Lesson 19 Accuracy and errors

# Accuracy and errors

Overview Resources
Activities to explore the approximate nature of measurements. This is carried out first via the context of successive subdivision of a number line and relating this to decimal notation. Then the difference between relative extension and absolute errors in measurement is explored through links to proportionality. Worksheets 1 and 2
Worksheet 3 for extension
Stopwatch
Rulers and tapes with centimetre and millimetre markers
The Cat in the Hat Comes Back (optional)
Continuous variables and their numeric representations.
• Approximation in decimal notation,
• Rational numbers on the number line model,
• Relative and absolute errors in measurements.
• EPISODE 1
How many numbers does this measurement cover?
In a sports’ setting the pupils recognise time measurements as approximate, or rounded. Pupils think of how to ‘un-round’ a measured time like 4.6 seconds to see just what the real time could actually be, using a time line. This then leads them to explore how many numbers there could be between any two points on the number line. A prerequisite is familiarity with decimals. For most groups it is a good idea to start this episode with estimating times, and discussing the lengths of one second and one tenth of a second.
EPISODE 2
How big is the error?
Pupils think of errors as having both an absolute size, which is its measured amount, and a relative size, which is in relation to the main measurement or for its purpose. The trigger for the first discussion is the importance of a 4p error in payment for two very different items. Pupils use their own intuitive knowledge and natural language to approach this distinction.
EPISODE 3 (EXTENSION)
Errors in rounding
Pupils reflect on the use of approximation in everyday life, ie. the acceptable range of errors when rounding to a convenient number of figures. For some pupils this allows an approach to proportionality expressed in percentage terms.

The episode starts with thinking about how appropriate any measurement is for its purpose, and therefore the need to understand accuracy. Then place values of decimals on the number line are used to link measurement work to continuity, through infinite sub-division of any interval on the number line. Then a general model for quantifying errors in relation to the measurement is approached.