Junior Science | Density, Floating and the Particle Model: Tutor Prep Guide (Three Formulas, Four Errors)

2026-11-13

Tutor lesson-prep guides · Junior Science

Students can recite that light things float and heavy things sink, so a kilogram of iron against a kilogram of wood ties them in knots. The gap is not the formula: they use heavy where they should use density. This lesson does three things only: one ratio, one comparison, one particle diagram.

Objectives — Students will be able to: (1) calculate density with rho = m/V in g/cm3 and convert to kg/m3; (2) compare an object density with water at 1.0 g/cm3 to predict floating or sinking; (3) use submerged fraction equals object density divided by liquid density to find what percentage of a floating body sits below the surface; (4) explain with the particle model why density is fixed for a substance and why heating usually lowers it; (5) state that liquid pressure increases with depth and compute simple values with rho times g times h.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Mass and volume	What units do we use for mass and for volume?	Mass in g or kg, volume in cm3, mL or m3
Particle model	How are particles arranged in a solid, a liquid and a gas?	Solid packed and fixed, liquid close but sliding, gas far apart and random
Division and units	What is 200 divided by 250?	0.8, with the unit g/cm3

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-3 min	Prior-knowledge check	Ask units, particle arrangement and division	Oral answers, gaps noted
3-9 min	Opening conflict	Hold up a kilogram of iron and a kilogram of wood and ask which floats	Class votes, then the demo runs
9-21 min	Act one	rho = m/V in three steps: mass, volume, divide	Everyone calculates one block and reports
21-32 min	Act two	Compare with water, submerged fraction, icebergs at 92 per cent	Oil, water and wood blocks in a clear beaker
32-40 min	Act three and practice	Particle model for density, liquid pressure rho times g times h	Groups of four do four items, tutor asks only
40-45 min	Exit check	Five quick oral questions	All five right before leaving

03 Teaching script (read it out)

Scene 1: Density is a ratio, not a weight

Create the conflict first: a kilogram of iron in one hand, a kilogram of wood in the other, and ask which will float. Most point at the wood. Then ask how both can weigh the same yet behave differently, and the wrong criterion, weight, comes into the open.

Only then write rho equals m divided by V. Three steps: weigh the mass on a balance in grams, find the volume from edge lengths for a regular solid or by displacement for an irregular one, then divide, giving g/cm3.

Model one: volume 250 cm3 and mass 200 g gives 200 divided by 250, so 0.8 g/cm3. Then a 6 cm cube of mass 172.8 g gives 216 cm3 and 172.8 divided by 216, also 0.8 g/cm3. The same number twice is what convinces students that density is an identity card for a substance.

Scene 2: Floating is one comparison

Fix one sentence: below 1.0 g/cm3 it floats, above it sinks, equal and it hovers. Wood at 0.8 floats, aluminium at 2.7 sinks, ice at 0.92 floats, iron at 7.9 sinks.

Then the submerged fraction: submerged volume divided by total volume equals object density divided by liquid density. Wood at 0.8 in water is 80 per cent submerged, so 200 of its 250 cm3 lie below the surface. Ice at 0.92 is 92 per cent submerged, which is the science behind the tip of the iceberg.

Add the balance: a floating body displaces its own mass in water, so a 200 g block displaces 200 g of water, which is 200 cm3. That also explains why the same wood floats deeper in oil at 0.9 g/cm3, where 0.8 divided by 0.9 is about 89 per cent submerged.

Scene 3: Particle model and liquid pressure

Draw two boxes, one densely packed and one sparse. Ask whether the particles themselves grow when a substance goes from gas to solid. They do not: only the spacing changes. That is why heating normally increases spacing and volume, lowering density, while ice at 0.92 floats on water as the well-known exception worth remembering as a fact at this level.

Then liquid pressure: deeper means more water pressing from above, so pressure rises with depth. Formula p equals rho times g times h. At a depth of 0.2 m, 1 000 times 10 times 0.2 gives 2 000 Pa, or 2 kPa.

Close with one line: depth drives pressure, density drives floating. Keeping the two words apart stops students from saying deep water is denser.

