A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure.

Problem solving with estimation and rounding

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

Overestimating vs underestimating

Rounding errors

Inequality notation to express error

Using inequality notation for errors in calculations

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

Work out an estimate for the area of the shape.

Here is a grassed garden with a summer house in the centre. Using estimation and rounding, estimate the area of the grass.

A piece of string was 32 cm measured to the nearest cm. A length of 5.6 cm (to 1 d.p) was cut off. What is the error interval for the remaining length $$x$$ cm?

critical thinking and well calculated estimates using data or information

openness of answers and flexibility so answers can be achieved in different ways

an appreciation there are a range of answers, the focus is on the working out

random guesses but use estimation and or rounding

Complete the statement. Fermi problems encourage:

Fermi problem : How long will it take to count to 1 million (without breaks, sleep, etc)?

Fermi problem : If you put 1 million pound coins in a box, what is the volume of the box in m³ ?

A degree of accuracy shows how precise a {{}} or measurement is. For example, to the nearest cm, nearest 10, 1 s.f. and so on. 

Alex buys paper £4.95, USB £$$\square$$, stamps £5.20, crisps £0.95, staples £1.10 and plug £1.99. He pays with a £20 note and receives about £2 back in change. Estimate the cost of the USB.

An error interval for a number $$y$$ shows the range of possible values of $$y$$. It is written as: 

When a number, $$x$$, is rounded to the nearest integer the result is 88. Identify the error interval.

A triangle has lengths 3.5 cm (2 s.f), 4.1 cm (2 s.f) and 4.8 cm (2 s.f). Write the error interval for the perimeter $$p$$ of the triangle.

A square has lengths in centimetres to 1 decimal place. The error interval of the area of the square is $$17.2225 \leq  x <18.0625 $$. Work out the length of the square to 1 d.p.

Starter Quiz

A degree of accuracy shows how precise a or measurement is. For example, to the nearest cm, nearest 10, 1 s.f. and so on.