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www.mathsrevision.com Types of Numbers Multiples and LCM Factors and HCF Prime numbers Prime Decomposition Squares, cubes and square roots Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 1 Starter Questions www.mathsrevision.com 1. Find all missing angles. 45 o Q2. Find the missing angle. 100 92 o o Q.3 Calculate (a) - 9 - (72 8) Sunday, 07 May 2017 (b) (-4) x (-13) Created by Mr. Lafferty @www.mathsrevision.com (c) (-15) 3 + 4 2 Types of Numbers www.mathsrevision.com Multiples Learning Intention Success Criteria 1. To explain that Multiples are the times tables 2. To explain how to find the Lowest Common Number. Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 1. To be able to write out multiples 2. Use sets of multiples to identify Lowest Common Multiples 3 Types of Numbers www.mathsrevision.com Multiples Example 1 : Find the first seven multiples of 3. M3 = 3, 6 , 9, 12, 15, 18,21 Example 2 : Find the first five multiples of 4. M4 = 4, 8 , 12, 16, 20, ……… Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 4 Types of Numbers www.mathsrevision.com Lowest Common Multiple Lowest Common Multiple Smallest Same Number We need to write out multiples in order to find the Lowest Common Multiple. Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 5 Types of Numbers www.mathsrevision.com Lowest Common Multiple Example : Find the LCM of 3 and 4. M3 = 3, 6 , 9, 12, 15, ……… M4 = 4, 8 , 12, 16, 20, ……… LCM = 12 Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 6 Types of Numbers www.mathsrevision.com Revision of Level E Now try Exercise 1 Ch5 (page 28) Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 7 Starter Questions www.mathsrevision.com 1. Calculate all the missing angles. 65 o Q2. Find the missing angle. 150 52 o o Q.3 Calculate (a) - 6 + (7 - 8) Sunday, 07 May 2017 (b) (-7) x (-19) Created by Mr. Lafferty @www.mathsrevision.com (c) (-3) x (-8) 4 8 Types of Numbers www.mathsrevision.com Using Factors Learning Intention Success Criteria 1. To explain that a factor divides into a number with no remainder 1. To identify factors using factor pairs 2. To explain how to find Highest Common Factors 2. Find HCF for two numbers by comparing factors. Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 9 Types of Numbers www.mathsrevision.com Factors Example : Find the factors of 56. Always divide by 1 and find its pair F56 = 1 and 56 From 2 find other factors and their pairs 2 and 28 4 and 14 7 and Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 8 10 Types of Numbers www.mathsrevision.com Highest Common Factor Highest Common Factor Largest Same Number We need to write out all factor pairs in order to find the Highest Common Factor. Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 11 Types of Numbers www.mathsrevision.com Highest Common Factor Example : Find the HCF of 8 and 12. F8 = 1 and 8 F12 = 1 and 12 2 and 4 2 and 6 3 and 4 HCF = 4 Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 12 Types of Numbers www.mathsrevision.com Revision of Level E Now try Exercise 2 Ch5 (page 30) Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 13 Starter Questions www.mathsrevision.com 1. Calculate the area of the following shape. 4 cm 5 cm Q2. Find the missing angle. Q.3 Calculate (a) - 6 +12 - 6 Sunday, 07 May 2017 (b) (-7) x (8) Created by Mr. Lafferty @www.mathsrevision.com (c) (-2) x (-18) 9 14 Types of Numbers www.mathsrevision.com Prime Numbers Learning Intention Success Criteria 1. To explain what a prime number is and to find all the prime numbers from 1 and 200. Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 1. To know the meaning of the term Prime Number. 2. Find all prime between 1 and 200. 15 Types of Numbers www.mathsrevision.com Prime Numbers Definition : A prime number is a number with exactly 2 factors. Example : Is 7 a prime number. Explain? Yes, only two factors 1,7 Example : Is 10 a prime number. Explain? No, more than two factors 1,2,5,10 Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 16 Strike the two’s, strike the three’s the Sieve of Eratosthenes 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 Sunday, 07 May 2017 3 13 23 33 43 53 63 73 83 93 when the multiples 4 14 24 34 44 54 64 74 84 94 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 Created by Mr. Lafferty sublime, the numbers that @www.mathsrevision.com 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100 remain are prime! 25 primes Below 100 17 Use the method of Eratosthenes to find all primes below 200 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 Sunday, 07 May 2017 Created by Mr. Lafferty What is the largest prime <200? @www.mathsrevision.com 46 primes below 200 18 Range 0 – 1000 1000 – 2000 2000 – 3000 3000 – 4000 4000 - 5000 5000 - 6000 6000 - 7000 7000 – 8000 8000 - 9000 9000 – 10 000 10 000 – 11 000 11 000 – 12 000 Sunday, 07 May 2017 Number of Primes 168 135 127 120 119 114 117 107 110 112 106 103 Created by Mr. Lafferty @www.mathsrevision.com ? 