Concept sections

Each of the 7 concept sections has detail in the following structure:

• the core mathematical idea
• key representations
• worked examples
• the explicit bridge to algebra
• key vocabulary
• common misconceptions
• diagnostic questions
• a progression spine from primary to KS4

#	Concept Area	Core Focus
1	Place Value and Unitising	Foundational to all number work
2	Laws of Arithmetic	The structural grammar
3	Equality, Equivalence, and the Equals Sign	Relational understanding of '$=$'
4	Zero and One as Identities	Additive and multiplicative identities
5	Directed Number	Positive, negative, position, and direction
6	Additive and Multiplicative Reasoning	The shift to proportional thinking
7	The Area Model	Visual distributive structure
8	Division	Three meanings of division
9	Scaled Multiplication Tables	Relational fluency with facts
10	Structural Approaches to Calculation	Decomposition, equivalence, strategic choice
11	Inverse Operations and Fact Families	Operations as reversible processes
12	Fractions, Decimals, and Percentages	Connected number representations
13	Factors, Multiples, Primes	Internal structure of numbers
14	Generalising from Patterns	From specific to general
15	Variable as a Concept	Unknown, generalised number, varying quantity
16	Expressions, Equations, and Identities	Distinguishing algebraic objects
17	Estimation, Approximation, and Sense-Checking	Reasonableness as a habit of mind