Estimations and Limits of Accuracy

Scheme of work: GCSE Higher: Year 10: Term 2: Estimations and Limits of Accuracy

Recognise the value of a digit using the place value table.
Round numbers to the nearest integer or given degree of accuracy not including decimal place or significant figure
Calculate square numbers up to 12 x 12.

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
Estimate answers; check calculations using approximation and estimation, including answers obtained using technology
Use inequality notation to specify simple error intervals due to truncation or rounding
Apply and interpret limits of accuracy, including upper and lower bounds

When rounding to the nearest ten, decimal place or significant figure students need to visualise the value at a position along the number line. For instance, 37 to the nearest 10 rounds to 40 and 5.62 to 1 decimal place rounds to 5.6.
When a value is exactly halfway, for instance 15 to the nearest 10, by definition it is rounded up to 20.
To estimate a solution it is necessary to round values to 1 significant figure in the first instance. However, students need to apply their knowledge of square numbers when estimating roots.

When rounding to a significant figure the values that are less significant become zero rather than being omitted. For instance, 435 to 1 s.f. becomes 400 rather than 4.
Students often have difficulty calculating the upper bound of a rounded value. For instance the upper bound for a number rounded to the nearest 10 as 20 is 25 not 24.999.
When using inequality notation to describe the limits of accuracy there can be confusion with the direction of the symbols.
Students often have difficulty knowing which bound to use when calculating the limits of accuracy for division and subtraction problems.