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Students learn how to calculate speed, density and pressure as compound measures. They apply this knowledge to plot and interpret distance and speed versus time graphs. This topic takes place in Term 4 of Year 10 for Foundation tier and Term 1 Year 10 for Higher. Compound measures follows on from Units of Measure.

know and apply formulae to calculate:

- rectangles
- rectilinear composite shapes
- area of triangles
- volume of cuboids

use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)

- use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
- round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures)
- change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts
- use compound units such as speed, rates of pay, unit pricing, density and pressure

- It is useful to calculate compound measures through the unitary method where ratios are in the form 1 : n.
- Distance – Time graphs can be extended to Speed-Time/Acceleration-Time graphs.
- Use algebraic techniques to manipulate the various formulae so that other measures can also be found.

- Density, pressure and time do not have to have fixed units. For instance a speed can be m/s or mph, density can be g/cm3 or kg/3.
- Students often have difficulty remembering which measure to divide by. The speed, pressure and density triangles are helpful to recall the relationship between the various measures.

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson. Writing Equivalent Ratios A few students immediately go […]