Year 5 numeracy: ten multistep word problems, worked step by step

Quick Answer

For a problem with more than one step, underline what is asked, list what you know, write the steps in order, carry the units through, and check the answer against the question. This page has ten original Year 5 problems worked that way, each with the wrong answer a child is likely to give.

Who is this for?

Parents of Year 5 children in any state, and the child sitting beside them. It is a labelled original Braintree practice set for learning at home. It is not a NAPLAN paper. About 40 minutes covers all ten if you do them across two sittings, with pencil and paper.

NAPLAN's published calculator provision covers Years 7 and 9 only, and the national page states none for Year 5. Work these ten by hand. For the real format, see the national site: the national NAPLAN site.

How do I break a long problem into steps?

Use the same five lines every time.

1. Question. Write what is being asked, in your own words, with the unit it should come out in.
2. Know. List the numbers you are given and what each one is. Cross out any number the question does not need.
3. Steps. Write each operation on its own line, in order, before you calculate anything.
4. Units. Say what each step's answer is measured in. Convert before you combine, not after.
5. Check. Read the question again. Does your answer say what was asked, in the right unit, and is it a sensible size?

The ten problems

Cover the worked methods below and try each one first.

Problem 1 (money and change). Mia buys 3 notebooks at $2.40 each and a pen for $1.85. She pays with a $10 note. How much change does she get?

Problem 2 (time). Zoe arrives at the cinema at 1:15 pm. The film starts 25 minutes later and runs for 1 hour 50 minutes. What time does the film finish?

Problem 3 (area, then cost). A rectangular veggie patch is 6 m long and 4 m wide. The soil in it is 30 cm deep. Mulch costs $3 for each square metre. How much does it cost to cover the whole patch?

Problem 4 (fraction, then subtraction). Sam has 48 stickers. He gives one quarter of them to his sister and 5 to a friend. How many stickers does Sam have left?

Problem 5 (table lookup, then calculation). Ari is in the Blue group for swimming lessons and goes to 8 lessons. He has a $20 voucher to take off the total.

Group	Cost per lesson
Red	$12
Blue	$15
Green	$18

How much does Ari pay?

Problem 6 (units). Lena has a ribbon 2 m long. She cuts 3 pieces, each 45 cm long. How many centimetres of ribbon are left?

Problem 7 (division, then rounding up). 135 students go on an excursion. Each bus holds 40 students and costs $210 to hire. What is the total cost of the buses?

Problem 8 (several steps). A bakery bakes 24 rolls on each tray. It bakes 7 trays in the morning and 5 trays in the afternoon. The rolls are sold in bags of 6, and a bag costs $4.50. How many bags can it fill?

Problem 9 (comparing prices). A pack of 5 pens costs $4.00. A single pen costs 90 cents. Ravi needs exactly 10 pens. Which way is cheaper, and by how much?

Problem 10 (perimeter, then cost). A school fences a rectangular playground 20 m long and 10 m wide on all four sides. Fencing is sold in panels 5 m long that cost $40 each. How much will the fencing cost?

Worked methods

Each method uses the five lines, then names the answer a child is likely to give by mistake. These are the slips each problem is built to expose; they are easy to fix.

Problem 1

• Question: change from $10, in dollars.
• Know: 3 notebooks at $2.40; a pen at $1.85; paid $10.
• Steps: 3 × $2.40 = $7.20. $7.20 + $1.85 = $9.05. $10.00 − $9.05 = $0.95.
• Units: dollars at every step.
• Check: the spend is just under $10, so the change should be small. $0.95 fits.
• Likely wrong answer: $5.75. The child adds $2.40 once, as if there were one notebook, and subtracts that from $10.

Problem 2

• Question: the finishing time, in hours and minutes.
• Know: arrives 1:15 pm; film starts 25 minutes later; runs 1 h 50 min.
• Steps: 1:15 pm + 25 min = 1:40 pm. 1:40 pm + 1 h 50 min = 3:30 pm.
• Units: clock time, then a length of time added to it.
• Check: the film runs close to two hours from 1:40, so just before 3:40. 3:30 fits.
• Likely wrong answer: 3:05 pm. The child adds the film length to the arrival time and forgets the 25-minute wait.

Problem 3 (contains an unneeded number)

• Question: the cost of mulch for the top of the patch, in dollars.
• Know: 6 m long; 4 m wide; soil 30 cm deep; $3 per square metre. The depth of the soil is not needed: mulch covers the top, which is flat. Cross out 30 cm.
• Steps: 6 × 4 = 24 square metres. 24 × $3 = $72.
• Units: square metres, then dollars.
• Check: the question asks about covering a surface, so an area is the right first step.
• Likely wrong answer: $60. The child finds the perimeter (6 + 4 + 6 + 4 = 20 m) and multiplies by $3.

Problem 4

• Question: how many stickers are left, as a count.
• Know: 48 stickers; gives away 1/4; gives away 5 more.
• Steps: 48 ÷ 4 = 12 given to the sister. 48 − 12 = 36. 36 − 5 = 31.
• Units: stickers throughout.
• Check: 31 is less than 48 and more than half of it, which fits giving away a quarter and a few more.
• Likely wrong answer: 12. The child stops after the first step and answers with the number given to the sister.

