#        # NCETM KS3 Mastery Resources

The NCETM have produced some resources to offer detail of the key themes in the mathematics curriculum at KS3 which can be found on their website. Alternatively, you can view the PDF files for each of the six themes below.

• 1 The structure of the number system
Theme 1 explores the key structures of number and the number system, such as place value, factors, multiples and powers
• 1.1 Place value, estimation and rounding
This core concept covers the structure of our place-value system (particularly as it relates to decimals) and rounding numbers to a required number of decimal places or significant figures
• 1.2 Properties of number
This core concept focuses on factors, multiples and primes. It explores various representations to support understanding of highest common factors and lowest common multiples. Positive integer exponents and associated real roots are also explored
• 1.3 Ordering and comparing
This core concept covers the conversion of decimals to fractions (and vice versa), ordering positive and negative integers, fractions and decimals, and the expression of numbers in standard form
• 1.4 Simplifying and manipulating expressions, equations and formulae
This core concept concerns the generalisation of number structures, the use of algebraic symbols and techniques for their manipulation. The rearranging of formulae is also explored by linking it to the manipulation of number sentences

• 2 Operating on number
Theme 2 is about students understanding the structures underpinning calculation using each of the four operations. It includes the solving of equations, which is essentially concerned with operations on, as yet, unknown numbers
• 2.1 Arithmetic procedures
This core concept offers guidance on developing a strong understanding of the mathematical structures that underpin the standard procedures for calculation with decimals, fractions and directed numbers
• 2.2 Solving linear equations
This core concept explores how linear equations are effectively the formulation of a series of operations on unknown numbers and how the solving of such equations is concerned with undoing these operations to find the value of the unknown

• 3 Multiplicative reasoning
Theme 3 addresses the idea that any two numbers can be connected by multiplication. This gives rise to ideas of ratio, proportionality, percentage increase and decrease, rates of change, enlargement, similarity and trigonometric ratios
• 3.1 Understanding multiplicative relationships
This core concept explores fractions, percentages, ratio and proportion (direct and inverse) as contexts in which multiplicative relationships are used
• 3.2 Trigonometry
This core concept introduces the trigonometric functions through the unit circle. Ideas of similarity, scale factor and multiplicative relationships are integrated to show how trigonometry can be used to solve a wide range of problems

• 4 Sequences and graphs
Theme 4 explores arithmetic and other sequences, coordinates, equations and graphs, and the modelling of situations graphically
• 4.1 Sequences
This core concept covers sequences through exploration of the mathematical structure. It also introduces the idea of the nth term of a linear sequence
• 4.2 Graphical representations
This core concept introduces the idea of x- and y-coordinates as the input and output of a function. Linear and quadratic functions are explored, as well as how linear graphs are used to solve simultaneous equations

• 5 Statistics and probability
Theme 5 explores the role of statistical diagrams and measures in summarising and displaying data. It also introduces probability as a way of predicting the likelihood of events
• 5.1 Statistical representations and measures
This core concept covers measures of central tendency, work with grouped data and measures of spread, as well as the construction of scatter graphs and pie charts
• 5.2 Statistical analysis
This core concept covers the idea of making informed choices about which statistical analysis and representation to use for discrete, continuous and grouped data. It also looks at the effect that these choices have on the interpretation of data
• 5.3 Probability
This core concept introduces probability as a way to quantify, explore and explain likelihood and coincidence, and to reason about uncertainty

• 6 Geometry
Theme 6 explores the properties of various geometrical shapes, the key transformations of translation, rotation, reflection and enlargement, and standard ruler and compass constructions
• 6.1 Geometrical properties
This core concept covers angle facts and the geometry of intersecting lines, similarity and congruence, and Pythagoras’ theorem
• 6.2 Perimeter, area and volume
This core concept covers how the various formulae for perimeter, area and volume are derived and connected, and the importance of reasoning mathematically in order to solve a wide range of problems
• 6.3 Transforming shapes
This core concept introduces the transformations of translation, rotation, reflection and, finally, enlargement. It highlights and discusses the degrees of freedom available, with regards to what does and doesn’t vary for each one
• 6.4 Constructions
This core concept explores the following constructions: triangles of given lengths; a perpendicular bisector of a line segment; a perpendicular to a given line through a given point; an angle bisector