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

Using inequality notation for errors in calculations

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

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

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

When a number, $$x$$, is rounded to the nearest integer the result is 35. Select the numbers which complete the error interval for $$x$$: $$\square \leq x <\square$$

A long road is made up of 3 sub roads. The 1st road measures 35 m (2 s.f), the 2nd road is 41 m (2 s.f) and the 3rd road is 48 m (2 s.f). Find the error interval for the length $$x$$ of the long road.

A wall is in an L-shape. All the lengths are given to 1 d.p or the nearest integer. Work out the error interval for the area of the wall.

A square has lengths in cm given to 1 decimal place. The error interval of the perimeter of the square is $$31 \leq  x <31.4 $$. Work out the length of the square correct to 1 d.p.

A square has lengths in cm to 1 decimal place. The error interval of the area of the square is $$30.8025 \leq  x <31.9225 $$. Work out the length of the square to 1 d.p.

The range of values include $$a$$ and $$b$$

The range of values include $$a$$ and not $$b$$

The range of values includes all the numbers strictly in between $$a$$ and $$b$$

The range of values do not include $$a$$ but include $$b$$

An error interval for a number $$x$$ shows the range of possible values of $$x$$. It is written as  $$ a\leq x < b$$. Explain what this means.

When a number, $$x$$, is rounded to the nearest integer the result is 63. Select the numbers which complete the error interval for $$x$$: $$\square \leq x <\square$$

When a number, $$x$$, is rounded to the nearest integer the result is 5. Select the numbers which complete the error interval for $$x$$: $$\square \leq x <\square$$

When a number, $$x$$, is rounded to the nearest integer the result is 10. Select the numbers which complete the error interval for $$x$$: $$\square \leq x <\square$$

Jun is correct as both are the same when rounded to 1 d.p

Jun is correct as both values will be the same when inputting into a calculator.

Jun is incorrect as they have different error intervals.

Jun rounds a number to the nearest integer and the result is 5. Izzy rounds a number to 1 d.p. and the result is 5.0. Jun says, "We must both have rounded the same number." Is Jun correct? 

$$x$$ and $$y$$ are both integers. $$x$$ = 650 (rounded to the nearest 10) and $$y$$ = 800 (rounded to the nearest 100). The greatest possible integer value of $$x+y$$ is {{}}.

Using inequality notation for errors in calculations

Lesson outcome