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These are the Transum resources related to the statement: "Approximation: decimal places, significant figures. Upper and lower bounds of rounded numbers. Percentage errors. Estimation".

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

- Estimating Estimation is a very important skill. Use this activity to practise and improve your skills.
- Rough Answers An exercise on rounding values in a calculation to find an approximate estimate of the answer.
- 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 Video A reminder of how to round numbers to significant figures, decimal places and to the nearest power of ten.
- Upper and Lower Bounds Determine the upper and lower bounds when rounding or truncating quantities used in calculations.
- Upper and Lower Bounds Video A reminder of how to find the limits of accuracy of rounded values.

Here are some exam-style questions on this statement:

- "
*A number, \(n\), when rounded to two decimal places is 7.32*" ... more - "
*Ayden is marking out the pitch for a ball game in a large field.*" ... more - "
*(a) Use your calculator to evaluate the following expression to five significant figures.*" ... more - "
*Minerva's Revenge, the longest rollercoaster in the Funville Theme Park, takes 95 seconds (to the nearest 5 seconds) to complete one circuit of the 2280 metre long track.*" ... more - "
*(a) Calculate the upper bound for the value of A giving your answer correct to 6 significant figures if:*" ... more - "
*If \( w = 12, x = 45°, y = \frac12 \text{and } z = 14\) calculate:*" ... 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".

These videos on Rounding and Significant Figures and Percentage Error are from Revision Village and are aimed at students taking the IB Maths Standard level course.

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