Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Multiples and LCM
Factors and HCF
Types of Types of NumbersNumbers
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Prime numbers
Prime Decomposition
Squares, cubes and square roots
11
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Starter Starter QuestionsQuestions
Q2. Find the missing angle.
Q.3 Calculate
(a) - 9 - (72 8) (b) (-4) x (-13) (c) (-15) 3+4
1. Find all missing angles.
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45o
100o 92
o
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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To be able to write out To be able to write out multiplesmultiples
1. To explain that Multiples are the times tables
2. To explain how to find the Lowest Common Number.
2.2. Use sets of multiples to Use sets of multiples to identify Lowest identify Lowest Common MultiplesCommon Multiples
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Types of NumbersTypes of NumbersMultiples
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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.
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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
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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
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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Now try Exercise 1Ch5 (page 28)
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Types of NumbersTypes of NumbersRevision of Level E
77
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To identify factors using To identify factors using factor pairsfactor pairs
1. To explain that a factor divides into a number with no remainder
2. To explain 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
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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
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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
1111
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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
1212
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Now try Exercise 2Ch5 (page 30)
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Types of NumbersTypes of NumbersRevision of Level E
1313
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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
1414
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To know the meaning of To know the meaning of the term Prime Number.the term Prime Number.
1. To explain what a prime number is and to find all the prime numbers from 1 and 200.
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
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Types of Types of NumbersNumbers
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Prime Numbers
Definition : A prime number is a number withexactly 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
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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
Wednesday 19 April 2023
17Created by Mr. Lafferty @www.mathsrevision.com
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?
Wednesday 19 April 2023
18Created by Mr. Lafferty @www.mathsrevision.com
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
?Wednesday 19 April 2023
19Created by Mr. Lafferty @www.mathsrevision.com
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
sheet
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Wednesday 19 April 2023
20Created by Mr. Lafferty @www.mathsrevision.com
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
sheet
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Wednesday 19 April 2023
21Created by Mr. Lafferty @www.mathsrevision.com
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Now try Exercise 3Ch5 (page 32)
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Types of NumbersTypes of NumbersRevision of Level E
2222
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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
2323
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To know the meaning of To know the meaning of the term prime the term prime decomposition.decomposition.
1. To explain what prime decomposition is and use it to decompose numbers into a product of prime numbers only. 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
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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
Prime Factors are 2, 2, 3
126
3
1
22
3
2525
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Types of Types of NumbersNumbers
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Prime Decomposition
Prime Factors are 2, 2, 3, 5, 11
660330
165
55
22
3
115
11
1
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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Types of NumbersTypes of Numbers
Some words to learn
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 Sum is what you get when numbers are added together
The Quotient is what you get when one number is divided by another.
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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Types of NumbersTypes of Numbers
Examples
The Difference between 45 and 20 is
The Product of 2,5 and 6 is
The Sum of 3, 5 and 9 is
The Quotient when 30 is divided by 5 is
17
25
60
6
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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Now try Exercise 9.1
Ch1 (page 15)
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Types of NumbersTypes of Numbers
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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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.
10 cm
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6 cm
114o
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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To understand what a To understand what a square, cube and square square, cube and square root of a number is.root of a number is.
1. To explain what a square, cube and square root of a number is.
2.2. Calculate the square, cube Calculate the square, cube and square root of a and square root of a number.number.
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Types of NumbersTypes of NumbersPrime Decomposition
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Square, Cube and Square, Cube and Square RootSquare Root
3232
When we multiply a number by itself we say we have squared the number.
2 4
2
3
34
We write above as
22 = 4 32 = 9 42 = 16
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Square, Cube and Square, Cube and Square RootSquare Root
3333
When we multiply a number by itself we say we have squared the number.
Calculate
92 = 102 =
a2 = a x aRead as a to the power 2
202 = 81 100 400
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Square, Cube and Square, Cube and Square RootSquare Root
3434
When we cube a number we mean
Calculate
33 = 43 = 53 =
a3 = a x a x a
23 = 2 x 2 x 2 = 8
27 64 125
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Now try Ex 10.1Q1 to Q5
Ch1 (page 17)
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Types of NumbersTypes of Numbers
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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Square, Cube and Square, Cube and Square RootSquare Root
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SQUARE ROOT“ A factor of a number that can be multiplied by
itself to produce the original number “
525 2552 because
749 4972 because
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Square, Cube and Square, Cube and Square RootSquare Root
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The square root of a number is another number than when you multiply it by itself
the answer is the original number
525 2552 because
81
Calculate
1219 11
Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Now try Ex 10.1Q6 to Q9
Ch1 (page 18)
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Types of NumbersTypes of Numbers
3838