part, not the second. Option D (18) is the 3 boxes of the 30 that she does not use.

Question 8 answer: C, 20

This asks for a part: the pages still unread. Bar 1: 48 in 3 boxes of 16, so 16 are read and 32 are left. Bar 2 is a new bar for the 32: 8 boxes of 4, so Tuesday is 3 × 4 = 12 pages. 32 − 12 = 20. Option A (12) stops at Tuesday's pages. Option B (14) takes 3/8 of the original 48 (18 pages) instead of 3/8 of the 32 left, so it removes 16 and 18 and leaves 14. Option D (32) forgets Tuesday.

Question 9 answer: D, 1/3 of 30, by 1

Both amounts are parts, of different wholes. 1/2 of 18 is 9 (2 boxes of 9). 1/3 of 30 is 10 (3 boxes of 10). So 1/3 of 30 is more, by 1. Option A (1/2 of 18, by 1) assumes the bigger fraction gives the bigger amount. Option B (equal) comes from comparing the fractions and ignoring the wholes. Option C (by 3) uses the 3 from the bottom number.

Question 10 answer: C, 3/5 of 40, by 4

Both amounts are parts, of different wholes. 3/5 of 40 is 24 (5 boxes of 8, take 3). 5/8 of 32 is 20 (8 boxes of 4, take 5). So 3/5 of 40 is more, by 4. Option A (by 24) gives one amount instead of the difference. Option B (5/8 of 32, by 4) picks the bigger fraction, but its whole is smaller. Option D (by 20) gives the smaller amount, not the difference.

Is the question asking for the part or the whole?

Before drawing, ask one question: is the number I am given the whole bar, or some of the boxes?

The question says	The given number is	The answer is	Seen in
"3/4 of 24"	the whole	a part, so smaller	Questions 1, 2, 3
"12 is 3/4 of a ribbon"	a part	the whole, so bigger	Questions 4, 5, 6
"of what is left"	the new whole	a part of the left-over	Questions 7, 8
"which is more, … of … or … of …"	two different wholes	two parts to compare	Questions 9, 10

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
Took the second fraction from the original amount, not from what was left	Questions 7, 8	Draw a new bar for the amount that is left before taking the second fraction
Divided by the top number instead of the bottom number	Questions 1, 2, 3	Say "the bottom number names the boxes" and count the boxes first
Gave the part when the whole was asked, or the whole when the part was asked	Questions 4, 5, 6, 10	Write "part" or "whole" beside the question before drawing
Chose the bigger fraction without checking its whole	Questions 9, 10	Work out both amounts, then compare

Can my child draw the bar for a new problem?

Do not calculate yet. For this problem, draw the bar or bars first:

A class has 36 pencils. 1/3 of them are in a box and 3/4 of the pencils that are not in the box are in a tin. How many pencils are in the tin?

Self-check: the first bar should have 3 boxes (12 each), with 1 shaded. The second bar is a new bar for the 24 that are not in the box: 4 boxes of 6, with 3 shaded. The answer is 18. If you took 3/4 of 36, go back to Questions 7 and 8.

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.
• For mixed OC practice with worked solutions, open the OC practice tests guide.
• For official sample material, see the OC past papers page, which also explains what the Department does and does not release.
• The free mock tests need a free classroom account. Create one only when your child is ready for a timed sitting.
• If you want a structured set of full OC tests after that, see what the OC course includes and check it matches your child's entry year before buying.

Sources and review

Official source (checked 2026-09-09, cache row no-calculator-any-section): NSW Department of Education, Opportunity Class practice tests: the test is computer-based, has three multiple-choice sections (Reading, Mathematical Reasoning, Thinking Skills) and does not allow calculators.

Where the questions came from: all ten questions and both models are original Braintree Coaching Australia material written for this page. None is taken from an official or third-party paper. Bar models are a method used on this page; the test does not require them.

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

Answer check: every answer was solved by hand, without a calculator, and each bar was counted against its denominator. A second solve on 2026-10-15 matched every answer, but that solver had seen the key, so it does not count as a blind solve. A blind solve and a named teacher review have not yet been recorded for this set. If you find an error, please tell us.

Last updated: 2026-10-15.