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Density Why does a heavy log float when a tiny pebble sinks?

Foundation and Higher · AQA · 45 minutes

Students vote on what makes a heavy log float while a tiny pebble sinks, then find out with density: mass for its size. They float and sink a virtual block, work through the three ways of the required practical and change units. Slides to present, a vote that shows who's stuck, practice and homework.

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The idea in one minute

Density is how much mass is packed into each bit of space: ρ = m ÷ V, the mass divided by the volume. With the mass in kilograms and the volume in cubic metres it comes out in kg/m³; in a lab, with grams and cubic centimetres, in g/cm³. 1 g/cm³ is 1000 kg/m³, so water is 1 g/cm³ or 1000 kg/m³. The particle model explains why a solid is usually denser than its liquid, and a liquid much denser than its gas: the same particles, so the same mass, take up more room the further apart they are. Something floats in a liquid when it is less dense than the liquid, whatever its mass: that is why a big log floats and a small pebble sinks.

The lesson starts with a vote before anyone explains. Students then float and sink a virtual block by changing its mass, its volume and the liquid (a model, not a substitute for the practical), and work through the required practical's three ways of measuring: a regular solid with a ruler, an irregular one with a eureka can or a measuring cylinder, and a liquid with a balance and a measuring cylinder. It is for Foundation and Higher; the unit changes and the stretch on a hollow ball lean towards Higher.

By the end, students can

  • work out a density with ρ = m ÷ V, in g/cm³ or kg/m³, and change between the two units
  • rearrange to find a mass (m = ρ V) or a volume (V = m ÷ ρ)
  • explain with the particle model why solids are usually densest and gases least dense
  • say whether something floats or sinks by comparing its density with the liquid's
  • describe how to measure the density of a regular solid, an irregular solid and a liquid

Key words

  • density
  • mass
  • volume
  • kg/m³
  • g/cm³
  • particle model
  • eureka can
  • measuring cylinder
  • meniscus
  • float
  • sink

Before this lesson

Students should know mass in grams and kilograms, the volume of a cuboid (length × width × height) and the solid, liquid and gas states.

Next: Gas pressure and temperature.

The lesson, step by step

45 minutes in total. The stretch is optional.

  1. 1 · Think5 min

    What makes it float?

    A 3 kg log floats down a river.

    A 3 g pebble sinks to the bottom.

    What decides whether something floats?

    A: Its mass

    B: Its volume

    C: Its mass for its volume

    D: Its shape

    Vote first. Then say why.

    5 min 1 · Hook · students think · the slides say “Think”

    What makes it float?

    A 3 kg log floats and a 3 g pebble sinks: students vote on what decides, before anyone explains.

    Say

    “A 3 kilogram log floats down a river. A 3 gram pebble, a thousand times lighter, sinks straight to the bottom. What decides whether something floats: its mass, its volume, its mass for its volume, or its shape?”

    Ask
    • If heavy things sink, why does the log float?
    • Would a log the size of a pebble float? Would a pebble the size of a log?
    Watch for

    Saying heavy things sink: keep that answer on the board, the explain step comes back to it.

    For the teacher

    Give a minute of silent thinking, then vote. Many choose A, heavy things sink, even though the log is far heavier than the pebble.

    Don't explain yet. C is density, the idea of the lesson. D is worth keeping too: a steel ship floats because its shape holds air, so the ship as a whole has a low density. The floating slide comes back to it.

    Take a vote with Ask the class: A mass, B volume, C mass for its volume, D shape. Keep the votes for the explain step.

    Shorter: Vote once, no discussion (−2 min).

