1. Chapter 5 Knowing and using number facts

2. Chapter Summary The chapter introduces the idea of ‘number sense’
It shows how important it is to support pupils in using number patterns to remember number facts
It offers activities which can support pupils to use facts they know to develop new facts
It outlines the rules which underpin the number system.

3. Number Sense
Read the paper ‘Fluency without fear’ on the companion website. Write a brief paragraph outlining your understanding of number sense.

4. Square numbers and triangle numbers
These are the first 5 triangle numbers Add together consecutive triangle numbers. For example = = 9 What do you notice? Can you prove your assertion using a diagram

5. The commutative property
For addition and multiplication we can write the numbers in any order. So = x 17 x 5 = 2 x 5 x 17 Why might this be helpful when carrying out calculations mentally?

6. The distributive property
Rather than calculate 13 x 8 I can calculate (10 x 8) + (3 x 8)
Use the distributive property to calculate
18 x 8
29 x 14
34 x 7
48 x 6

7. The associative property
8 x 5 x 2 = (8 x 5) x 2 = 8 x (5 x 2)
Carry out the following calculations using the associative property
8 x 7 x 2 x 5

8. Misconceptions Tell me an even number which is also a prime number
Tell me a multiple of 3 which is even
Tell me a multiple of 10 that is in the 3 times table

9. Divisibility Rules
If the last two digits of a number are divisible by 4 then the entire number is divisible by 4
If the last three digits of a number are divisible by 8 then the entire number is divisible by 8
Why do these rues work?

10. Observing the teaching of knowing and using number facts
Watch the video ‘Using a counting stick’ on the companion website:
How does the counting stick help pupils memorise new facts by using facts they already know?
How might you use the counting stick to model other aspects of the number system?