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      Converting between other compound measures

      Lesson details

      Learning outcome

      I can convert between other compound measures.

      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.

      Teacher tip

      "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.

      Licence

      This content is © Oak National Academy Limited (2025), 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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      Prior knowledge starter quiz

      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$$^3$$


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