The shape of the lesson
By the end of the lesson, learners can
- Length, mass and capacity: In the lab, pick a quantity, type a value and switch between units.
- Area units are squared: A square of side 1 cm is 10 mm by 10 mm (Fig. 1), so it contains \(10 \times 10 = 100\) squares of 1 mm 2.
- Volume and capacity: Volume units are cubed: cube the length factor.
- Units in problems: Exam questions mix units on purpose.
- Direction: to a smaller unit, multiply; to a bigger unit, divide.
- Length: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
- Area: square the length factor, e.g. \(1\text{ m}^2 = 10\,000\text{ cm}^2\).
- Volume: cube it, e.g. \(1\text{ m}^3 = 1\,000\,000\text{ cm}^3\).
- Capacity: \(1\text{ cm}^3 = 1\) ml, \(1000\text{ cm}^3 = 1\) l, \(1\text{ m}^3 = 1000\) l.
- Mixed units: change everything to one unit before calculating.
One picture every idea returns to
Convert a length first, then square it for area or cube it for volume. Since \(1\text{ m} = 100\text{ cm}\), \(1\text{ m}^2 = 100^2 = 10\,000\text{ cm}^2\) and \(1\text{ m}^3 = 100^3 = 1\,000\,000\text{ cm}^3\). For capacity, \(1\text{ cm}^3 = 1\text{ ml}\) and \(1000\text{ cm}^3 = 1\) litre.
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, Same amount, new units.. Metres, litres and kilograms are easy to swap once you know the multipliers. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 11 min | Teach and check: Length, mass and capacity | In the lab, pick a quantity, type a value and switch between units. Project tab 1 of the lab (Area and perimeter lab, units) and let a student drive it while the class predicts. Model the worked example Big unit to small unit on the board, one line at a time. | Whole class, then pairs |
| 11 to 17 min | Teach and check: Area units are squared | A square of side 1 cm is 10 mm by 10 mm (Fig. 1), so it contains \(10 \times 10 = 100\) squares of 1 mm 2. Model the worked example m² to cm² on the board, one line at a time. Your turn: Convert \(7500\text{ cm}^2\) to \(\text{m}^2\). | Pairs |
| 17 to 23 min | Teach and check: Volume and capacity | Volume units are cubed: cube the length factor. Model the worked example m³ to cm³ on the board, one line at a time. Your turn: Convert \(4500\text{ mm}^3\) to \(\text{cm}^3\). | Pairs |
| 23 to 30 min | Teach and check: Units in problems | Exam questions mix units on purpose. Model the worked example How many glasses? on the board, one line at a time. | Mix-Pair-Share |
| 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, 16 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 Units in problems, 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.
Mix-Pair-Share
Students mix around the room until you call pair; they pair with the nearest classmate, discuss the prompt, then mix again. Three prompts of rising difficulty, three different partners.
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 |
|---|---|
| Check the answer makes sense: 3.75 km is a long walk, so the number of metres must be LARGE (3750), not 0.003 75. | If the number got smaller when you moved to a smaller unit, you divided when you should have multiplied. |
| \(1\text{ m}^2\) is NOT \(100\text{ cm}^2\). | A square metre is 100 cm by 100 cm, which is \(10\,000\text{ cm}^2\). Using 100 is the most common lost mark in this topic. |
| \(1\text{ m}^3\) is 1000 litres, not 100 and not 1 million. | Go through cm 3 if unsure: \(1\,000\,000\text{ cm}^3 \div 1000 = 1000\) litres. |
| When the answer must be a whole number of objects (glasses, bottles, tiles), decide whether to round down (how many can be FILLED) or up (how many are NEEDED). | Do not just round to the nearest. |
Units of measure and conversions: worksheet
6 questions, 16 marks. Written in the style of the papers; no past paper question is reproduced.
Convert (a) 4.7 km to metres (b) 380 g to kilograms (c) 2.05 litres to millilitres.
Convert (a) \(5\text{ m}^2\) to \(\text{cm}^2\) (b) \(830\text{ mm}^2\) to \(\text{cm}^2\).
A container has a volume of \(0.024\text{ m}^3\). Write this volume in (a) \(\text{cm}^3\) (b) litres.
A rectangular carpet measures 3.5 m by 280 cm. Carpet costs $12.50 per square metre.
Calculate the cost of the carpet.
A solid cube has edges of 2 cm. It is cut into small cubes with edges of 2 mm.
How many small cubes are made?
A water tank is a cuboid 1.2 m long, 75 cm wide and 50 cm high. It is full of water.
The water is used to fill bottles that each hold 330 ml.
Calculate the greatest number of bottles that can be completely filled.
