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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.

May 1, 2019

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson. I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making. When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback. […]

April 17, 2019

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]

March 26, 2019

Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]