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Year 11
Higher

Advanced problem solving with compound measures

I can use my knowledge of compound measures to solve problems.

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New
New
Year 11
Higher

Advanced problem solving with compound measures

I can use my knowledge of compound measures to solve problems.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Average speed cameras are a context involving average speed.
  2. Engineers care about the density of materials.
  3. Divers care about the pressure exerted on them when diving.

Keywords

  • Rate of flow - Rate of flow measures the volume of fluid that passes through a particular pipe/channel per unit of time.

Common misconception

E.g 4.5 hours is 4 hours and 50 minutes

Encouraging pupils to use ratio tables to represent proportional relationships using minutes allows them to appreciate the multiplier of 60 when converting hours to minutes, or minutes to seconds

There has been a push to encourage the UK to turn off running water when brushing teeth. If the average person has a tap running at a rate of 0.2L/s and takes 2 minutes to brush their teeth, how much water is wasted for this person? How much would be wasted if 50 million people do this every day?
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
The amount of space occupied by a closed 3D shape is known as __________.
Correct answer: volume
area
surface area
capacity
vacuum
Q2.
Work out the volume of a cuboid with a length of 20 cm, width of 80 cm and a height of 10 cm. Give your answer in cm$$^3$$.
1600 cm$$^3$$
16 000 000 cm$$^3$$
Correct answer: 16 000 cm$$^3$$
160 cm$$^3$$
Q3.
How many cm$$^3$$ are in 1 litre?
Correct Answer: 1000, one thousand, 1000 cm^3
Q4.
How many litres are in 1 m$$^3$$?
Correct Answer: 1000, 1000 L, 1000 litres
Q5.
Put the following volumes in descending order, the largest volume at the top and the smallest at the bottom.
1 - A cube with lengths = 0.15 m
2 - A triangular prism with base = 120 mm, height = 240 mm and length = 200 mm
3 - A cuboid of length = 8 cm, width = 9 cm and height = 0.1 m
4 - A trapezium faced prism h = 4 cm, parallel lengths = 5cm & 3cm and depth = 0.4 m
Q6.
A car travels at 36 mph for 20 minutes, then for 42 mph for 10 minutes. Find the average speed for the whole journey. Give your answer in mph.
Correct Answer: 38, 38 mph

Exit quiz

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6 Questions

Q1.
__________ measures the volume of fluid that passes through a particular pipe/channel per unit of time.
Correct answer: Rate of flow
Rate of speed
Rate of time
Rate of volume
Rate of rate
Q2.
Match the correct unit with the correct statement.
Correct Answer:1 m$$^3$$/h ,A flow of 1 m$$^3$$ per 1 hour.

A flow of 1 m$$^3$$ per 1 hour.

Correct Answer:1 L/s,A flow of 1 L per 1 hour.

A flow of 1 L per 1 hour.

Correct Answer:1 cm$$^3$$/s,A flow of 1 cm$$^3$$ per 1 second.

A flow of 1 cm$$^3$$ per 1 second.

Correct Answer:1 m$$^3$$/s,A flow of 1 m$$^3$$ per 1 second.

A flow of 1 m$$^3$$ per 1 second.

Correct Answer:1 L/h,A flow of 1 L per 1 hour.

A flow of 1 L per 1 hour.

Q3.
This cuboid was full of water and then is empty after 2 hours. The lengths of the cuboid are 40 cm by 20 cm by 30 cm. Work out the rate of flow and give the answer in cm$$^3$$ per minute.
Correct Answer: 200
Q4.
A swimming pool is in the shape of a cuboid with lengths 5 m by 8 m by 1.2 m. The hose pumps water at a constant rate of 2 L per second. Work out how many hours it will take to fill the pool.
24 000 hours
4000 hours
Correct answer: 6.67 hours (2 d.p.)
1.1 hour (1 d.p.)
3.34 hours (2 d.p.)
Q5.
A car travels at a speed of $$4x$$ km/h for 30 minutes and then for $$5x$$ km/h for 90 minutes. Find the average speed of the car.
$$5.75x$$ km/h
$$5.1x$$ km/h
$$4.5x$$ km/h
Correct answer: $$4.75x$$ km/h
Q6.
The mass of Cube A : Cube B is in the ratio 1 : 4. The ratio of the lengths of the cubes is in the ratio of 1 : 4. Which statement is correct?
The densities of Cube A : Cube B is 1 : 4
The densities of Cube A : Cube B is 1 : 10
Correct answer: The densities of Cube A : Cube B is 1 : 16
The densities of Cube A : Cube B is 1 : 64