Year 3 numeracy: ten problems solved three ways

Quick Answer

A Year 3 child understands a number problem when they can show it with objects, draw it and write it as a number sentence. This page from Braintree Coaching Australia has ten original problems, each solved all three ways, and six questions you can ask to hear your child's thinking without giving the answer.

Who is this for?

This page is for parents of children in Year 3, in any state. It is a companion to our Year 3 NAPLAN practice set and does not replace it. It is not a practice test.

All ten problems are original work by Braintree Coaching Australia. They are not NAPLAN questions, and we do not say what NAPLAN result any problem would match. We do not claim that doing them raises a result.

For the real test, ACARA's published scheduling gives Year 3 numeracy 45 minutes, and the Year 3 tests other than writing are taken online. For how the online test adapts to the answers a child gives, read ACARA's page on tailored tests. Writing is the only Year 3 test taken on paper.

Why ask a Year 3 child to explain?

Some wrong answers come from a rule that has been remembered and not understood. "Take the small digit from the big digit" works for 48 − 5 and gives the wrong answer for 41 − 17. "How many more" sounds like adding, and "half" sounds as if it only works on even numbers.

When a child shows what they did with counters, a drawing and a number sentence, the mistake is easy to see and easy to talk about. When they cannot, you have learned something just as useful.

ACARA says the best preparation for NAPLAN is teaching and learning the curriculum. That is why this page asks you to talk through a few problems rather than work through many. Do one or two in a sitting, then stop. The number of problems is our suggestion, not an ACARA figure. Our Year 3 preparation guide and our guide to free NAPLAN practice resources set out how much is enough.

The ten tasks

Each task below is solved three ways. The three ways are our teaching approach, not a NAPLAN requirement.

• Counters: objects the child can hold and move. Coins, buttons, dried pasta or paper clips all work.
• Picture: a drawing that keeps the steps in order. A number line is a straight line marked with numbers that you jump along. A bar is a strip drawn as long as the number it stands for.
• Number sentence: the same steps written with numbers and signs, such as 38 + 7 = 45.

Try the problem with your child before you read the methods. Let them choose which way to start.

Three ways to solve each one

Task 1. Adding across a ten

Sam has 38 stickers. A friend gives him 7 more. How many stickers does Sam have now?

Answer: 45.

• Counters: Count out 38 counters. Count out 7 more in a separate pile. Move 2 from the small pile to the big one to make 40, then count the 5 left over: 45.
• Picture: Draw a number line. Mark 38, jump 2 to 40, then jump 5 to 45.
• Number sentence: 38 + 2 + 5 = 45. The 7 was split into 2 and 5.

Task 2. Taking away across a ten

There are 52 books on a shelf. 6 are borrowed. How many are left?

Answer: 46.

• Counters: Show 52 as 5 bundles of ten and 2 single counters. Take away the 2 singles. Open one bundle and take away 4 more. Count what remains: 46.
• Picture: On a number line, start at 52, jump back 2 to 50, then jump back 4 to 46.
• Number sentence: 52 − 2 − 4 = 46. The 6 was split into 2 and 4.

Task 3. "How many more?"

Ben has 17 shells. Lia has 25 shells. How many more shells does Lia have than Ben?

Answer: 8.

• Counters: Make two rows, one of 17 counters and one of 25, lined up in pairs. The counters in the longer row with no partner are the extra ones. Count them: 8.
• Picture: Draw two bars, one for 17 and a longer one for 25. Mark the extra length on the longer bar and label it with a question mark.
• Number sentence: 17 + ? = 25, or 25 − 17 = ?. Either gives 8.

Notice that the words "how many more" do not mean the child should add 17 and 25.

Task 4. Sharing equally

20 grapes are shared equally among 4 children. How many grapes does each child get?

Answer: 5.

• Counters: Draw 4 circles for plates. Deal 20 counters one at a time, round and round. Count one plate: 5.
• Picture: Draw 4 groups with the same number of dots in each, until 20 dots are drawn.
• Number sentence: 20 ÷ 4 = 5, which is the same fact as 4 × 5 = 20.

Task 5. Half of an odd number

Nina has 9 cookies. She shares them fairly between herself and her brother, cutting one cookie in half if she needs to. How much does each of them get?

Answer: 4 and a half cookies each.

