During key stage 3, pupils concentrate on 3 major areas of maths: - Number and algebra.
- Space, shape and measures.
- Handling data.
Throughout all three areas, they are taught how to use and apply mathematics to tackle demanding problems by breaking them into smaller, more manageable tasks. They learn how to explain their reasoning and begin to give mathematical justifications for their solutions.
1. Number and Algebra
Children are taught: - about positive and negative numbers
- about mathematical concepts such as 'factor', 'multiple' and 'prime number'
- about squares, square roots, cubes and cube roots
- about index notation and laws
- how fractions, decimals and percentages relate to each other
- about equivalent fractions
- about ratio and proportion
- how to use brackets and the correct order of operations
- about re-organising calculations to do them efficiently
- how to change simple fractions to decimals or percentages and vice versa
- how to calculate with fractions, decimals and percentages
- how to remember and use facts, such as:
- all the whole number pairs that add to 100
- multiplication tables to 10 x 10
- related division facts
- about estimating answers, rounding numbers and other ways to approach calculations mentally
- how to use standard ways to do written calculation
- how to use a calculator effectively
- making sense of the answers calculators give in terms of the original problem
- the most efficient ways to approach different kinds of problems
- how to check their work
- about giving answers in terms of the original problem and to a suitable level of accuracy
- how to use letter symbols in algebra
- how to set up and use simple equations to solve problems
- various formulae
- about the links between graphs and their equations or functions
- how to solve inequalities
- sequences of numbers and the rules that govern them
- expressing functions in words and symbols
At the end of Key Stage 3 (age 14), most children are able to: - do calculations involving decimals, fractions, percentages, factors, powers and roots in their heads
- multiply and divide any whole number by 10, 100 and other powers of 10
- estimate and approximate answers to calculations
- use standard written methods for addition, subtraction, multiplication and division involving whole numbers, decimals and fractions
- give one number as a percentage or fraction of another
- use efficient methods to add, subtract, multiply and divide fractions
- use the relationships between fractions, decimals, percentages, ratio and proportion to solve problems
- find and use prime factors of numbers
- use calculators efficiently and interpret the display in the context of the problem
- use index notation and simple instances of index laws
- set up and use equations and their graphs to solve word problems
- simplify and transform algebraic expressions, knowing how to substitute positive and ngative numbers for symbols
- generate terms of a sequence and use algebra to describe the nth term of a simple sequence
2. Shape, Space and Measures
Children are taught: - about the properties of angles in certain situations
- about the properties of triangles, rectangles, circles, cubes and other 2- and 3-D shapes
- simple proofs
- how to use Pythagoras' theorem
- about reflections, rotations, enlargements and translations, and how these transformations affect shapes
- about coordinates
- how to use instruments and scales for measuring
- about the approximate nature of all measurements
- how to use appropriate units
- how to convert between one unit and another
- the appropriate metric equivalents of pounds, feet, miles, pints and gallons
- compound measures such as speed and density
- how to use instruments such as rulers, protractors and compasses to construct 2- and 3-D shapes
- how to use formulae to calculate the area and the volume of 2- and 3-D shapes
At the end of Key Stage 3 (age 14), most children are able to: - use a ruler, protractor and compasses to construct lines, angles and two-dimensional or three-dimensional shapes
- use the properties of straight-sided shapes, and intersecting and parallel lines, to solve problems
- recognise when two triangles are congruent
- rotate, reflect, translate and enlarge 2-D shapes and understand how these transformations affect their sides, angles and position
- know and use formulae to calculate:
- areas of straight-sided shapes
- the circumferences and areas of circles
- volumes of cuboids
- use 2-D diagrams to analyse 3-D shapes
- write instructions for a computer to generate and transform shapes and paths
3. Handling Data
Children are taught how to: - identify questions that can be answered by observing and experimenting
- decide what data they need to collect to solve problems
- plan what information they need to ensure results are fair and representative
- carry out experiments and tests
- gather data in different ways
- present data in different
- relate emerging results to the original questions
- interpret diagrams and graphs to draw conclusions
- compare different sets of observations
- evaluate and check results
At the end of Key Stage 3 (age 14), most children are able to: - design a survey or experiment
- gather the data they need from different sources
- summarise raw data using range and measures of average
- choose the right kind of graph to show the data they have gathered
- interpret diagrams and graphs and draw conclusions
- calculate probabilities and solve problems in situations where there are limited numbers of equally likely outcomes (for example, when rolling a dice)
- estimate probabilities from data gathered in experiments.
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