Problem 5

• Question: the amount Ari pays after the voucher, in dollars.
• Know: Blue group costs $15 a lesson (read from the Blue row); 8 lessons; $20 off.
• Steps: 8 × $15 = $120. $120 − $20 = $100.
• Units: dollars.
• Check: put your finger on the Blue row again before you answer. The cost per lesson is $15.
• Likely wrong answer: $124. The child reads the Green row ($18): 8 × $18 = $144, then takes off $20.

Problem 6

• Question: ribbon left, in centimetres.
• Know: 2 m; 3 pieces of 45 cm. 2 m = 200 cm.
• Steps: 3 × 45 = 135 cm used. 200 − 135 = 65 cm.
• Units: convert metres to centimetres first, so both numbers are in centimetres before you subtract.
• Check: 65 cm is less than the 200 cm the ribbon began with, and about one and a half pieces' worth.
• Likely wrong answer: 133 cm. The child subtracts 2 from 135 and ignores that one is metres and the other centimetres.

Problem 7

• Question: the total cost of the buses, in dollars.
• Know: 135 students; 40 per bus; $210 per bus.
• Steps: 135 ÷ 40 = 3 buses with 15 students left over. The 15 still need a bus, so 4 buses. 4 × $210 = $840.
• Units: buses, then dollars.
• Check: 3 buses hold only 120 students, so 3 is too few. 4 buses hold 160.
• Likely wrong answer: $630. The child uses 3 buses and drops the remainder.

Problem 8 (contains an unneeded number)

• Question: the number of bags that can be filled.
• Know: 24 rolls per tray; 7 trays and 5 trays; 6 rolls per bag; $4.50 per bag. The price is not needed because the question asks how many bags, not how much they cost. Cross out $4.50.
• Steps: 7 + 5 = 12 trays. 12 × 24 = 288 rolls. 288 ÷ 6 = 48 bags.
• Units: trays, rolls, then bags.
• Check: 6 rolls per bag and 24 per tray means 4 bags a tray. 12 trays × 4 = 48.
• Likely wrong answer: 288. The child stops at the number of rolls and never turns it into bags.

Problem 9

• Question: which is cheaper for 10 pens, and the difference in dollars.
• Know: a pack of 5 for $4.00; one pen for $0.90; 10 pens needed.
• Steps: 10 ÷ 5 = 2 packs. 2 × $4.00 = $8.00. 10 × $0.90 = $9.00. $9.00 − $8.00 = $1.00.
• Units: dollars. Compare the cost of the same 10 pens both ways.
• Check: each way buys exactly 10 pens, so the two totals can be compared fairly.
• Likely wrong answer: single pens, cheaper by $3.10. The child compares $4.00 for a pack of 5 with $0.90 for one pen.

Problem 10

• Question: the cost of the fencing, in dollars.
• Know: 20 m long; 10 m wide; all four sides; panels 5 m; $40 a panel.
• Steps: 20 + 10 + 20 + 10 = 60 m of fence. 60 ÷ 5 = 12 panels. 12 × $40 = $480.
• Units: metres, then panels, then dollars.
• Check: all four sides are fenced, so the fence must be longer than one length plus one width.
• Likely wrong answer: $240. The child adds length and width once (30 m) and stops halfway round.

Where do children stop too early?

Look across the ten and the same few slips recur. They are habits, and each one has a fix in the table.

Slip	Where it appears	What helps
Stopping after the first step	4, 8	Write the Question line first, then tick it off against the last step.
Mixing units	6	Convert before you combine; write the unit beside every number.
Using a number the problem did not need	3, 8	Cross it out on the Know line and say why.
Reading the wrong row or label	5	Point at the row; say what the number is out loud.
Dropping a remainder	7	Ask whether a part-full bus still has to be paid for.
Answering a nearby question	3, 9	Re-read the question in the Check line.
Counting something once that should be counted more than once	1, 10	Ask how many of each thing the question gives, and use every one.

A good routine for a parent: do not give the answer. Ask, "What is the question asking for?" then "Which of these numbers do you need?" then "What do you do first?"

Can my child write the steps for a new problem?

Write only the steps, not the answer.

Transfer problem. Tom saves $5 each week for 6 weeks. Then he buys a game for $12.50. How much money does Tom have left?

Ask your child to write the Question, Know, Steps, Units and Check lines without calculating. Parent note: the steps are 6 × $5 = $30, then $30 − $12.50 = $17.50.

Where to go next

• Year 5 preparation overview: NAPLAN Year 5 preparation
• Short single-skill set: Year 5 maths worksheets
• Two longer multistep items with one-line methods: NAPLAN Year 5 practice set
• Free practice resources compared: NAPLAN practice tests: free online resources compared
• National format details: the national NAPLAN site

Sources and review

Official source (checked 2026-10-15): ACARA, NAPLAN: what's in the tests, for the published format and calculator provision.

Where the problems came from: all ten problems are original Braintree Coaching Australia material with invented names, shops and prices. None is a NAPLAN item. The likely wrong answers are the slips each problem is built to expose; they are not counted from marking records.

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

Answer check: every answer was solved a second time and the operations in each problem were counted before publication. A named teacher review has not yet been recorded for this set. If you find an error, please tell us.

Last updated: 2026-10-15.