A range of values where every value in the range estimates to the given value.

An error interval for a number $$x$$ shows the range of possible values of $$x$$.  It is written as an inequality $$a ≤ x < b$$

Inequality notation to express error

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

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

Smallest = $$7.5$$, Largest = $$8.4 \dot 9$$

Smallest = $$7.5$$, Largest = $$8.9 \dot 9$$

Smallest = $$7.5$$, Largest = $$8.5 \dot 9$$

When a number is rounded to the nearest integer the result is 8. Identify the correct range for the unrounded number.

Smallest = $$18.5$$, Largest = $$19.5 \dot 9$$

Smallest = $$18.5$$, Largest = $$19.4 \dot 9$$

When a number is rounded to the nearest integer the result is 19. Identify the correct range for the unrounded number.

When a number, $$x$$, is rounded to the nearest integer the result is 8. Identify the error interval for $$x$$.

When a number, $$x$$, is rounded to 2 significant figures the result is 7.8. Identify the error interval for $$x$$.

A distance $$x$$ km is given as 2.345 km correct to the nearest metre. Identify the error interval for $$x$$.

Which of the following is not an integer?

Smallest integer = 514, largest integer = 525

Smallest integer = 514, largest integer = 524

Smallest integer = 515, largest integer = 525

Smallest integer = 515, largest integer = 524

State the smallest and largest integers that round to 520 when rounded to the nearest 10.

Smallest integer = 3849, largest integer = 3949

Smallest integer = 3850, largest integer = 3949

Smallest integer = 3850, largest integer = 3950

Smallest integer = 3855, largest integer = 3950

State the smallest and largest integers that round to 3900 when rounded to the nearest 100.

When does 0.4999999 NOT round to give 0.5?

Work out 3.4 km + 348 m + 6000 cm. Give your answer in metres.

Work out 0.05 km + 6.32 m + 123 cm. Give your answer in centimetres.

Inequality notation to express error

Lesson outcome