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

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

Converting between other compound measures

Maths

Checking and further securing understanding of direct proportion in context

Compound measures for speed

Compound measures for density

Compound measures for pressure

Converting between metric speed measures

Converting between metric and imperial speed measures

Combining speeds

Combining densities

Advanced problem solving with compound measures

In this unit, pupils will be exploring the multiplicative relationship between different compound measures. Ratio will be one of the ways in which this is explored and the skills from the prior unit will aid understanding. There are also links to the volume units as volume is required for the density formula.

In this unit, pupils explore the multiplicative relationship between different compound meaures and units such as speed, rates of pay, density and pressure.

Compound measures

The length of a square is 4 cm. Work out the area of the square in mm.

Match the equivalent areas with the different units of measure.

Match the equivalent volumes with the different units of measure.

Cube Z has a mass = 9 kg and a volume of 360 cm $$^3$$

Cube W has a mass = 3.5 kg and a volume = 700 cm $$^3$$

Cube X has a mass = 4 g and a volume = 0.05 m$$^3$$

Cube Y has a mass = 2000 g and a volume = 80 000 cm$$^3$$

Put the following in order of density, put the cube with the biggest density at the top.

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.

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.

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?

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

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

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

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

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.

The amount of space occupied by an open 3D shape. 

The amount of space occupied by a closed 2D shape. 

The amount of space occupied by a closed 3D shape. 

A square has a length of 12 cm. What is this length in mm?

A square has lengths 12 m. What is this length in cm?

Match the volumes with the following cubes or cuboids. 

Match the lengths of the cubes with the volume.

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

Converting between other compound measures

Lesson outcome