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These are the topics related to the standard: Apply and extend previous understandings of numbers to the system of rational numbers."

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

- Decimal Plus Practise mental and written methods for adding and subtracting decimal numbers.
- Decimal Products Find two decimal numbers that add up to exactly one. What is the product of these two decimals?
- Decimal Times Practise mental and written methods for multiplying and dividing decimal numbers.
- Fraction Line Arrange the fractions in order from smallest to largest.
- Fractions A series of self-marking exercises on adding, subtracting, multiplying and dividing fractions.
- Fractions, Decimals, Percentages An exercise on converting fractions to decimals, decimals to percentages and percentages to fractions.

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

- 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.
- Fractions A fraction is a part of a number. Fractions are either vulgar or decimal. Vulgar fractions can be proper, improper or mixed. Equivalent fractions have the same value. Pupils, at all stages of their learning, should practise using fractions. From dealing with halves, the most basic fraction, to manipulating algebraic fractions containing surds, this topic is always relevant. Proficiency also depends on reasonable numeracy skills particularly the multiplication tables and finding the lowest common multiple of two numbers. Pupils also need to be able to convert vulgar fractions to decimals and percentages and vice versa. Be wary of teaching the 'rules' for manipulation fractions by rote. Pupils need to understand the reason why and the time-honoured key to understanding starts with the imaginary pizza and the much-used fraction wall.
- Negative Numbers A negative number is a real number that is less than zero. Such numbers are often used to represent the amount of a loss or absence. For example, a debt that is owed may be thought of as a negative asset, or a decrease in some quantity may be thought of as a negative increase. Negative numbers are also used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. Here are some activities designed to strengthen a pupil's understanding of negative numbers.