Measurement questions use rates, scale, mass and time, sometimes in mixed units; put everything in the same unit, then check the answer's size. For students entering Year 7 or 8, the cooperative test is on 27 February 2027.
A measurement question is about quantities with units: litres, metres, grams, seconds, hours. In our ACER-style questions, those quantities come from something happening. A hose fills a pool, a shadow grows, a camera takes photos through the night.
ACER's stated aim for the test is mathematical ability rather than school achievement. In our measurement questions, the conversion or rate can be simple, but your child has to decide which quantities to compare and in what unit.
Something filled, used or travelled at a steady pace
Find the amount for a single unit
Scale and proportion
Quantities that grow in the same ratio, such as heights and shadows
Compare by multiplying, not by adding
Parts of a whole
A container and its contents weighed together
Separate what changed from what stayed
Time
Clock times, days and intervals
Count in hours and minutes, not tens
How should your child work a measurement question?
Read the situation, find the maths, check: in measurement the last step is a check on size.
Put everything in the same unit
Kilograms and grams, minutes and seconds: change them before any other working. Write the unit beside every number.
Find the rate for a single unit
How long for each litre? How much shadow for each metre of height? A unit rate makes the rest straightforward.
Scale up or down
Multiply the unit rate by the amount the question asks about.
Check the size
A paddling pool fills in minutes, not seconds or days. A flagpole is taller than a fence post. If the size is wrong, the method is wrong.
Four worked examples
We wrote all of these ourselves at the level of ACER's Level 1 Mathematics, starting with the easiest. They are not taken from ACER. Each one shows the answer and the working; as you read, ask your child which unit each step uses.
Worked explanation 1
A garden hose fills a 9-litre bucket in 45 seconds. At the same rate, how long will it take to fill a paddling pool that holds 120 litres?
AA.
6 minutes
BB.
10 minutes
CC.
13⅓ minutes
DD.
90 minutes
Answer: B
Answer: B (10 minutes)
45 seconds for 9 litres is 45 ÷ 9 = 5 seconds for each litre. 120 litres take 120 × 5 = 600 seconds. 600 ÷ 60 = 10 minutes.
The trap: 6 minutes tempts children who treat 45 seconds as 0.45 of a minute. 45 seconds is three-quarters of a minute, not 0.45.
Why the other options are wrong
A (6 minutes): 6 minutes treats 45 seconds as 0.45 minutes.
C (13⅓ minutes): 13⅓ minutes counts the number of bucket-loads as if each took a minute.
D (90 minutes): 90 minutes works out 120 × 45 seconds but forgets the bucket holds 9 litres.
Worked explanation 2
At 3 pm on a sunny day, a fence post 1.2 m tall casts a shadow 1.8 m long on flat ground. At the same moment, the school flagpole casts a shadow 13.5 m long. How tall is the flagpole?
AA.
7.5 m
BB.
9 m
CC.
12.9 m
DD.
20.25 m
Answer: B
Answer: B (9 m)
At the same moment every object's shadow has the same size compared with its height. The post's shadow is 1.8 ÷ 1.2 = 1.5 times its height. So the flagpole's height is 13.5 ÷ 1.5 = 9 m. Check: 9 × 1.5 = 13.5.
The trap: 12.9 m tempts children who see the shadow is 0.6 m longer than the post and take 0.6 m off the flagpole's shadow too. Shadows grow by multiplying, not by adding a fixed amount.
Why the other options are wrong
A (7.5 m): 7.5 m divides 13.5 by 1.8 but forgets to multiply by the post's height of 1.2 m.
C (12.9 m): 12.9 m takes off a fixed 0.6 m instead of using how many times longer the shadow is.
D (20.25 m): 20.25 m multiplies by 1.5 instead of dividing, making the pole taller than its shadow.
Worked explanation 3
A scientist weighs a glass flask completely full of sea water: it weighs 1.25 kg. After pouring out one-third of the water, the flask and the water left in it weigh 950 g. What is the mass of the empty flask?
AA.
350 g
BB.
600 g
CC.
650 g
DD.
900 g
Answer: A
Answer: A (350 g)
Change to grams: 1.25 kg = 1250 g. Pouring out one-third of the water removed 1250 − 950 = 300 g, so all the water weighed 3 × 300 = 900 g. The empty flask is 1250 − 900 = 350 g.
The trap: 650 g tempts children who take 300 g off the 950 g only once. That still leaves one-third of the water in the flask; two lots of 300 g must come off.