  2. 2 · Watch12 min

    Density: mass for its size

    density = mass ÷ volume: ρ = m ÷ V

    m in kg, V in m³: ρ in kg/m³

    m in g, V in cm³: ρ in g/cm³

    Aluminium: m = 540 g, V = 200 cm³

    ρ = 540 ÷ 200 = 2.7 g/cm³

    Mass ÷ volume, never volume ÷ mass

    2 · Watch

    Two units: g/cm³ and kg/m³

    1 g/cm³ = 1000 kg/m³

    (1 m³ = 1 000 000 cm³, and 1 kg = 1000 g)

    g/cm³ to kg/m³: × 1000

    kg/m³ to g/cm³: ÷ 1000

    Water: 1 g/cm³ = 1000 kg/m³

    Aluminium: 2.7 g/cm³ = 2700 kg/m³

    The kg/m³ number is the bigger one.

    2 · Watch

    Particles: why solids are densest

    Solid: particles close, in a fixed pattern

    Liquid: still close, but they move past each other

    Gas: far apart, so the same mass takes far more space

    1 g of water: about 1 cm³; as steam about 1700 cm³

    Same particles, same mass: only the spacing changes

    The exception: ice is a little less dense than water

    Further apart: bigger volume, lower density

    2 · Watch

    Float or sink?

    Less dense than the liquid: it floats

    Denser than the liquid: it sinks

    Log: about 0.6 g/cm³ in water (1.0): floats

    Pebble: about 2.6 g/cm³ in water: sinks

    A steel ship holds air: on average less dense than water

    Back to the vote: which was right?

    Compare densities, not masses.

    2 · Watch

    Try it: float or sink?

    200 g, 250 cm³: ρ = 0.8 g/cm³

    Predict: 300 g, the same size?

    Then swap the water for honey.

    Watch how much is under the surface.

    Predict first: 300 ÷ 250 = ?

    DensityDensity 0.8 g/cm³ (ρ = m ÷ V) · it floats in water (1 g/cm³)

    2 · Watch

    Rearranged: mass and volume

    ρ = m ÷ V

    m = ρ × V

    V = m ÷ ρ

    Ice: V = 0.50 m³, ρ = 920 kg/m³

    m = 920 × 0.50 = 460 kg

    Units must match: kg with m³, g with cm³

    Write what you know, with units, first.

    12 min 2 · Explain · you explain · the slides say “Watch”

    Density, its units, particles and floating

    ρ = m ÷ V; g/cm³ and kg/m³; why solids are usually densest; floating when less dense than the liquid; then rearranging.

    Say

    “Density is the mass packed into each cubic centimetre, or each cubic metre. Mass divided by volume, always that way round.”

    Ask
    • Which is denser: 100 g in 50 cm³, or 100 g in 200 cm³?
    • Water is 1 g/cm³. How many kg/m³ is that?
    • The same particles as a gas: what has changed, and what hasn't?
    Watch for

    Dividing the volume by the mass: ask which number goes on top, and why (mass for each cm³).

    Density: mass ÷ volume

    A block of aluminium: m = 540 g, V = 200 cm³

    ρ = m ÷ V = 540 ÷ 200 = 2.7 g/cm³

    In kg/m³: 2.7 × 1000 = 2700 kg/m³

    Rearranged: m = ρ V

    A block of ice: V = 0.50 m³, ρ = 920 kg/m³

    m = ρ × V = 920 × 0.50 = 460 kg

    For the teacher

    Density: ρ = m ÷ V. ρ is the Greek letter rho. Mass in kilograms and volume in cubic metres give kg/m³; in a lab, grams and cubic centimetres give g/cm³.

    Units: 1 g/cm³ = 1000 kg/m³ (1 m³ is 1 000 000 cm³, and 1 kg is 1000 g). From g/cm³ to kg/m³, multiply by 1000; back, divide by 1000. Water: 1 g/cm³ = 1000 kg/m³. A check: the kg/m³ number is always the bigger one.

    Particles: in a solid they are close together in a fixed pattern; in a liquid still close but able to move past each other; in a gas far apart. The same particles have the same mass, so the further apart they are, the bigger the volume and the lower the density. 1 g of water is about 1 cm³; as steam at 100 °C it takes up about 1700 cm³. Ice is the famous exception: it is a little less dense than water, which is why it floats.

