Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Multiples and LCM

Factors and HCF

Types of Types of NumbersNumbers

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Prime numbers

Prime Decomposition

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

012345678Starter Starter QuestionsQuestions

%

65Q2. Simplif y

135

2Q3. Find 66 of 300

3

Q4. I scored 20 out of 25 in Maths and 30 out 40.

By working out each percentage score fi nd my best

subject.

Q1. Find all missing angles.

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45o

100o 92

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Time Left : mins

31o

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Remember times tables Remember times tables and use them for and use them for multiples.multiples.

1. We are learning that multiples are simply values in the times tables

2. We are learning how to find the Lowest Common Multiple.

2.2. Apply sets of multiples Apply sets of multiples to identify Lowest to identify Lowest Common MultiplesCommon Multiples

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Types of NumbersTypes of NumbersMultiples

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Types of Types of NumbersNumbers

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Multiples

Example 1 :Find the first seven multiples of 3.

M3 = 3, 6 , 9, 12, 15, 18,21

M4 = 4, 8 , 12, 16, 20, ………

Example 2 :Find the first five multiples of 4.

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Types of Types of NumbersNumbers

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Lowest Common Multiple

We need to write out multiples in order to findthe Lowest Common Multiple.

LowestCommonMultiple

SmallestSameNumber

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Types of Types of NumbersNumbers

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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

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Now try Exercise 1Ch5 (page 28)

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Types of NumbersTypes of Numbers

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Starter Starter QuestionsQuestions

Q2. Find the missing angle.

Q.3 Calculate

(a) - 6 + (7 - 8) (b) (-7) x (-19) (c) (-3) x (-8) 4

1. Calculate all the missing angles.

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65o

150o 52

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Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Identify factors using Identify factors using factor pairsfactor pairs

1. We are learning that a factor divides into a number with no remainder

2. We are learning how to find Highest Common Factors

2.2. Find HCF for two numbers Find HCF for two numbers by comparing factors.by comparing factors.

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Types of NumbersTypes of NumbersUsing Factors

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Types of Types of NumbersNumbers

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HCF = 4

F8 = 1 and 8

2 and 4

F12 = 1 and 12

2 and 6

3 and 4

Highest Common Factor

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Types of Types of NumbersNumbers

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Highest Common Factor

We need to write out all factor pairs in order to findthe Highest Common Factor.

HighestCommonFactor

LargestSameNumber

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Types of Types of NumbersNumbers

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Factors

Example : Find the factors of 56.

F56 = 1 and 56

Always divide by 1 and find its pair

2 and 28

4 and 14

7 and 8

From 2 find other factors and their pairs

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Now try Exercise 2Ch5 (page 30)

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Types of NumbersTypes of Numbers

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Starter Starter QuestionsQuestions

Q2. Find the missing angle.

Q.3 Calculate

(a) - 6 +12- 6 (b) (-7) x (8) (c) (-2) x (-18) 9

1. Calculate the area of the following shape.

5 cm

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4 cm

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. understand the term understand the term Prime Number.Prime Number.

1. We are learning what a prime number is.

2.2. Find all prime between 1 Find all prime between 1 and 200.and 200.

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Types of NumbersTypes of NumbersPrime Numbers

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Types of Types of NumbersNumbers

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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

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

Strike the two’s, strike the three’s the Sieve of Eratosthenes

when the multiples sublime, the numbers that remain are prime!

25 primes

Below 100

46 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

Use the method of Eratosthenes to find all primes below 200

What is the largest prime <200?

10311 000 – 12 000

10610 000 – 11 000

1129000 – 10 000

1108000 - 9000

1077000 – 8000

1176000 - 7000

1145000 - 6000

1194000 - 5000

1203000 – 4000

1272000 – 3000

1351000 – 2000

1680 – 1000

Number of Primes

Range

?

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100

Strike the two’s, strike the three’s the Sieve of Eratosthenes

when the multiples sublime, the numbers that remain are prime!

Work

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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

Strike the two’s, strike the three’s the Sieve of Eratosthenes

when the multiples sublime, the numbers that remain are prime!

Work

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Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Now try Exercise 3Ch5 (page 32)

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Types of NumbersTypes of Numbers

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Starter Starter QuestionsQuestions

Q2. Find the missing angle.

Q.3 Calculate

(a) -16 -12- 6 (b) (-9) x (5) (c) (-22) x (-11) 2

1. Calculate the area of the following shape.

8 cm

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5 cm

119o

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Understand the term Understand the term prime decomposition.prime decomposition.

1. We are learning what prime decomposition is.

2.2. Decompose numbers to a Decompose numbers to a product of prime only.product of prime only.

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Types of NumbersTypes of NumbersPrime Decomposition

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Types of Types of NumbersNumbers

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A number is either Prime or Composite. (except for 0)If it is composite, like 12, it can always be expressed asa “product of primes”

Example : Express 12 as a “product of primes”

Prime Decomposition

12

3

3 4

22

12

= 3 x 4

= 3 x 2 x 2All Prime !

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Types of Types of NumbersNumbers

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Prime Decomposition

18

3

3 6

23

18

= 3 x 6

= 3 x 3 x 2All Prime !

Level 2

11 Apr 202311 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Now try Exercise 4Ch5 (page 35)

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Types of NumbersTypes of Numbers