The structure of the number system
Theme 1 comprises four core concepts: place value, estimation and rounding; properties of number; ordering and comparing; simplifying and manipulating expressions, equations and formulae.
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Secondary Mastery Professional Development
Materials that will assist you in your professional development and support you in teaching for mastery with confidence
These materials are now available for KS3 and KS4. The materials offer a ‘fine-grained’ description of the key themes and big ideas of the national curriculum by detailing:
- broad mathematical themes
- a number of core concepts within each theme
- a set of ‘knowledge, skills and understanding’ statements within each core concept
- a collection of focused key ideas within each statement of knowledge, skills and understanding.
Click on the diagram for an overview of the structure at KS3 or read a document with more detail and all numerical codes.
Materials and guidance for KS3
Operating on number
Theme 2 comprises two core concepts: arithmetic procedures; solving linear equations.
Multiplicative reasoning
Theme 3 comprises two core concepts: understanding multiplicative relationships; trigonometry.
Sequences and graphs
Theme 4 comprises two core concepts: sequences; graphical representations.
Statistics and probability
Theme 5 comprises three core concepts: statistical representations and measure; statistical analysis; probability.
Geometry
Theme 6 comprises four core concepts: geometrical properties; perimeter, area and volume; transforming shapes; constructions.
Materials and guidance for KS4
Using and applying numerical structure
Theme 7 comprises two core concepts: using structure to calculate and estimate; using structure to transform and evaluate expressions.
The remaining themes for the KS4 materials are currently in production and will be published during this academic year. The table below details which core concepts will be covered in each theme.
| Theme Number | Topic | Core Concepts |
| 8 | Proportional reasoning | Working with direct and inverse proportion Understanding graphical representations of proportionality |
| 9 | Sequences, functions and graphs | Exploring linear equations and inequalities Exploring non-linear sequences Exploring quadratic equations, inequalities and graphs Exploring functions |
| 10 | Statistics and probability | Statistical measures and analysis Statistical representations and analysis Probability |
| 11 | Geometry | Transformations and relative position Reasoning with the properties of a circle Trigonometry 3D shapes |
Each of the core concept pages within this section highlights specific classroom and professional development resources that support the use of these materials. These are also available elsewhere, arranged by type of resource. All the KS3 content is wholly consistent with the DfE guidance for teaching maths at KS3, published in the 2021 autumn term.
