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 precursors 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 × 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)
Solve linear equations with x on one side
x+a=b
xa=b
ax=b
ax+b=c
axb=c
b+/ax=c
x + 3 = 5
x + 3 = 2
x + 3 = 0
x + 3 = 1
x + 3 = 5
x + a = b
x>0 when ...
x=0 when ...
x<0 when ...
x  3 = 5
x  3 = 2
x  3 = 0
x  3 = 1
x  3 = 5
x  a = b
x>0 when ...
x=0 when ...
x<0 when ...
8  x = 3
9 5