An overestimate is an estimate for a calculation which is greater than the exact answer.

An underestimate is an estimate for a calculation which is less than the exact answer.

Overestimating vs underestimating

Maths

In this unit, pupils have learnt how to round to a given number of decimal places or significant figures and explored the effect of using rounded numbers for calculations. In the future unit, pupils will investigate the bounds and perform calculations to determine a best/worst case scenario.

The prior unit on place value allowed pupils to develop the skills needed to estimate and round values. By understanding the value of each digit, pupils can determine what other values are close to the original value. This unit continues the exploration of the infinite nature of sets of numbers.

Estimation and rounding

An __________ is an estimate for a calculation which is greater than the exact answer.

An __________ is an estimate for a calculation which is less than the exact answer.

Match each calculation with a calculation that gives its overestimate.

Perimeter of a square with lengths 7.89 m

Perimeter of a square with lengths 4.67 m

Perimeter of a square with lengths 0.498 m

Match the following calculations which give an overestimated area.

$$\frac{899}{4.40+6.35}\approx\frac{900}{4+6}$$

$$\frac{712}{8.98+9.45}\approx\frac{700}{10+10}$$

$$\frac{37.4}{4.49+6.41}\approx\frac{40}{5+6}$$

Match which calculations are an overestimate, underestimate or hard to tell.

$$\frac{59-42}{3.67+1.23}\approx\frac{60-40}{3+1}$$

$$\frac{59-42}{3.67+1.23}\approx\frac{55-45}{4+2}$$

$$\frac{59-42}{3.67+1.23}\approx\frac{60-50}{4+2}$$

__________ are the digits in a number that contribute to the accuracy of the number.  The first significant figure is the first non-zero digit.

Which of the following are good, quick estimate calculations for 577 ÷ 19.57?

Which of the following are a correct estimate for $${11.239\times3.12}\over{0.488}$$?

Match each calculation to its approximate answer. 

A square plot of grass has a length of 7.88 m (2 d.p). Select the correct estimate for the area of the square grass plot.

Izzy thinks of a number. Truncated to 1 s.f., it is 500. Rounded to the nearest 50, it is 600. It is multiple of 5 and a palindrome . All of its digits are prime numbers. Izzy's number is {{}}

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