Primary 5 Maths | Displacement Method: a Tutor Prep Guide | Water level rise, base area and millilitre conversion

2026-11-10

Tutor lesson-prep guides · Primary Maths

A stone has no length, width or height to measure, so students stall. Displacement swaps a hard question for an easy measurement: however far the water rises is how much space the stone takes.

Objectives — By the end the student can: (1) explain that the water rises because the object occupies space the water used to hold; (2) find a volume as base area times rise, for example a base of 10 by 6 centimetres with a 2.5 centimetre rise giving 150 cubic centimetres; (3) work out that water rising from 120 to 175 millilitres means a stone of 55 cubic centimetres; (4) state that 1 cubic centimetre is 1 millilitre and 1 litre is 1000 millilitres, and write the right unit in the answer.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Volume of a cuboid	Volume of a box 8 by 5 by 4	160 cubic centimetres
Capacity units	How many millilitres in a litre	1000 millilitres
Decimal multiplication	What is 10 times 6 times 2.5	150

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Diagnose	Drop a stone into water and ask why the level rises	They say the stone takes up space
5-15 min	Rise in level	Read 120 and 175 millilitres off the cylinder	Work out 55 millilitres
15-25 min	Base area times rise	A base of 10 by 6 with a 2.5 centimetre rise	Get 150 cubic centimetres
25-33 min	Units	How many cubic centimetres is 55 millilitres; how many millilitres in a litre	Say 55 cubic centimetres
33-40 min	Reverse the question	150 cubic centimetres into a 10 by 6 base	The rise is 2.5 centimetres
40-45 min	Exit check	Mark three questions at once	Work independently

03 Teaching script (read it out)

Scene 1: The water rises because the object takes its space

Run the experiment before writing any formula. Fill a cylinder with 120 millilitres and mark the level; lower in the stone, watch it reach 175 millilitres, and mark again.
Ask whether there is more water. There is not. What is new is the stone, which occupies space the water used to hold, so the water has to rise.
Students must see this happen, or displacement becomes a formula with no origin.

Student should do: point at both marks, say how many millilitres the level rose, and say why.

Scene 2: Base area times rise is the object volume

Inside one container, the risen water is a cuboid: its base is the container base and its height is the rise.
A base of 10 by 6 centimetres with a 2.5 centimetre rise gives 10 times 6 times 2.5, which is 150 cubic centimetres.
Stress the same container: in a narrower cup the same stone pushes the level up more, so the rise alone is not the volume; it must be multiplied by the base area.

Student should do: measure the length and width of the base, multiply by the rise, and get the stone volume.

Scene 3: Millilitres and cubic centimetres, one to one

One cubic centimetre is one millilitre, and one litre is 1000 millilitres, so one litre is also 1000 cubic centimetres.
From 120 to 175 millilitres the difference is 55 millilitres, which is 55 cubic centimetres.
The unit follows the question: cubic centimetres for volume, millilitres for capacity. The commonest error is writing 55 litres, wrong by a factor of a thousand.

Student should do: write 55 millilitres and 1 litre in cubic centimetres and explain the conversion.

04 Question types and worked steps

Type	Example	Steps	Answer
Volume from a level difference	Water rises from 120 to 175 millilitres	Subtract to get 55 millilitres, which is 55 cubic centimetres	55 cubic centimetres
Base area times rise	Base 10 by 6 centimetres, rise 2.5 centimetres	10 times 6 times 2.5	150 cubic centimetres
Rise from a volume	150 cubic centimetres in a 10 by 6 base	150 divided by 60	A rise of 2.5 centimetres
Unit conversion	How many cubic centimetres is 55 millilitres	One millilitre is one cubic centimetre	55 cubic centimetres

Sanity check (teach this): Sanity check: the rise must be smaller than the height of the container, so a rise above that means the base was divided wrongly; the volume of an object does not change when the container does, but the rise does, so the rise alone is never the volume; one millilitre is one cubic centimetre and one litre is 1000 millilitres, so 55 litres is out by a thousand; the level is read in millilitres and the volume written in cubic centimetres, equal numbers but never interchangeable units; the exit check allows 300 seconds for three questions at Primary 5.

05 Independent practice (3 questions)

Question	Answer	What to watch
Level difference	A cylinder rises from 120 to 175 millilitres; find the stone volume	55 cubic centimetres
Base area	Base 10 by 6 centimetres, rise 2.5 centimetres	150 cubic centimetres
Reverse	Volume 150 cubic centimetres, base area 60 square centimetres	A rise of 2.5 centimetres
Conversion	How many cubic centimetres in a litre	1000 cubic centimetres

06 Common mistakes and what to say

Mistake	Student writes	Say this
Treating the rise as the volume	A 2.5 centimetre rise answered as 2.5 cubic centimetres	2.5 is a height, not a volume. Multiply by the base: 10 times 6 times 2.5.
Keeping the old rise in a new container	Using a narrow cup rise for a wide cup	The rise goes with the base area. The same stone lifts a narrow cup further.
Reading the level off the eye line	Eyes above or below the water surface	Keep your eye level with the surface. Either way the reading is off, and every millilitre is a cubic centimetre lost.
Units written as litres	A stone volume of 55 litres	Fifty-five millilitres is small, so 55 cubic centimetres. Fifty-five litres is a bucketful.

07 Homework (paper, section and question numbers)

Primary maths chapter index — All chapters by level
Teaching guide index — Same structure, other subjects
Redo this chapter — Questions 1 to 4 again, with units on every answer

08 Exit check (last 5 minutes)

Question	Answer	Decision
Water rises from 120 to 175 millilitres; the stone volume	55 cubic centimetres	Answering 175 means only one level was read; reteach act one
Base 10 by 6, rise 2.5 centimetres; the volume	150 cubic centimetres	Answering 2.5 means the rise was taken as the volume; act two again
How many millilitres in a litre	1000	Answering 100 is a decimal slip; reteach act three

09 Tutor FAQ

Is the experiment compulsory?

At least once. Once students see the level actually move, the formula means something; from a diagram alone they merge rise and volume.

What about objects that float?

A floating object displaces less than its own volume, so displacement does not apply. Primary 5 handles sinking objects only.

Can the overflow method be used?

Yes: fill the container to the brim and catch what spills, since the overflow equals the volume. But it floods desks, so the level rise comes first.

Find a tutor — free Tutor Registration →

A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.