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

Checking understanding of rounding

Securing understanding of rounding

Rounding to three decimal places

Rounding to any number of decimal places

Rounding integers to one significant figure

Rounding integers to significant figures

Rounding decimals to significant figures

Degrees of accuracy

Estimating numerical calculations

Checking by estimating

Truncating

Rounding errors

Inequality notation to express error

Using inequality notation for errors in calculations

Problem solving with estimation and rounding

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.

This unit helps pupils understand rounding to different decimal places, and significant figures. Pupils will also learn how to truncate numbers and understand the contexts in which these skills are useful. The unit ends will an exploration of rounding and inequality errors.

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 {{}}

Overestimating vs underestimating

Lesson outcome