GCSE Maths: Rounding, Estimation and Bounds

Accuracy questions look small on a GCSE Mathematics paper but they are everywhere: rounding a final answer, estimating a calculation to check a calculator result, writing an error interval, and, on the Higher tier, working out the largest or smallest possible value of a calculation from rounded measurements. This material trains the measures-and-accuracy content of the GCSE subject content for England.

The quiz has twelve questions. The first part covers rounding to significant figures and decimal places, including leading zeros, a round-up that carries into the previous digit, and trailing zeros that must be kept. Next you estimate a calculation by rounding every number to one significant figure and decide whether an estimate is an overestimate. Three questions ask for error intervals in inequality notation: a length given to one decimal place, a number that was truncated rather than rounded, and a mass rounded to the nearest 10 grams. The Higher-tier questions calculate the upper bound of a sum and of a speed, the lower bound of a difference, and the most accurate value that both bounds of a result agree on. The wrong options come from the usual mistakes: counting leading zeros, including the upper end of an interval, treating truncation as rounding, dividing upper by upper, and subtracting lower from lower.

The flashcards define significant figures, decimal places, truncation, error intervals and degree of accuracy, show upper and lower bounds with a worked example, and set out which bounds to combine for addition, subtraction and division.

The printable written work has eight problems with full working: rounding numbers with awkward zeros, estimating a fraction-style calculation, three error intervals, the bounds of the area of a rectangle, the bounds of an average speed, the bounds of a difference in masses, choosing a sensible accuracy for a quotient, and explaining the difference between truncating and rounding a calculator display.

Rounding, estimation and error intervals are content for both tiers; calculating with bounds is Higher tier, and most of those items are labelled. The material suits Year 10 and Year 11 students, and it is a good warm-up before a calculator paper, where a quick estimate is the best check of a long calculation.

• Round numbers to a given number of decimal places or significant figures
• Estimate calculations by rounding to one significant figure and judge over- or underestimates
• Write error intervals for rounded and truncated values using inequality notation
• Find upper and lower bounds of sums, differences, products and quotients (Higher)
• Choose a suitable degree of accuracy for a result from its bounds (Higher)

Practice material written by Zestly, based on the DfE GCSE mathematics subject content (DFE-00233-2013), Number: measures and accuracy (N14, N15, N16).