# 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.

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**Move on to memorise the basic facts**

Memorising means that the student has fast recall without returning to any strategy.

**Addition**

- 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**

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- 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

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**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**

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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**

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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):**

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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.