Chapter 5 Knowing and using number facts Chapter

Chapter 5 Knowing and using number facts

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.

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

Square numbers and triangle numbers These are the first 5 triangle numbers Add together consecutive triangle numbers. For example 1+3=4 3+6=9 What do you notice? Can you prove your assertion using a diagram

The commutative property For addition and multiplication we can write the numbers in any order. So 15 + 7 + 5 + 3 = 15 + 7 + 3 2 x 17 x 5 = 2 x 5 x 17 Why might this be helpful when carrying out calculations mentally?

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 29 34 48 x x 8 14 7 6

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 • 22 + 14 + 6 + 8 + 5 + 3 • 8 x 7 x 2 x 5

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

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?

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?