AQA · GCSE · Mathematics
Course version: 8300 · Version from Sept 2015
Measures and accuracy: estimate answers check calculations using approximation and estimation, including answers obtained using technology
This skill means rounding numbers to convenient values to estimate an answer, then using that estimate to check whether a calculation—including one done on a calculator or other technology—is…
Study notes
From the checked teaching notes for this specification point.
The idea
This skill means rounding numbers to convenient values to estimate an answer, then using that estimate to check whether a calculation—including one done on a calculator or other technology—is reasonable. For example, to estimate 4.87 × 3.12, round to 5 × 3 = 15; if a calculator shows 151.944, the estimate shows the decimal point is misplaced. You should also check answers obtained using technology by comparing the display with a mental or written approximation, and by considering whether the size and unit of the answer make sense in context.
What earns the marks
- Rounds numbers to one significant figure or to convenient values to form an estimate, for example 19.8 ÷ 4.1 ≈ 20 ÷ 4 = 5.
- Uses the estimate to check whether an exact or technology-obtained answer is reasonable, identifying errors such as a misplaced decimal point.
- Checks answers obtained using technology by comparing the display with an approximation and by considering the context and units.
- Selects the most appropriate estimated value from options, rejecting values that are not consistent with the approximation.
Common mistakes and how to put them right
Rounding each number in a way that changes the operation, for example estimating 8.2 × 0.49 as 8 × 0 = 0.
Put it right by rounding 0.49 to 0.5, giving 8 × 0.5 = 4.
Accepting a calculator display without checking, for example 3.6 × 2.5 shown as 90.
Put it right by estimating 4 × 2.5 = 10, so the display is ten times too large.
Estimating with too much precision, such as rounding 4.87 to 4.9 rather than 5.
Put it right by rounding to one significant figure for a quick check.
Exam tips
- Round each number to one significant figure before multiplying or dividing to get a quick estimate.
- Write your estimate down and compare it with the exact or calculator answer; if they differ by a factor of ten or more, recheck the calculation.
- For technology answers, check the units and the size of the number against the context of the question.
Try the lesson
The start of the Measures and accuracy: estimate answers check calculations using approximation and estimation, including answers obtained using technology lesson, made from checked teaching notes for this specification point.
Have a go first
By rounding each number to one significant figure, estimate the value of 38 × 21.
Listen
This skill means rounding numbers to convenient values to estimate an answer, then using that estimate to check whether a calculation—including one done on a calculator or other technology—is reasonable. For example, to estimate 4.87 × 3.12, round to 5 × 3 = 15; if a calculator shows 151.944, the estimate shows the decimal point is misplaced. You should also check answers obtained using technology by comparing the display with a mental or written approximation, and by considering whether the size and unit of the answer make sense in context.
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