# Does it add up? The new KS3 maths programme of study

The main change in KS3 maths is the increased focus on mathematical reasoning and being able to express mathematical arguments formally. The idea behind these changes is that students are able to develop a clearer understanding of mathematical concepts which will better prepare them for GCSEs and further education.

For the first time, the new maths curriculum specifically mentions the need for teachers to challenge gifted students by offering them richer and more sophisticated problems rather than moving to key stage 4 material. For those who do not grasp mathematical concepts as quickly, the focus will be on enabling them to have additional practice to consolidate their understanding.

Changes have been made within all topics:

### Working Mathematically

Develop fluency

Students should be taught to:

• Extend their understanding of the number system and place value to include decimals, fractions, powers and roots
• Rearrange and simplify expressions

Reason mathematically

Students should be taught to:

• Make and test conjectures about patterns and relationships; look for proof and counter examples
• Begin to reason deductively in geometry, number and algebra, including using geometrical constructions
• Interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning

Problem solving

• Solve and evaluate the outcomes of multi-step problems
• Develop their use of formal mathematical knowledge to interpret and solve problems, including in financial mathematics

### Number

Students should be taught to:

• Understand and use place value for decimals, measures and integers of any size
• Order positive and negative integers, decimals and fractions
• Use the concepts and vocabulary of:

- prime numbers, factors (or divisors), multiple, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation

• Use product notation and the unique factorisation property
• Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a<x?b
• Appreciate the infinite nature of the sets of integers, real and rational numbers

### Algebra

Students should be taught to:

• Use equations in the Cartesian plane when recognising, sketching and producing graphs of linear and quadratic functions
• Use piece-wise linear graphs to find approximate solutions to contextual problems

### Ratio, proportion and rates of change

Students should be taught to:

•  Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

### Geometry and measures

Students should be taught to:

• Identify and construct congruent triangles

(Loci and bearings has been removed form this unit.)

## Selected KS3 maths resources

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