19 Worksheet – www.mathsrevision.com Strike the two’s, strike the three’s the Sieve of Eratosthenes 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 3 13 23 33 43 53 63 73 83 93 4 14 24 34 44 54 64 74 84 94 Sunday,when 07 Maythe 2017multiples 5 15 25 35 45 55 65 75 85 95 6 16 26 36 46 56 66 76 86 96 7 17 27 37 47 57 67 77 87 97 8 18 28 38 48 58 68 78 88 98 9 19 29 39 49 59 69 79 89 99 10 20 30 40 50 60 70 80 90 100 Createdthe by Mr.numbers Lafferty sublime, that remain are prime! @www.mathsrevision.com 20 Worksheet – www.mathsrevision.com Strike the two’s, strike the three’s the Sieve of Eratosthenes 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 Sunday,when 07 Maythe 2017multiples Createdthe by Mr.numbers Lafferty sublime, that remain are prime! @www.mathsrevision.com 21 Types of Numbers www.mathsrevision.com Revision of Level E Now try Exercise 3 Ch5 (page 32) Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 22 Starter Questions www.mathsrevision.com 1. Calculate the area of the following shape. 5 cm 8 cm Q2. Find the missing angle. 119 o Q.3 Calculate (a) -16 -12 - 6 Sunday, 07 May 2017 (b) (-9) x (5) Created by Mr. Lafferty @www.mathsrevision.com (c) (-22) x (-11) 2 23 Types of Numbers www.mathsrevision.com Prime Decomposition Learning Intention Success Criteria 1. To explain what prime decomposition is and use it to decompose numbers into a product of prime numbers only. Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 1. To know the meaning of the term prime decomposition. 2. Decompose numbers to a product of prime only. 24 Types of Numbers www.mathsrevision.com Prime Decomposition A number is either Prime or Composite. (except for 0) If it is composite, like 12, it can always be expressed as a “product of primes” Example : Express 12 as a “product of primes” 2 12 2 6 3 3 Prime Factors are 2, 2, 3 Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 1 25 Types of Numbers Prime Decomposition www.mathsrevision.com Example : Express 660 as a “product of primes” 2 660 2 330 3 165 5 55 11 11 1 Prime Factors are 2, 2, 3, 5, 11 Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 26 Types of Numbers www.mathsrevision.com Some words to learn The Sum is what you get when numbers are added together The Difference between two numbers is found by subtracting one number from the other The Product is what you get when numbers are multiplied together The Quotient is what you get when one number is divided by another. Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 27 Types of Numbers www.mathsrevision.com Examples The Sum of 3, 5 and 9 is 17 The Difference between 45 and 20 is 25 The Product of 2,5 and 6 is 60 The Quotient when 30 is divided by 5 is Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 6 28 www.mathsrevision.com Types of Numbers Now try Exercise 9.1 Ch1 (page 15) Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 29 Starter Questions www.mathsrevision.com 1. Calculate the area of the following shape. 6 cm 10 cm Q2. Find the missing angle. 114 o Q.3 Calculate (a) -16 -12 - 6 Sunday, 07 May 2017 (b) (-9) x (5) Created by Mr. Lafferty @www.mathsrevision.com (c) (-22) x (-11) 2 30 Types of Numbers www.mathsrevision.com Prime Decomposition Learning Intention Success Criteria 1. To explain what a square, cube and square root of a number is. 1. To understand what a square, cube and square root of a number is. 2. Calculate the square, cube and square root of a number. Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 31 www.mathsrevision.com Square, Cube and Square Root When we multiply a number by itself we say we have squared the number. 4 3 2 2 3 We write above as 22 = 4 Sunday, 07 May 2017 32 = 9 Created by Mr. Lafferty @www.mathsrevision.com 4 42 = 16 32 www.mathsrevision.com Square, Cube and Square Root When we multiply a number by itself we say we have squared the number. Read as a to the power 2 a2 = a x a Calculate 92 = 81 Sunday, 07 May 2017 102 = 100 Created by Mr. Lafferty @www.mathsrevision.com 202 = 400 33 Square, Cube and Square Root www.mathsrevision.com When we cube a number we mean a3 = a x a x a 23 = 2 x 2 x 2 = 8 Calculate 33 = 27 Sunday, 07 May 2017 43 = 64 Created by Mr. Lafferty @www.mathsrevision.com 53 = 125 34 www.mathsrevision.com Types of Numbers Now try Ex 10.1 Q1 to Q5 Ch1 (page 17) Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 35 www.mathsrevision.com Square, Cube and Square Root SQUARE ROOT “ A factor of a number that can be multiplied by itself to produce the original number “ 25 5 because 5 25 49 7 because 7 49 Sunday, 07 May 2017 2 Created by Mr. Lafferty @www.mathsrevision.com 2 36 www.mathsrevision.com Square, Cube and Square Root The square root of a number is another number than when you multiply it by itself the answer is the original number 25 5 because 5 25 2 Calculate 81 9 Sunday, 07 May 2017 121 11 Created by Mr. Lafferty @www.mathsrevision.com 37 www.mathsrevision.com Types of Numbers Now try Ex 10.1 Q6 to Q9 Ch1 (page 18) Sunday, 07 May 2017 Created by Mr. Lafferty @www.mathsrevision.com 38