    Floating: something floats in a liquid when it is less dense than the liquid, and sinks when it is denser. Mass alone does not decide: the log is heavy but less dense than water; the pebble is light but about 2.6 g/cm³. Back to the vote: C was right. A steel ship floats because the ship with the air inside it is, as a whole, less dense than water: D's shape matters through density.

    Then the Try it slide. The block starts at 200 g and 250 cm³, 0.8 g/cm³, floating in water. Ask for a prediction for 300 g (1.2 g/cm³: it sinks), then swap the water for honey (1.42 g/cm³: it floats again). The simulation also shows how much of the block is under the surface and the liquid it pushes aside.

    Rearranging: m = ρ × V and V = m ÷ ρ. Cover what you want in the triangle, or rearrange as in any formula. Keep the units matched: kg with m³, g with cm³.

    On the Try it slide, ask for a prediction (float or sink?) before each change, and let a student move the slider.

    Shorter: Skip the particles slide; say it in a sentence, then the Try it slide (−4 min).

  3. 3 · Your turn12 min

    The required practical

    Mass: on a balance, in grams

    Regular solid: ruler, V = length × width × height

    Irregular: eureka can, catch the water it pushes out

    Or: the rise in a measuring cylinder's water level

    Liquid: zero the balance with the empty cylinder

    Read the meniscus's bottom, eye level with it

    Open the Practical quiz. Volume first.

    3 · Your turn

    Worked, then yours

    I do: 5.0 × 2.0 × 2.0 cm, 54 g: 54 ÷ 20 = 2.7 g/cm³

    You do: 4.0 × 2.5 × 2.0 cm, 178 g: its density?

    I do: 40 → 65 cm³, 65 g: 65 ÷ 25 = 2.6 g/cm³

    You do: 30 → 48 cm³, a 153 g key: its density?

    I do: 92 g empty, 138 g with 50 cm³: 46 ÷ 50 = 0.92

    You do: 110 g empty, 158 g with 40 cm³: its density?

    Volume first; then mass ÷ volume.

    Write here

    Its answers' slide comes with your copy.

    12 min 3 · Your turn · students write

    The required practical, then yours

    The three ways of measuring density, worked from made-up results; students answer the Practical quiz, then solve twins of worked examples.

    Say

    “Three things to find the density of: a regular block, an irregular stone and a liquid. The mass always comes from a balance; the volume is what changes.”

    Ask
    • How would you find the volume of a stone? Why not a ruler?
    • Why put the empty measuring cylinder on the balance first?
    Watch for

    Taking the water level after the stone goes in as its volume: it is the rise in the level.

    A regular block: a ruler

    5.0 cm × 2.0 cm × 2.0 cm: V = 20 cm³

    On the balance: m = 54 g

    ρ = 54 ÷ 20 = 2.7 g/cm³

    Then theirs

    A block 4.0 cm × 2.5 cm × 2.0 cm has a mass of 178 g. Its density?

    An irregular stone: the water rises

    Water at 40 cm³; with the stone in, 65 cm³

    V = 65 − 40 = 25 cm³; m = 65 g

    ρ = 65 ÷ 25 = 2.6 g/cm³

    Then theirs

    Water at 30 cm³ rises to 48 cm³ with a 153 g key in it. Its density?

    A liquid: take the cylinder away

    Empty measuring cylinder: 92 g; with 50 cm³ of oil: 138 g

    m = 138 − 92 = 46 g

    ρ = 46 ÷ 50 = 0.92 g/cm³

    Then theirs

    Empty: 110 g; with 40 cm³ of salt water: 158 g. Its density?

    Each question gives made-up results from the density practical. Work out the volume first, then the density, in g/cm³. Show your working on paper.

