# Representation & Structure

Representations expose mathematical structure.

# Procedural Variation

Calculations are connected and pupils use the relationships to make connections.

# Conceptual Variation

Representing the same concepts in different ways to draw out essential features.

Making connections between the different representations is important.

# Mathematical Thinking

Children and teachers need to think mathematically. This means to:

• look for pattern,

• make connections,

# Fluency

Having instant recall of number bonds to ten and within ten and being able to apply these to multiples

40 + 20 = 60  and bridging ten  8 + 5 = 8 + 2 + 3 = 13  is crucial for mastery of the curriculum.

Learn the facts so that the mind is freed up to think about concepts.

# Coherence

The NCETM have produced PD material with exemplified small steps mapped out from Year 1 to Year 6.

They have split the curriculum up into a small number of areas called ‘spines’ –

Spine 1: Number, Addition and Subtraction,

Spine 2: Multiplication and Division and

Spine 3: Fractions.

Each spine is composed of a number of segments, and a recommended teaching sequence for segments across the three spines.

An explanation of the structure of these materials, with guidance on how teachers can use them, is contained in a Getting Started video.