• Counters: Deal 9 counters to two piles, one at a time. Each pile gets 4 and one counter is left. Use a paper cookie or a circle drawn on paper for the last one, cut it in half and give one half to each pile.
• Picture: Draw a bar made of 9 equal boxes. Split it into two equal parts. The ninth box has to be cut down the middle.
• Number sentence: 9 ÷ 2 = 4 and a half. Half of 8 is 4, and half of 1 is a half.

Task 6. Money and change

Mia buys a pencil for 65 cents and a ruler for 30 cents. She pays with a one-dollar coin. How much change does she get?

Answer: 5 cents.

• Counters: Use real or paper coins. Make 65 cents from a 50 cent, a 10 cent and a 5 cent coin. Add a 20 cent and a 10 cent coin for the ruler. Together that is 95 cents. Count up from 95 to 100 to find the change.
• Picture: Draw a number line from 0 to 100 with a mark at 95. The gap between 95 and 100 is the change.
• Number sentence: 65 + 30 = 95, then 100 − 95 = 5.

Task 7. Time

A film starts at 3:15 and goes for 45 minutes. What time does it finish?

Answer: 4:00.

• Counters: Use a paper clock or a clock with moving hands. Start the minute hand at 15 minutes past 3 and move it forward 45 minutes, in steps of 15 if that helps.
• Picture: Draw a number line with 3:15, 3:30 and 4:00. The first jump is 15 minutes (3:15 to 3:30) and the second is 30 minutes (3:30 to 4:00), which together make 45.
• Number sentence: 15 + 30 = 45. The film starts at 3:15, so 15 minutes gets to 3:30 and 30 more gets to 4:00.

Task 8. Length

A ribbon is 1 metre long. Mum cuts off 35 centimetres. How much ribbon is left?

Answer: 65 centimetres.

• Counters: Use a strip of paper or a measuring tape that shows 100 centimetres. Fold or mark off 35 centimetres and measure what remains.
• Picture: Draw a long bar and label it 100. Shade 35 at one end and label the rest with a question mark.
• Number sentence: 100 − 35 = 65. The child needs to know that 1 metre is 100 centimetres.

Task 9. Taking away across a ten, where a rule goes wrong

A box holds 41 pencils. 17 are given out. How many are left?

Answer: 24.

• Counters: Show 41 as 4 bundles of ten and 1 single. There are not enough singles to take 7, so open one bundle. That gives 3 bundles and 11 singles. Take away 1 bundle and 7 singles. 2 bundles and 4 singles are left.
• Picture: On a number line, start at 41, jump back 10 to 31, then jump back 7 to 24.
• Number sentence: 41 − 10 − 7 = 24.

A child who subtracts the smaller digit from the larger one in each column gets 36. Ask them to check with the counters.

Task 10. Equal groups

There are 3 bags with 4 apples in each bag. How many apples are there altogether?

Answer: 12.

• Counters: Make 3 piles of 4 counters. Count them all: 12.
• Picture: Draw 3 rows of 4 dots, or a number line with three jumps of 4: 4, 8, 12.
• Number sentence: 4 + 4 + 4 = 12, which is also 3 × 4 = 12.

"Altogether" does not mean the child should add 3 and 4.

What can I ask without giving the answer?

Use these six questions in any order. None of them contains an answer, and none needs you to know it before you start.

1. "What is the problem asking you to find?"
2. "Can you show me with something you can hold?"
3. "How did you start, and why that way?"
4. "Can you draw it so I can see each step?"
5. "How could you check your answer a different way?"
6. "Does your answer make sense for this story?"

Wait for the whole answer before you say anything. If your child is stuck, ask question 2 again with different objects, rather than showing them how.

What should we try next?

Give your child a number sentence and ask them to make up a story for it. For example, offer 25 − 17 and let them invent the people and things. Then ask them to solve their own story with counters, and again with a drawing, and check that both agree with the sentence.

Making up a problem is harder than solving one. If the story does not fit the sentence, try the six questions above on the story, not on the child.

For worked Year 3 numbers across reading, language and numeracy, return to the Year 3 practice set. For the test itself, see the Year 3 practice tests guide.

Sources and review

About the problems: all ten tasks, their three methods and the six questions are Braintree Coaching Australia's own teaching material. They are not NAPLAN items.

About the facts: the numeracy session length and the online format are taken from ACARA's NAPLAN pages, read on 15 October 2026. We state no number of questions for the real test because ACARA publishes none.

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

Review status: a named teacher review has not yet been recorded for the thirty methods on this page. If something is unclear, please tell us.

Last updated: 2026-10-15.