New
New
Year 11
Higher

Converting between other compound measures

I can convert between other compound measures.

New
New
Year 11
Higher

Converting between other compound measures

I can convert between other compound measures.

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Lesson details

Key learning points

  1. The units for density can be converted to alternative units.
  2. The units for pressure can be converted to alternative units.

Keywords

  • Pressure - Pressure is the perpendicular force applied to the surface of an object per unit area over which that force is distributed.

  • Density - The density of a substance is measured as the substance's mass per unit of volume.

Common misconception

Pupils understand they multiply by 100 when converting m to cm, but when converting m^2 to cm^2, fail to recognise the need to multiply by 100^2. This is also the same with volume conversions.

Illustrate a 1m^2 square and the equivalent 100cm^2 square, calculating the area and allowing pupils to see the equivalence of 1 m^2 = 10 000 cm^2. Also apply this to a 1m^3 and 100cm^3, thus allowing students to see 1m^2 = 100 000 cm^3.

"What is heavier, 1kg of feathers or 1 kg of gold?" Pupils should know they are both the same mass, but discuss WHY other pupils make a mistake? It is because they visualise the 1kg of feathers to be larger. The inverse proportional relationship between volume and mass is fundamental in density.
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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6 Questions

Q1.
What is volume?
The amount of space occupied by an open 3D shape.
The amount of space occupied by a closed 2D shape.
Correct answer: The amount of space occupied by a closed 3D shape.
The amount of space occupied by an open 3D shape.
Space
Q2.
A square has a length of 12 cm. What is this length in mm?
Correct answer: 120 mm
1200 mm
0.12 mm
1.2 mm
Q3.
A square has lengths 12 m. What is this length in cm?
120 000 cm
1.2 cm
120 m
Correct answer: 1200 cm
Q4.
Match the volumes with the following cubes or cuboids.
Correct Answer:27 cm$$^3$$,A 3 cm by 3 cm by 3 cm cube.

A 3 cm by 3 cm by 3 cm cube.

Correct Answer:8 cm$$^3$$,A 2 cm by 2 cm by 2 cm cube.

A 2 cm by 2 cm by 2 cm cube.

Correct Answer:1 000 cm$$^3$$,A 10 cm by 10 cm by 10 cm cube.

A 10 cm by 10 cm by 10 cm cube.

Correct Answer:6 cm$$^3$$,A 1 cm by 2 cm by 3 cm cuboid.

A 1 cm by 2 cm by 3 cm cuboid.

Correct Answer:9 cm$$^3$$,A 2 cm by 4.5 cm by 1 cm cuboid.

A 2 cm by 4.5 cm by 1 cm cuboid.

Q5.
Match the lengths of the cubes with the volume.
Correct Answer:Cube with length 4 cm,Volume of cube = 64 cm$$^3$$

Volume of cube = 64 cm$$^3$$

Correct Answer:Cube with length 3 cm,Volume of cube = 27 cm$$^3$$

Volume of cube = 27 cm$$^3$$

Correct Answer:Cube with length 5 cm,Volume of cube = 125 cm$$^3$$

Volume of cube = 125 cm$$^3$$

Correct Answer:Cube with length 1 mm,Volume of cube = 1 mm$$^3$$

Volume of cube = 1 mm$$^3$$

Correct Answer:Cube with length 4 mm,Volume of cube = 64 mm$$^3$$

Volume of cube = 64 mm$$^3$$

Q6.
If the volume of a cube is given as the expression 27$$x^3$$. What is the length of the cube in terms of $$x$$?
Correct Answer: 3x, 3 x

6 Questions

Q1.
The length of a square is 4 cm. Work out the area of the square in mm.
16 cm$$^2$$
160 mm$$^2$$
Correct answer: 1600 mm$$^2$$
16 000 mm$$^2$$
Q2.
Match the equivalent areas with the different units of measure.
Correct Answer:2 cm$$^2$$,200 mm$$^2$$

200 mm$$^2$$

Correct Answer:2 m$$^2$$,20 000 cm$$^2$$

20 000 cm$$^2$$

Correct Answer:2 km$$^2$$,2 000 000 m$$^2$$

2 000 000 m$$^2$$

Correct Answer:2 000 000 mm$$^2$$,2 m$$^2$$

2 m$$^2$$

Q3.
Match the equivalent volumes with the different units of measure.
Correct Answer:6 cm$$^3$$,6 000 mm$$^3$$

6 000 mm$$^3$$

Correct Answer:6 000 000 cm$$^3$$,6 m$$^3$$

6 m$$^3$$

Correct Answer:6 km$$^3$$,6 000 000 000 m$$^3$$

6 000 000 000 m$$^3$$

Correct Answer:60 cm$$^3$$,60 000 mm$$^3$$

60 000 mm$$^3$$

Correct Answer:6 m$$^3$$,6 000 000 000 mm$$^3$$

6 000 000 000 mm$$^3$$

Q4.
Put the following in order of density, put the cube with the biggest density at the top.
1 - Cube Z has a mass = 9 kg and a volume of 360 cm $$^3$$
2 - Cube W has a mass = 3.5 kg and a volume = 700 cm $$^3$$
3 - Cube X has a mass = 4 g and a volume = 0.05 m$$^3$$
4 - Cube Y has a mass = 2000 g and a volume = 80 000 cm$$^3$$
Q5.
There are two cubes with the same mass, but different lengths. Cube A has lengths 4 cm and Cube B has lengths 8 cm. Which of the following is true?
The densities are the same because the masses are the same.
The density of Cube B will be half the density of Cube A.
The density of Cube A will be half the density of Cube B.
Correct answer: The density of Cube A will be 8 times the density of Cube B.
The density of Cube B will be 8 times the density of Cube A.
Q6.
A box has density given a mass of $$M$$ kg and a volume $$V$$ m$$^3$$. The same box has a pressure as a result of a force of $$N$$ newtons applied to an area of $$A$$ m$$^2$$. Match the statements.
Correct Answer:This doubles the density.,Mass = $$M$$ kg and the Volume = $$\frac{1}{2} V$$ m$$^3$$

Mass = $$M$$ kg and the Volume = $$\frac{1}{2} V$$ m$$^3$$

Correct Answer:This halves the density.,Mass = $$M$$ kg and the Volume = $$2 V$$ m$$^3$$

Mass = $$M$$ kg and the Volume = $$2 V$$ m$$^3$$

Correct Answer:This quadruples the pressure. ,Force = $$4 N$$ newtons is applied to an an Area = $$A$$ m$$^2$$

Force = $$4 N$$ newtons is applied to an an Area = $$A$$ m$$^2$$

Correct Answer:This quarters the pressure.,Force = $$N$$ newtons is applied to an an Area = $$4A$$ m$$^3$$

Force = $$N$$ newtons is applied to an an Area = $$4A$$ m$$^3$$