    1. A rectangular block measures 4.0 cm by 3.0 cm by 2.5 cm. What is its volume, in cm³?
    2. On a balance, the same block has a mass of 81 g. What is its density, in g/cm³?
    3. A stone is lowered on a thread into a full eureka can. 35 cm³ of water runs into the measuring cylinder. The stone's mass is 91 g. What is its density, in g/cm³?
    4. Why is the eureka can filled until water runs out of its spout, and left until it stops, before the stone goes in?
      1. So that all the water the stone pushes aside comes out of the spout
      2. So that there is enough water for the stone to float in
      3. So that the water is the same temperature as the stone
    5. A measuring cylinder holds water up to 60 cm³. A brass key of mass 119 g is lowered in, and the level rises to 74 cm³. What is the key's density, in g/cm³?
    6. An empty measuring cylinder on a balance reads 96 g. With 50 cm³ of oil poured in, it reads 142 g. What is the oil's density, in g/cm³?
    7. How should you read the volume of water in a measuring cylinder?
      1. From above, at the top of the curved surface
      2. With your eye level with the bottom of the curved surface (the meniscus)
      3. Where the water touches the glass at the side
    For the teacher

    The mass: on a balance, in grams. The volume three ways. A regular solid: measure its length, width and height with a ruler and multiply. An irregular solid: fill a eureka can until water runs out of the spout, wait for it to stop, then lower the object in on a thread and catch the water it pushes out in a measuring cylinder; or read the water level in a measuring cylinder before and after, and take one from the other. A liquid: put the empty measuring cylinder on the balance and zero it (or take its mass away later), pour in a measured volume, and read the mass.

    Reading a measuring cylinder: eye level with the bottom of the curved surface, the meniscus. Errors to talk about: air bubbles on the stone (the volume reads too big), water splashing out of a measuring cylinder, drops left in the eureka can's spout.

    Work the examples aloud while the slower ones finish the quiz; the twins check they take the rise in the level and the cylinder's mass away.

    Students open the Practical quiz on their own devices. If you have the equipment, measure one stone for real alongside it. Open the answers slide once most have done the twins.

    Shorter: Do the first two pairs and quiz questions 1–3 only (−4 min).

    Longer: Measure a real stone or key in pairs, with a eureka can or a measuring cylinder, and compare densities (+3 min).

  4. 4 · Vote and practise12 min

    Vote first

    A 300 g stone pushes 120 cm³ of water

    out of a eureka can. Its density in kg/m³?

    A: 2.5 kg/m³

    B: 400 kg/m³

    C: 2500 kg/m³

    D: 0.0025 kg/m³

    Choose on your own, then say why.

    4 · Vote and practise

    Practise: show your working

    1. 600 g of wood, 750 cm³: its density in g/cm³?

    2. 2.0 kg, 0.0025 m³: its density in kg/m³?

    3. 0.92 g/cm³ in kg/m³; 7800 kg/m³ in g/cm³

    4. Why does 1 g of steam take up far more space?

    5. 0.20 m³ of concrete at 2400 kg/m³: its mass?

    Stuck? Write m = and V = with units.

    Write here

    4 · Vote and practise

    Reason it out

    6. 184 g of oil at 0.92 g/cm³: its volume?

    7. A 0.95 g/cm³ toy in oil (0.92), then water (1.0)

    8. Air bubbles on the pebble: density too big or small?

    9. 2.0 × 3.0 × 5.0 cm, 0.267 kg: density in kg/m³?

    10. Cylinder 85 g; with 60 cm³ of liquid 160.6 g

    Stretch: a hollow steel ball that floats

    Compare densities to decide float or sink.

    12 min 4 · Who's stuck? · students vote · the slides say “Vote and practise”

    Vote, then practise

    One question shows who changes units the wrong way or divides the wrong way; then practice in levels, and a hollow ball as the stretch.

    Say

    “Choose an answer on your own. Nobody talks until everyone has chosen.”

