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These are the topics related to the standard: Know that there are numbers that are not rational, and approximate them by rational numbers."

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

- Fraction Order Arrange the fractions and decimals in order from smallest to largest.
- Number Systems Place the numbers in the correct sets in this concentric circles Venn diagram.

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.
- Decimals Working with decimals, for most pupils, presents little difficulty if the pupils have confidence working with whole numbers. The topic of decimals provides an extension to the place value system with the addition of tenths, hundredths, thousandths etc. For many pen and paper multiplication and division calculations the decimal numbers can be considered as whole numbers then the answers adjusted accordingly. So 2.4 x 2.34 can be considered as 24 x 234 รท 1000. The numbers are multiplied by ten and one hundred respectively then the answer needs to be divided by the ten and one hundred to compensate. Pupils should use their understanding of place value to round decimal numbers. They should also use decimal numbers in the context of measures and money. This topic also contains activities which encourage pupils to investigate and explore the properties of decimal numbers and gain a better understanding of them.
- 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".