# Key Knowledge (Number) Progression

Key Knowledge Progression

This has been designed to indicate the progression of “Basic Facts” known as “Key knowledge” to support strategy learning. It also indicates the progression of Basic Facts learning.

Move on to memorise the basic facts
Memorising means that the student has fast recall without returning to any strategy.

• Add on 0
• Add on 1
• Doubles
• Make to 5
• Make to 10

• Count on from larger number up to 10
• Count on from larger number up to 20
• Derived facts from 11-20

Subtraction

• Properties of 0
• Properties of 1
• Halves
• Count back by 8 – 3,
• Count back by 14 – 6
• Inverse of addition
• 5+3 = 8 8 – 3 = 5

Multiplication

• 2x Doubles
• 10x Place value
• 5x Filling in the gaps ends with 0 if even number and 5 if an odd number
• 1x
• 4x Double doubles
• 3x smaller numbers
• 9x patterns
• 6x move 1 up from 5x
• 8x double 4x
• 7x – no set pattern!

Internal patterns:

10x      1 2 3 + 0

5x        5 0 5 0

2x      2 4 6 8 0

8x      8 6 4 2 0

4x      4 8 2 6 0

6x      6 2 8 4 0

3x 3    6 9 2 5 8 1 4 0

7x 7    4 1 8 5 2 9 6 3

Divisibility Rules

10 x ends in 0

2x even numbers

5x 0 or 5

3x sum of digits divisible of 3

9x sum of digits divisible by 9

6x sum of digits divisible by 2 and 3

Other multiplication tables

100x, 1000x 25x 125x 11.1x etc

Fractions, Percentages and Decimals

1/5 = 20% = 0.2

1/8 = 12.5%

½ x table 0.5

1/10 x table 0.1

1/5 x table 0.2

¼ x table 0.25

1/8x table 0.125

Power series (Exponents):

Square numbers

Triangular numbers

Cubic numbers

Prime numbers – odd and not divisible by 3 or 5

49 77 91 (why are these interesting)

Instant recall of Formulae, rules etc

Area = length x height

Area of a circle = 3.14 (pi) x radius squared.