New
New
Year 11
•
Foundation
Problem solving with compound measures
I can use my knowledge of compound measures to solve problems.
New
New
Year 11
•
Foundation
Problem solving with compound measures
I can use my knowledge of compound measures to solve problems.
Lesson details
Key learning points
- Average speed cameras are a context involving average speed.
- Engineers care about the density of materials.
- 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
volume
area
surface area
capacity
vacuum
Q2.
Which of the following shows the volume of a cuboid with a length of 20 cm, width of 80 cm and a height of 10 cm?
1600 cm$$^3$$
16 000 000 cm$$^3$$
Correct answer: 16 000 cm$$^3$$
16 000 cm$$^3$$
160 cm$$^3$$
Q3.
How many cm$$^3$$ are in 1 litre?
Correct Answer: 1000, one thousand, 1000 cm^3
1000, one thousand, 1000 cm^3
Q4.
How many litres are in 1 m$$^3$$?
Correct Answer: 1000, 1000L, 1000 litres
1000, 1000L, 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
1
- A cube with lengths = 0.15 m
2 - A triangular prism with base = 12 cm, height = 24 cm and length = 20 cm
2
- A triangular prism with base = 12 cm, height = 24 cm and length = 20 cm
3 - A cuboid of length = 8 cm, width = 9 cm and height = 10 cm
3
- A cuboid of length = 8 cm, width = 9 cm and height = 10 cm
4 - A trapezium faced prism h = 4 cm, parallel lengths = 5cm & 3cm and depth = 40 cm
4
- A trapezium faced prism h = 4 cm, parallel lengths = 5cm & 3cm and depth = 40 cm
Q6.
A cylinder has a radius of 12 cm and a height of 1.3 m. Work out the volume of the cylinder in cm $$^3$$. Give your answer to 3 significant figures.
Correct Answer: 58 800, 58 800 cm^3
58 800, 58 800 cm^3
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 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.
1 m$$^3$$/h -
A flow of 1 m$$^3$$ per 1 hour.
Correct Answer:1 L/s,A flow of 1 L per 1 second.
1 L/s -
A flow of 1 L per 1 second.
Correct Answer:1 cm$$^3$$/s,A flow of 1 cm$$^3$$ per 1 second.
1 cm$$^3$$/s -
A flow of 1 cm$$^3$$ per 1 second.
Correct Answer:1 m$$^3$$/s,A flow of 1 m$$^3$$ per 1 second.
1 m$$^3$$/s -
A flow of 1 m$$^3$$ per 1 second.
Correct Answer:1 L/h,A flow of 1 L per 1 hour.
1 L/h -
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
200
Q4.
A swimming pool in the shape of a cuboid has lengths 5 m by 8 m by 1.2 m. The hose pumps water at a constant rate of 2 L per second. How many hours it will take to fill the pool?
24 000 hours
4000 hours
Correct answer: 6.67 hours (2 d.p.)
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. What is the average speed of the car?
$$5.75x$$ km/h
$$5.1x$$ km/h
$$4.5x$$ km/h
Correct answer: $$4.75x$$ km/h
$$4.75x$$ 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. Cube A has a mass of 24 g and a length of 2 cm. 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 : 16
The densities of Cube A : Cube B is 1 : 64