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.
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 × 24 = (40 + 3) × (20 + 4) = 40 × 20 + 40 × 4 + 3 × 20 + 3 × 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)
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.
Download the full documents here
The Secondary PD material is based around:
six 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.
Coherent steps to solve linear equations with x on one side by Jayne Webster, Secondary Mastery Specialist
Procedural variation - Intelligent Practice
Calculations are connected and pupils use the relationships to make connections.
Apply to different context and make connections.