The shape of the lesson
By the end of the lesson, learners can
- Let the water measure it: Lower the solid into the measuring cylinder and read the level before and after.
- Two routes to a volume.
- Regular solid: volume from measured dimensions, then ρ = m ÷ V.
- Irregular solid: volume = final reading − initial reading (the rise).
- Never divide the mass by the whole final reading; subtract the starting volume first.
One picture every idea returns to
For a regular solid, calculate the volume from its measured dimensions. For an irregular solid, use displacement: the volume is the rise in level in a measuring cylinder, or the water collected from a Eureka can. In every case, ρ = m / V.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, The volume that the water gives away.. A regular block surrenders its volume to a ruler. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Let the water measure it | Lower the solid into the measuring cylinder and read the level before and after. Project tab 3 of the lab (Measuring density) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Two routes to a volume | Two routes to a volume. Model the worked example Worked example on the board, one line at a time. | Rally Coach |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 18 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Two routes to a volume, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Rally Coach
Pairs share one worksheet. One partner solves the first question aloud while the other coaches, checking each line and offering a prompt rather than the answer; they swap roles for the next question.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| When using a single measuring cylinder, the classic error is dividing the mass by the whole final reading. | That includes the water that was already there. The volume of the solid is only the rise in level, the final reading minus the initial reading. Forgetting to subtract the initial volume gives a density that is far too small. |
Measuring density: worksheet
6 questions, 18 marks. Written in the style of the papers; no past paper question is reproduced.
Describe how to find the density of a small regular metal cube.
Describe how to find the density of a small irregular stone using a measuring cylinder, water and a balance.
A measuring cylinder reads 25 cm³. A pebble of mass 60 g is added and the level rises to 45 cm³. Calculate the density of the pebble.
In the previous experiment, a student divides the mass by the final reading of 45 cm³ instead of the rise. Explain why this is wrong.
A rectangular metal block measures 2.0 cm by 3.0 cm by 5.0 cm and has a mass of 81 g. Calculate its density.
A cylinder holds 50 cm³ of water. A metal object of mass 49.5 g is lowered in, raising the level to 68 cm³.
(a)State the volume of the object. (b)Calculate its density.Answer key and marking notes
- Measure the length of one side with a ruler and calculate the volume (side cubed). ✓
- Find the mass on a balance. ✓
- Calculate density = mass ÷ volume. ✓
- Part fill the cylinder with water and read the initial volume. ✓
- Lower the stone in fully and read the new, higher volume. ✓
- Volume of the stone = final reading − initial reading. ✓
- Find the mass on a balance, then density = mass ÷ volume. ✓
Volume. 45 − 25 = 20 cm³
ρ = m ÷ V = 60 ÷ 20ρ = 3.0 g/cm³
- The 45 cm³ includes the water that was already there, not just the pebble. ✓
- The pebble's volume is only the rise (the final reading minus the initial reading), so dividing by 45 gives a density that is too small. ✓
Volume. 2.0 × 3.0 × 5.0 = 30 cm³
ρ = m ÷ V = 81 ÷ 30ρ = 2.7 g/cm³
(a) 68 − 50 = 18 cm³
(b) ρ = 49.5 ÷ 18
ρ = 2.75 g/cm³
1 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
A student wants to find the density of an irregular stone. Which set of apparatus is sufficient?
- Aa balance and a measuring cylinder of water
- Ba ruler and a stopwatch
- Ca thermometer and a balance
- Da measuring cylinder only
Quiz key
The balance gives the mass and displacement in the measuring cylinder gives the volume; density = mass ÷ volume. A ruler (B) cannot measure the volume of an irregular shape, and a measuring cylinder alone (D) gives no mass.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.