    Ask
    • Which is on top, the mass or the volume? And which way is 1000: bigger or smaller?
    Watch for

    Answers of 2.5 kg/m³ or 0.0025 kg/m³: work in g/cm³ first, then multiply by 1000.

    Show your working on paper. Write the mass and the volume with their units first. 1 g/cm³ = 1000 kg/m³. The stretch is optional.

    The question that shows who's stuck

    1. A stone of mass 300 g pushes 120 cm³ of water out of a eureka can. What is its density in kg/m³?
      1. 2.5 kg/m³
      2. 400 kg/m³
      3. 2500 kg/m³
      4. 0.0025 kg/m³
    In your Classroom, as they answer (an example)
    • A7
    • B3
    • C11
    • D4

    Each wrong answer is a different mistake. While they answer, your Classroom shows who chose which, so you know in seconds whom to help with what.

    1. A block of wood has a mass of 600 g and a volume of 750 cm³. What is its density, in g/cm³?
    2. A plastic box has a mass of 2.0 kg and a volume of 0.0025 m³. What is its density, in kg/m³?
    3. Change the units: 0.92 g/cm³ = ___ kg/m³, and 7800 kg/m³ = ___ g/cm³.
    4. 1 g of water is about 1 cm³. As steam it takes up about 1700 cm³. Why?
      1. The particles in steam are much smaller
      2. The particles in steam weigh less
      3. The same particles are much further apart, so the same mass takes up far more space
      4. Steam has fewer particles in each gram
    5. Concrete has a density of 2400 kg/m³. What is the mass, in kg, of a concrete block with a volume of 0.20 m³?
    6. Olive oil has a density of 0.92 g/cm³. What volume, in cm³, does 184 g of it take up?
    7. A plastic toy has a density of 0.95 g/cm³. It is put in oil (0.92 g/cm³), then in water (1.0 g/cm³). What happens?
      1. It floats in both
      2. It sinks in both
      3. It floats in water and sinks in oil
      4. It floats in oil and sinks in water
    8. Kai measures a pebble's volume by the rise of the water in a measuring cylinder. Air bubbles cling to the pebble. What does this do to the density he works out?
      1. It comes out too big
      2. It comes out too small
      3. It makes no difference
    9. A metal block measures 2.0 cm by 3.0 cm by 5.0 cm and has a mass of 0.267 kg. What is its density in kg/m³?
    10. An empty measuring cylinder has a mass of 85 g. With 60 cm³ of a liquid in it, its mass is 160.6 g. What is the liquid's density, in g/cm³?
    11. Stretch: a sealed, hollow steel ball has a mass of 600 g and takes up 750 cm³. Its average density is ___ g/cm³, so in water it ___. Solid steel (7.8 g/cm³) the same size would have a mass of ___ g.

    Support · Write m = and V = with their units before anything else. Work in g/cm³ first; to change to kg/m³, multiply by 1000, and check the kg/m³ number is the bigger one.

    For the teacher

    Everyone chooses before anyone explains. Then ask in turn: what is the mass? The volume? Mass ÷ volume in g/cm³? And in kg/m³?

    Questions 1–3 build fluency; 4–6 change the look (particles, rearranging); 7–8 ask for reasons; 9–10 are exam-style. The stretch is a hollow steel ball that floats: the ship from the hook, in small.

    Students show their working on paper or the board; the quiz keeps their final answers.

    If many chose 2.5 or 0.0025 kg/m³, go back to the units slide before they practise: water is 1 g/cm³ and 1000 kg/m³.

    Shorter: After the vote, questions 1–5 only (−5 min).

    Longer: The stretch: a hollow steel ball, then why a steel ship floats (+8 min).

  5. 5 · Show what you know4 min

    The density of a pebble

    A pebble's mass: 52 g

    Lowered into a measuring cylinder,

    the water rises from 30 cm³ to 50 cm³

    What is its density in g/cm³?

    And in kg/m³?

    Volume first: the rise in the level.

