Key Messages:

  • Small connected steps are easier to take.

  • Focusing on one key point each lesson allows for deep and sustainable learning.

  • Certain images, techniques and concepts are important pre-cursors to later ideas. Getting the sequencing of these right is an important skill in planning and teaching for mastery.

  • When introducing new ideas, it is important to make connections with earlier ones that have already been understood.

​​

When something has been deeply understood and mastered, it can and should be used in the next steps of learning.

For example:

Before teaching the expansion of 2 brackets pupils need to:

  • understand that a product of two elements where each element is made up of two parts can be shown as four partial products as in 43 Γ— 24 = (40 + 3) Γ— (20 + 4) = 40 Γ— 20 + 40 Γ— 4 + 3 Γ— 20 + 3 Γ— 4.

  • be fluent in their number facts for multiplication

  • be fluent in the addition, subtraction and multiplication of negative numbers

  • be fluent in algebraic simplification (collecting like terms and multiplication)

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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 β€˜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.

Download the full documents here

Spine 1

Spine 2

Spine 3

​The Secondary PD material is based around:

  • six broad mathematical themes

  • a number of core concepts within each theme

  • a set of β€˜knowledge, skills and understanding’ statements within each core concept

  • a collection of focused key ideas within each statement of knowledge, skills and understanding.

Coherent steps to solve linear equations with x on one side by Jayne Webster, Secondary Mastery Specialist
x+a=b
x-a=b
ax=b
ax+b=c
ax-b=c
b+/-ax=c

Procedural variation - Intelligent Practice

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

Mathematical Thinking

Generalise

Fluency

Apply to different context and make connections.

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