Why the other options are wrong
B (600 g): 600 g is the water still in the flask, not the flask itself.
C (650 g): 650 g takes off only one more third, leaving a third of the water behind.
D (900 g): 900 g is the mass of all the water, not the flask.
Worked explanation 4
A nature club films a flower bud slowly opening. Their camera takes one photo every 3 minutes, starting at 7:40 pm on Friday. The photos are joined into a video that shows 25 photos every second, and the finished video lasts 12 seconds. At about what time on Saturday did the camera take its last photo?
AA.
12:40 am
BB.
4:40 am
CC.
10:40 am
DD.
10:40 pm
Answer: C
Answer: C (10:40 am)
The video shows 12 × 25 = 300 photos. With one photo every 3 minutes, they cover about 300 × 3 = 900 minutes of real time. 900 ÷ 60 = 15 hours. 15 hours after 7:40 pm on Friday is 10:40 am on Saturday. (Strictly, 300 photos have 299 gaps, so the last photo is at 10:37 am, which is still about 10:40 am.)
The trap: 4:40 am tempts children who turn 900 minutes into 9 hours, as if an hour had 100 minutes. 900 minutes is 15 hours.
Why the other options are wrong
A (12:40 am): 12:40 am treats the 300 photos as 300 minutes, forgetting the photos are 3 minutes apart.
B (4:40 am): 4:40 am changes 900 minutes into 9 hours instead of 15 hours.
D (10:40 pm): 10:40 pm adds 15 hours as if the start were 7:40 in the morning; 15 hours after 7:40 pm is the next morning.
Why are time questions easy to get wrong?
Time doesn't count in tens. An hour rolls over into the next at a different point from a decimal, so habits from ordinary arithmetic give wrong answers.
Minutes are not decimals. Seconds can't be turned into part of a minute by putting a decimal point in front of them.
Long intervals need hours. A big number of minutes should be changed to hours and minutes before adding it to a clock time.
Crossing midnight or noon changes the day or the am and pm. Write the day beside the time.
In the time-lapse question, the working is short once the photos are turned into minutes and the minutes into hours. The trap in our question sits at that last conversion.
What is the "container and contents" idea?
Some questions weigh or measure things together: a flask and its water, a box and its contents, a bus and its passengers. Just part of it changes.
The trick is to look at what changed between the readings. In the flask question, pouring out part of the water lowers the mass by exactly the mass of that water.
From there, your child can work out all the water, then the empty flask. A sketch with the flask and water labelled keeps them apart.
What traps should your child watch for?
Each slip below gives an answer that looks plausible, which is why the size check matters. When your child misses one, ask for the unit beside every number in their working.
Comparing by adding instead of multiplying. Shadows, maps and recipes scale; a fixed difference doesn't carry over.
Mixing units. Kilograms in a line of working and grams in the next give answers that look plausible and are wildly wrong.
Taking away just once. If part of a container's contents is removed, check how much is still inside before subtracting.
Forgetting the size check. An answer that is far too big or too small for the situation is the quickest mistake to catch.
Does your child need to estimate?
Yes, at times. Some questions ask for an "about" answer. In ours, the options are far enough apart that a sensible estimate picks the right one.
On the day there are no rulers, books or papers, calculators, watches or mobile phones, so rounding to friendly numbers before multiplying is a real time-saver.
The test has 32–36 multiple-choice questions in 40 minutes. A quick estimate before the full working also tells your child which options can be ruled out at once.
The kitchen is a measurement lab. Weigh a full and a half-empty jar and work out what the empty jar weighs.
Time a tap filling a jug, then predict a bigger container, or measure a shadow and a person at the same time of day.
Ask for the unit every time your child gives a number, and whether the size is sensible. Those checks catch the slips this page lists.
Four examples show the method. Practice test 1 has a full Mathematics section on ACER's time, and its results by skill show whether measurement is costing marks.
Measurement has its own lesson in the app (Interactive and Notes) and skill drills. It sits with the other kinds on the ACER Maths sample questions page. Area and length overlap with geometry, steady rates are patterns in another form, and rates from a table are under data questions.
See where your child stands
Practice test 1 marks every answer and shows results by skill: what your child already does well and the three skills to work on next.
Sample
Practise for the real test
Practice test 1 is free. Then packs from A$109 for 12 months, or A$9 a week, per exam.
