Numerical Relationships By the end of the presentation you will be able to: Work out and write down the first 15 square numbers Work out and write down the first 15 cube numbers Find multiples of numbers and recognise that they are times tables Find factors of numbers and put them in order of size Find all the prime numbers in a 1-100 grid About this PowerPoint: Created by Mandy Robinson - www.mandymaths.co.uk Graphics/animations licensed to Mandy Robinson by PRESENTERMEDIA (These can only be used in this presentation and must not be reproduced)

Square Numbers your turn We say: one squared We write: 12 We mean: 1 x 1 The answer is: 1 We say: two squared We write: 22 We mean: 2 x 2 The answer is: 4 your turn

Cube Numbers your turn We say: one cubed We write: 13 We mean: 1 x 1 x 1 The answer is: 1 We say: two cubed We write: 23 We mean: 2 x 2 x 2 The answer is: 8 your turn

Multiples A multiple is formed by multiplying a given number by the counting numbers The counting numbers are 1, 2, 3, 4, 5, 6... Multiples are just the times tables

Multiples What are the multiples of 2? They are the 2 times table 1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 … The multiples of 2 are: 2,4,6,8,10,12,14,16…

Multiples What are the multiples of 3? They are the 3 times table 1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 … The multiples of 3 are: 3,6,9,12,15,18,21,24…

Multiples 13,26,39,52,65 What are the first 5 multiples of 13? They are the 13 times table 1 x 13 = 13 2 x 13 = 26 3 x 13 = 39 4 x 13 = 52 5 x 13 = 65 The first 5 multiples of 13 are: 13,26,39,52,65

Multiples Find the Missing Multiples: 6, 12, 18, ____, ____ ___, 8, 12, 16, ____, ____, 28 ___, 24, 36, 48, 60, ____ 24 30 4 20 24 12 72

Multiples are always equal to or bigger than the original number

Factors A factor is a number which divides exactly into a given number leaving no remainder

Factors How many different groups can you make with 6 counters?

Factors How many different groups can you make with 6 counters?

Factors How many different groups can you make with 6 counters?

Factors How many different groups can you make with 6 counters?

Factors 1 group of 6 3 groups of 2 6 groups of 1 2 groups of 3 How many different groups can you make with 6 counters? 1 group of 6 3 groups of 2 6 groups of 1 2 groups of 3 The factors of 6 are: 1, 2, 3, 6

Factors What are the factors of 8? 1 x 8

Factors What are the factors of 8? 1 x 8

Factors What are the factors of 8? 1 x 8 2 4

Factors What are the factors of 8? 1 x 8 2 4

Factors What are the factors of 8? 1 x 8 2 4 3 Title page.

Factors What are the factors of 8? 1 x 8 2 4 3 Title page.

This is a repeated number so STOP Factors What are the factors of 8? 1 x 8 2 4 3 This is a repeated number so STOP The factors of 8 are: 1, 2, 4, 8

Factors What are the factors of 36? 1 x 24 2 12 3 8 4 6 5

Factors What are the factors of 36? 1 x 36 2 12 3 8 4 6 5

Factors What are the factors of 36? 1 x 36 2 12 3 8 4 6 5

Factors What are the factors of 36? 1 x 36 2 18 3 8 4 6 5

Factors What are the factors of 36? 1 x 36 2 18 3 8 4 6 5

Factors What are the factors of 36? 1 x 36 2 18 3 12 4 6 5

Factors What are the factors of 36? 1 x 36 2 18 3 12 4 6 5

Factors What are the factors of 36? 1 x 36 2 18 3 12 4 9 5 6

Factors What are the factors of 36? 1 x 36 2 18 3 12 4 9 5 6

Factors What are the factors of 36? 1 x 36 2 18 3 12 4 9 5 6

This is a repeated number so STOP Factors What are the factors of 36? 1 x 36 2 18 3 12 4 9 5 6 This is a repeated number so STOP The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

Multiples and Factors What are the first six multiples of 4? What are the factors of 24?

Venn Diagram Factors of 24 Multiples of 4 Multiples of 6

Definitions Even Number Any number that can be divided by 2 without leaving a remainder Odd Number Any number that cannot be divided by 2 without leaving a remainder Composite Number A number that can be divided by at least one other number (a factor) other than 1 or itself Prime Number A number with exactly 2 factors,1 and itself

Prime numbers 1 is a special number 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 1 is a special number Why? Let’s find all the prime numbers 1 has only one factor and so is neither prime nor composite Cross out 1 because it is not prime

Cross out 1 because it is not prime Prime numbers x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Cross out 1 because it is not prime

Prime numbers x Circle it 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 What is the first prime number? What is special about this number? It is the only even prime number Circle it

Prime numbers x x x x x x x x x x x x x x x x x x x x x x x x x x x x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

Prime numbers in real life