Answer key and marking notes
- (a) \(4.7 \times 1000 = 4700\) m
- (b) \(380 \div 1000 = 0.38\) kg
- (c) \(2.05 \times 1000 = 2050\) ml
- (a) \(5 \times 10\,000 = 50\,000\text{ cm}^2\)
- (b) \(830 \div 100 = 8.3\text{ cm}^2\)
- (a) \(0.024 \times 1\,000\,000 = 24\,000\text{ cm}^3\)
- (b) \(24\,000 \div 1000 = 24\) litres
- \(280\text{ cm} = 2.8\text{ m}\).
- Area \(= 3.5 \times 2.8 = 9.8\text{ m}^2\).
- Cost \(= 9.8 \times 12.50 = \$122.50\).
- 2 cm = 20 mm, so each edge holds \(20 \div 2 = 10\) small cubes.
- Number of cubes \(= 10 \times 10 \times 10 = 1000\).
- Same units: 1.2 m = 120 cm.
- Volume \(= 120 \times 75 \times 50 = 450\,000\text{ cm}^3 = 450\,000\) ml.
- \(450\,000 \div 330 = 1363.6...\)
- Only whole bottles count, so round DOWN: 1363 bottles.
6 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.
Convert \(0.68\text{ m}^2\) to \(\text{cm}^2\).
- A\(6800\text{ cm}^2\)
- B\(68\text{ cm}^2\)
- C\(680\text{ cm}^2\)
- D\(680\,000\text{ cm}^2\)
Convert \(25\,000\text{ mm}^3\) to \(\text{cm}^3\).
- A\(25\text{ cm}^3\)
- B\(2500\text{ cm}^3\)
- C\(250\text{ cm}^3\)
- D\(25\,000\,000\text{ cm}^3\)
A carton holds 1.8 litres of milk. How many cups, each holding 120 ml, can be filled from the carton?
- A15
- B0.015
- C1.5
- D216
A rectangular floor measures 4.5 m by 320 cm. What is its area in \(\text{m}^2\)?
- A\(14.4\text{ m}^2\)
- B\(1440\text{ m}^2\)
- C\(144\text{ m}^2\)
- D\(1.44\text{ m}^2\)
A water tank is a cube with edges of 1.5 m. How many litres does it hold when full?
- A3375 litres
- B337.5 litres
- C3 375 000 litres
- D3.375 litres
A rectangular board measures 1.2 m by 80 cm. It is covered exactly, with no gaps, by square stickers of side 4 cm. How many stickers are used?
- A600
- B6
- C60
- D6000
Quiz key
\(1\text{ m}^2 = 100 \times 100 = 10\,000\text{ cm}^2\), so \(0.68 \times 10\,000 = 6800\text{ cm}^2\). The tempting \(68\text{ cm}^2\) uses \(1\text{ m}^2 = 100\text{ cm}^2\), converting like a length. 680 uses 1000, and 680 000 uses the cubic factor \(1\,000\,000\).
\(1\text{ cm}^3 = 10^3 = 1000\text{ mm}^3\). Centimetres cubed are bigger, so divide: \(25\,000 \div 1000 = 25\text{ cm}^3\). The tempting 2500 divides by 10 (the length factor) and 250 divides by 100 (the area factor). 25 000 000 multiplies when it should divide.
\(1.8\text{ l} = 1.8 \times 1000 = 1800\text{ ml}\), and \(1800 \div 120 = 15\) cups. The tempting 0.015 divides 1.8 by 120 without converting the litres. 1.5 uses 1 litre = 100 ml, and 216 multiplies instead of dividing.
\(320\text{ cm} = 3.2\text{ m}\), so area \(= 4.5 \times 3.2 = 14.4\text{ m}^2\). The tempting 1440 multiplies 4.5 by 320 with mixed units. 144 comes from working in cm2 (\(450 \times 320 = 144\,000\)) and dividing by 1000 instead of \(10\,000\); 1.44 divides by \(100\,000\).
Volume \(= 1.5^3 = 3.375\text{ m}^3\). Since \(1\text{ m}^3 = 1\,000\,000\text{ cm}^3 = 1000\) litres, the tank holds \(3.375 \times 1000 = 3375\) litres. The tempting 337.5 uses \(1\text{ m}^3 = 100\) litres. 3 375 000 is the volume in cm3 (ml) with no change to litres, and 3.375 stops at cubic metres.
1.2 m = 120 cm. Along the edges: \(120 \div 4 = 30\) and \(80 \div 4 = 20\), so \(30 \times 20 = 600\) stickers. (Check: \(120 \times 80 = 9600\text{ cm}^2\), and \(9600 \div 16 = 600\).) The tempting 6 comes from finding the area as \(0.96\text{ m}^2\) and using \(1\text{ m}^2 = 100\text{ cm}^2\): \(96 \div 16 = 6\). 60 uses 1000 and 6000 uses \(100\,000\) for the area factor.
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.