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Compound Measures builds on ratio by treating speed, density and pressure as one quantity divided by another. This unit develops the skill of keeping the units matched to the calculation.
Students convert clock times, read a distance-time graph, and use speed as distance divided by time, including a journey in two stages. They then find density and pressure, and convert a speed between metres per second and kilometres per hour.
By the end of this unit students will be able to:
Students should be secure with the following before beginning this unit.
2:30 p.m. is 14:30. A duration of 1 hour 30 minutes is 1.5 hours. Writing 1.30 hours treats 30 minutes as 30 hundredths of an hour.
On a distance-time graph the vertical change is the distance and the horizontal change is the time. A horizontal section means the object is still. A steeper section is faster. The speed on one section is not the average speed for the whole journey.
Speed equals distance divided by time. Distance equals speed multiplied by time. Time equals distance divided by speed. Kilometres with hours gives kilometres per hour. For a two-stage journey, use the total distance and the total time. The mean of the two speeds is not the average speed unless the times are equal.
Density equals mass divided by volume. A heavier object is not denser if it is also larger. Pressure equals force divided by area. The same force on a smaller area gives a greater pressure. Change metres per second to kilometres per hour by multiplying by 3.6, because 1 metre per second is 3.6 kilometres per hour.
| Misconception | Teaching focus |
|---|---|
| Writing 1 hour 20 minutes as 1.20 hours. | 20 minutes is 20/60 of an hour. The decimal is about 1.33 hours, not 1.20. |
| Reading a horizontal section of a distance-time graph as a distance of zero. | The gradient is zero, so the speed is zero. The distance stays at the height of that line. |
| Averaging the two speeds on a two-stage journey. | Add the distances and add the times, then divide. That is the average speed for the whole journey. |
| Using the mass as the density, or the force as the pressure. | Density needs mass and volume. Pressure needs force and area. Write the formula before substituting. |
| Multiplying by 3.6 when changing km/h into m/s. | A speed in m/s is the smaller number, so divide by 3.6. Multiply by 3.6 only when changing m/s into km/h. |
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Students learn to convert between analogue and digital time using the 12 and 24-hour clock.
Later, as learning progresses, they begin to calculate using correct time notation.
Students learn to plot and interpret distance vs time graphs.
Later, as learning progresses, they work out the average speed from a distance vs time graph.
Students learn to calculate speed as a compound measure of distance and time.
Later, as learning progresses, students begin to manipulate the speed, distance and time formula to calculate any measure using the other two.
Students learn how to solve complex problems involving speed, distance and time.
Later, as learning progresses, they model multiple parts of a journey algebraically to set up and solve linear equations.
Students learn how to calculate the density of an object using its volume and mass.
As learning progresses, students use algebraic techniques to calculate the mass or capacity when density is given.
Students learn how to solve problems involving units of speed by converting between metres per second and kilometres per hour. They apply their understanding to calculate time, distance, and speed in a variety of realistic contexts.
Later, as learning progresses, students interpret worded problems, make sensible assumptions, and estimate arrival times using compound measures and time conversions.
Students learn how to find the pressure of an object as a compound measure of force and area.
As learning progresses, students use algebraic techniques to calculate the force or area when the pressure is known.
Students learn to plot and interpret speed versus time graphs.
Later, as learning progresses, they understand how acceleration and retardation correspond to a positive or negative gradient.
Additional practice working with speed, distance and time.
The problem-solving activity challenges students to solve a real-life problem involving two journeys.
👉 Read more: How to solve average speed problems for two-stage journeys
Students are challenged to solve a range of problems involving speed, density, pressure and rates of change.
There are six real-life problem-solving questions based on
Students revise how to calculate density and pressure as compound measures.
Later, as learning progresses, they use density and pressure to solve problems involving the surface area and volume of 3D shapes.
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