    Write here

    4 min 5 · Exit · students show · the slides say “Show what you know”

    The density of a pebble

    A pebble in a measuring cylinder shows who takes the rise in the level and who can change the units.

    Say

    “Write the mass and the volume first, with their units.”

    Watch for

    Using 50 cm³, the level after, as the pebble's volume.

    Write the mass and the volume with their units first.

    1. A pebble of mass 52 g is lowered into a measuring cylinder, and the water rises from 30 cm³ to 50 cm³. What is its density, in g/cm³?
    2. What is the pebble's density in kg/m³?
    For the teacher

    A pebble of mass 52 g is lowered into a measuring cylinder: the water rises from 30 cm³ to 50 cm³.

    What is its density in g/cm³? And in kg/m³?

    Those who used the level instead of the rise, or changed units the wrong way, need it again next lesson; set the homework.

    Longer: Why does a steel ship float when a steel nail sinks? Answer with density. (+4 min).

One to one: before each calculation, ask the student to say aloud what the mass is, what the volume is and which units each is in; let them drive the virtual block while you only ask them to predict float or sink before each change.

Homework: Density

Write the mass and the volume with their units before each calculation. 1 g/cm³ = 1000 kg/m³. Show your working.

  1. A block has a mass of 250 g and a volume of 100 cm³. Find its density in g/cm³, then in kg/m³.
  2. Change 0.79 g/cm³ into kg/m³, and 11 300 kg/m³ into g/cm³.
  3. A block measures 10 cm by 5.0 cm by 4.0 cm and has a mass of 1.08 kg. Find its density in g/cm³.
  4. A measuring cylinder holds water up to 25 cm³. A 162 g metal nut is lowered in and the level rises to 43 cm³. Find the nut's density. Does it float in water?
  5. A concrete paving slab has a volume of 0.024 m³. Concrete's density is 2400 kg/m³. Find the slab's mass.
  6. Explain, using the particle model, why the same mass of steam takes up far more space than water.

Print the worksheet with working space and homework. Teacher answers come with your Library copy.

Teaching density: common questions

Is density on Foundation and Higher, and in combined science?

Yes. In AQA GCSE Physics (8463) density and its required practical are for both tiers, and AQA's combined science (Trilogy) has them too. The whole lesson suits both tiers; changing units with kg/m³ and the hollow ball in the stretch lean towards Higher.

Should students use kg/m³ or g/cm³?

Both. kg/m³ is the SI unit and exam answers often ask for it; in the practical, masses come in grams and volumes in cubic centimetres, so g/cm³ is natural there. 1 g/cm³ = 1000 kg/m³: work in g/cm³ first, then multiply by 1000, and check the kg/m³ number is the bigger one.

Is floating and sinking part of the density topic?

Comparing an object's density with the liquid's is a simple rule that makes density matter, and the hook and the simulation use it. The full reason, upthrust from the liquid's pressure, comes in AQA's pressure in a fluid section, for Higher in physics only. This lesson keeps to the density rule.

Can the simulation stand in for the required practical?

No. The virtual block shows the idea (density decides float or sink, whatever the mass), but the practical is about measuring: reading a measuring cylinder, using a eureka can, and thinking about errors. The Practical quiz uses made-up results; measure a real stone or key if you can.

Why does ice float if solids are denser than liquids?

Water is the well-known exception. As it freezes, its particles settle into an open pattern that takes up a little more space than the liquid, so ice is about 0.92 g/cm³ and floats on water. Most other substances are densest as solids.

Can I use the lesson without creating an account?

Yes. Read the lesson, print the worksheet and open its slides without signing in; nothing you draw there is kept. A free teacher account keeps the whole lesson in your Library to change and teach, with the simulation, the quizzes, the answers and the answer slides.

Curriculum reference: AQA GCSE Physics 8463: 4.3.1.1 (density of materials: ρ = m ÷ V, the particle model of solids, liquids and gases, and the required practical on the density of regular and irregular solids and liquids).

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