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These are the Transum resources related to the statement: "Pupils should be taught to use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x≤b".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Rounding Ten Round the numbers to the nearest whole number or the given power of ten.
- Rounding Video A reminder of how to round numbers to significant figures, decimal places and to the nearest power of ten.
- Rounding DP A self marking exercise requiring students to round numbers to a given number of decimal places.
- Rounding SF A self marking exercise requiring students to round numbers to a given number of significant figures.
- Rounding Snap If the last card put down equals the previous card to the nearest whole number then all players race to shout SNAP!
- Rough Answers An exercise on rounding values in a calculation to find an approximate estimate of the answer.
- Upper and Lower Bounds Video A reminder of how to find the limits of accuracy of rounded values.
- Upper and Lower Bounds Determine the upper and lower bounds when rounding or truncating quantities used in calculations.

Here are some exam-style questions on this statement:

- "
*A number, \(n\), when rounded to two decimal places is 7.32*" ... more - "
*The height of a tree is 9 metres to the nearest metre.*" ... more - "
*(a) Work out an estimate for the value of \( \sqrt{48.3 \times 82.01}\).*" ... more - "
*Ralph used his calculator to work out the value of C, the circumference of a circle. Unfortunately he put his banana down on his desk so that it covered most of the calculator screen. All that can be seen are the first two digits of the answer.*" ... more - "
*(a) Calculate the upper bound for the value of A giving your answer correct to 6 significant figures if:*" ... more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Approximation Approximating a quantity is often to get a value that is easier to use or understand, at the cost of making it less precise. This approximation is very important in dealing with answers to mathematical problems and making them relevant to the real world. Rounding to a given number of decimal places or significant figures is required of pupils. The error introduced when approximating a value may be further magnified with subsequent calculations. Understanding this error and how it can be minimised is another important aspect of this topic. See also the "Rounding" and "Estimating" Topic pages.
- Estimating The ability to estimate values is an often overlooked part of Mathematics. Estimating lengths, weights, time, angles and solutions to problems should be practised regularly. Pupils should make sensible estimates of a range of measures in relation to everyday situations. A basic ability to estimate quantities without counting, like when choosing a checkout line at the supermarket, can be called a person’s innate ‘number sense’. Practising this kind of estimating may actually improve a pupil’s ability in other areas of mathematics. This is one of the findings of research published in Psychological Science, a journal of the Association for Psychological Science. Practising estimation can be a lot of fun when presented as a game, challenge or group activity and provides the opportunity for the teacher to introduce variety in the mathematics classroom.
- Rounding The objective of rounding is often to get a number that is easier to use, at the cost of making it less precise. This approximation is very important in dealing with answers to mathematical problems and making them relevant to the real world. Rounding to a given number of decimal places or significant figures is required of pupils. See also the "Approximating" Starters. Once the principles of rounding have been understood, a fun way to practise the skills is to play "Rounding Snap".

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