# Compound Measures

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.

##### Prerequisite Knowledge

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.)

##### Success Criteria
• 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

##### Key Concepts
• 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.

##### Common Misconceptions
• 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.

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