04 Question types and worked steps

Type	Example	Steps	Answer
Find the density	Mass 200 g, volume 250 cm3. Density?	Write the formula, substitute, then attach the unit	200 divided by 250 is 0.8 g/cm3
Predict floating	Aluminium at 2.7 g/cm3 is placed in water. Float or sink?	Compare with 1.0; larger sinks	Sinks, because 2.7 is above 1.0
Submerged fraction	A 250 cm3 block at 0.8 g/cm3 floats. How much is submerged?	Find the ratio 0.8 over 1.0, then multiply by total volume	80 per cent, so 200 cm3
Liquid pressure	What is the pressure at a depth of 0.2 m?	p = rho g h with rho in kg/m3 and h in metres	1 000 times 10 times 0.2 is 2 000 Pa

Sanity check (teach this): Sanity check to teach: after every density answer ask whether the number is plausible, and give three anchors, water 1.0, aluminium 2.7, iron 7.9. A result of 0.08 or 80 means a unit or decimal slip. For submerged fraction the answer must lie between 0 and 100 per cent, so anything above 100 per cent means the ratio was inverted, liquid over object instead of object over liquid.

05 Independent practice (3 questions)

Question	Answer	What to watch
1. A block has mass 200 g and volume 250 cm3. Find its density.	0.8 g/cm3	Whether the unit is written
2. How much of that block is under water?	200 cm3, or 80 per cent	Whether they used the ratio rather than guessing half
3. Ice at 0.92 g/cm3 floats. What fraction is submerged?	92 per cent	Whether they link it to the iceberg tip
4. Find the pressure at a depth of 0.2 m.	2 000 Pa, or 2 kPa	Whether rho was 1 000 kg/m3

06 Common mistakes and what to say

Mistake	Student writes	Say this
Using heavy instead of dense	Iron is heavy so it sinks, wood is light so it floats	A kilogram of iron and a kilogram of wood weigh the same, yet one sinks and one floats, so the test is not weight but grams per cubic centimetre.
Inverting the formula	rho equals V divided by m	Density is mass per unit volume, so mass goes on top: m over V. Written the other way the unit becomes cm3 per g, which is upside down.
Mixing units	Mass 0.2 kg and volume 250 cm3, so 0.0008	Mixing kilograms with cubic centimetres is wrong by a factor of a thousand. Use grams with cm3, or kilograms with m3, never one of each.
Reading the fraction as a force	80 per cent submerged means 80 N of upthrust	80 per cent is a volume ratio, not a force. Upthrust equals the weight of displaced water: 200 cm3 of water is 200 g, about 2 N.

07 Homework (paper, section and question numbers)

Science subject index (matter and particles) — Reread the states of matter and particle model chapter and copy three key points
School practice paper: density and floating — Do questions 1 to 5; question 4 must show the submerged-fraction step
Kitchen measurement task — Weigh a fruit, find its volume by displacement, calculate density, predict floating and write two sentences

08 Exit check (last 5 minutes)

Question	Answer	Decision
Formula for density?	rho equals m divided by V	V over m means rewrite it on the spot
Density of water?	1.0 g/cm3, or 1 000 kg/m3	Both units should be known
What happens if density is above water?	It sinks	Saying floats means re-teach the comparison direction
How much of a 0.8 g/cm3 block is submerged?	80 per cent	Saying 100 per cent means the ratio was skipped
Liquid pressure rises with what?	Depth	Should add that more water presses from above

09 Tutor FAQ

A student asks why an iron ship floats

Do not explain the whole ship by density; use average density. Most of the hull is air, so the ship as a whole is less dense than water. A foil demo helps: the same foil crumpled sinks, shaped into a bowl it floats.

Students misread the water level when finding volume

Teach two habits: read the starting level before adding the object, and keep the eye level with the bottom of the meniscus. Require them to write volume equals final reading minus starting reading rather than quoting a single number.

How do I make density as an identity card believable

Give three samples of the same wax in different sizes to three groups, have each calculate, then put all three answers on the board. Three identical numbers persuade far more than repeating the definition.

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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.