Making connections to other topics within Key Stage 3

Algebra

There are strong connections with substituting into expressions and formulae and in manipulation of algebraic expressions.

Ratio, proportion and rates of change

Pupils will be required to use and apply number skills in fractions, percentages and decimals to solve problems involving ratio, proportion and rates of change.

Geometry and measures

Pupils will be required to use and apply number skills in fractions, percentages and decimals to solve problems involving calculating, angles, lengths, areas, perimeters and volumes.

Probability and Statistics

There is a strong connection with how to use and apply number skills in fractions, percentages and decimals less than 1 to solve problems involving probability.

Making connections to this topic in Year 6

In year 6 pupils will have used and applied number in a range of contexts:

Notes and guidance on number - addition, subtraction, multiplication and division (non-statutory) suggest:

Pupils practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division

They undertake mental calculations with increasingly large numbers and more complex calculations

Pupils continue to use all the multiplication tables to calculate mathematical statements in order to maintain their fluency

Pupils round answers to a specified degree of accuracy, for example, to the nearest 10, 20, 50 etc., but not to a specified number of significant figures

Pupils explore the order of operations using brackets; for example, 2+1 × 3 = 5 and (2+1) × 3 = 9

Common factors can be related to finding equivalent fractions

Notes and guidance on number - fractions (decimals and percentages) (non-statutory) suggest:

Pupils should practise, use and understand the addition and subtraction of fractions with different denominators by identifying equivalent fractions with the same denominator. They should start with fractions where the denominator of one fraction is a multiple of the other (for example, 12 + 18 = 58) and progress to varied and increasingly complex problems.

Pupils should use a variety of images to support their understanding of multiplication with fractions. This follows earlier work about fractions as operators (fractions of), as numbers, and as equal parts of objects, for example, as parts of a rectangle.

Pupils use their understanding of the relationship between unit fractions and division to work backwards by multiplying a quantity that represents a unit fraction to find the whole quantity (for example, if 14 of a length is 36cm, then the whole length is 36 × 4 = 144cm).

They practise calculations with simple fractions and decimal fraction equivalents to aid fluency, including listing equivalent fractions to identify fractions with common denominators.

Pupils can explore and make conjectures about converting a simple fraction to a decimal fraction (for example, 3 ÷ 8 = 0.375). For simple fractions with recurring decimal equivalents, pupils learn about rounding the decimal to three decimal places, or other appropriate approximations depending on the context. Pupils multiply and divide numbers with up to two decimal places by one-digit and two-digit whole numbers. Pupils multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money.

Pupils are introduced to the division of decimal numbers by one-digit whole number, initially, in practical contexts involving measures and money. They recognise division calculations as the inverse of multiplication.

Pupils also develop their skills of rounding and estimating as a means of predicting and checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy and checking the reasonableness of their answers.

Cross-curricular and real life connections

Opportunities for practising number skills occur in almost all other subjects. Science and the Social Scientists are the most obvious ones in the processing of data (including time, money, weights, areas, numbers of people); but there is much in Foreign Languages (converting currencies, arising in stories), PE (looking at distances run, averaging scores, times for different activities).

Night train from Teachers TV illustrates maths in real life. The twelve maths sequences were filmed on a sleeper train and include how fast and how far does the train travel, how much food is carried, how many sheets are there, how do the carriages get cleaned, and is that bed really big enough? Each sequence poses a question intended to stimulate mathematical discussion rather than to elicit a correct answer to a computation.

In the hotel from Teachers TV illustrates maths in real life. Mathematic sequences from behind the scenes at a London hotel. Each sequence poses a question intended to stimulate mathematical discussion rather than to elicit a correct answer to a computation. The mathematical content rewards repeated viewing and provides a rich source of mathematical imagery.

Cricket match from Teachers TV illustrates maths in real life. Ten maths sequences filmed during a cricket match which encourage pupils to think mathematically. Cricket is a game based on numbers and maths, offering questions about how fast a ball travels, how high, what the score is, and why cricket pitches are often oval.