Transcript Document

Types of Numbers
www.mathsrevision.com
Level 2
Multiples and LCM
Factors and HCF
Prime numbers
Prime Decomposition
17-Jul-15
Created by Mr. Lafferty
Time Left : 0
8 mins
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Starter Questions
Level 2
31o
www.mathsrevision.com
Q1. Find all missing angles.
100 92
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65
Q2. Simplify
135
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45
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Q3. Find 66 % of 300
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Q4. I scored 20 out of 25 in Maths and 30 out 40.
By working out each percentage score find my best
17-Jul-15
subject.
Created by Mr. Lafferty
Types of Numbers
Multiples
www.mathsrevision.com
Level 2
Learning Intention
Success Criteria
1. We are learning that
multiples are simply values
in the times tables
1. Remember times tables and
use them for multiples.
2. We are learning how to
find the Lowest Common
Multiple.
2. Apply sets of multiples to
identify Lowest Common
Multiples
17-Jul-15
Created by Mr. Lafferty
Types of Numbers
Multiples
www.mathsrevision.com
Level 2
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, ………
17-Jul-15
Created by Mr. Lafferty
Types of Numbers
Lowest Common Multiple
www.mathsrevision.com
Level 2
Lowest
Common
Multiple
Smallest
Same
Number
We need to write out multiples in order to find
the Lowest Common Multiple.
17-Jul-15
Created by Mr. Lafferty
Types of Numbers
Lowest Common Multiple
www.mathsrevision.com
Level 2
Example :
Find the LCM of 3 and 4.
M3 = 3, 6 , 9, 12, 15, ………
M4 = 4, 8 , 12, 16, 20, ………
LCM = 12
17-Jul-15
Created by Mr. Lafferty
Types of Numbers
www.mathsrevision.com
Level 2
Now try Exercise 1
Ch5 (page 28)
17-Jul-15
Created by Mr. Lafferty
Starter Questions
Level 2
www.mathsrevision.com
1.
Calculate all the missing angles.
65
o
Q2. Find the missing angle.
150 52
o
o
Q.3 Calculate
(a)
17-Jul-15
- 6 + (7 - 8)
(b) (-7) x (-19)
Created by Mr. Lafferty
(c) (-3) x (-8)  4
Types of Numbers
Using Factors
www.mathsrevision.com
Level 2
Learning Intention
Success Criteria
1. We are learning that a
factor divides into a
number with no remainder
1. Identify factors using
factor pairs
2. We are learning how to
find Highest Common
Factors
2. Find HCF for two numbers
by comparing factors.
17-Jul-15
Created by Mr. Lafferty
Types of Numbers
Highest Common Factor
www.mathsrevision.com
Level 2
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
17-Jul-15
Created by Mr. Lafferty
Types of Numbers
Highest Common Factor
www.mathsrevision.com
Level 2
Highest
Common
Factor
Largest
Same
Number
We need to write out all factor pairs in order to find
the Highest Common Factor.
17-Jul-15
Created by Mr. Lafferty
Types of Numbers
Factors
www.mathsrevision.com
Level 2
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
17-Jul-15
Created by Mr. Lafferty
8
www.mathsrevision.com
Types of Numbers
Now try Exercise 2
Ch5 (page 30)
17-Jul-15
Created by Mr. Lafferty
Starter Questions
Level 2
www.mathsrevision.com
1.
Calculate the area of the following shape.
4 cm
5 cm
Q2. Find the missing angle.
Q.3 Calculate
(a)
17-Jul-15
- 6 +12 - 6
(b) (-7) x (8)
Created by Mr. Lafferty
(c) (-2) x (-18)  9
Types of Numbers
Prime Numbers
www.mathsrevision.com
Level 2
Learning Intention
Success Criteria
1. We are learning what a
prime number is.
1. understand the term
Prime Number.
2. Find all prime between 1 and
200.
17-Jul-15
Created by Mr. Lafferty
Types of Numbers
Prime Numbers
www.mathsrevision.com
Level 2
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
17-Jul-15
Created by Mr. Lafferty
Strike the two’s, strike the three’s the Sieve of Eratosthenes
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when the multiples sublime, the numbers that remain are prime!
25 primes
Below 100
Use the method of Eratosthenes to find all primes below 200
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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
What is the largest prime <200?
46 primes below 200
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
Number of Primes
168
135
127
120
119
114
117
107
110
112
106
103
?
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
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
when the multiples sublime, the numbers that remain are prime!
Worksheet – www.mathsrevision.com
Strike the two’s, strike the three’s the Sieve of Eratosthenes
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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
when the multiples sublime, the numbers that remain are prime!
Types of Numbers
www.mathsrevision.com
Level 2
Now try Exercise 3
Ch5 (page 32)
17-Jul-15
Created by Mr. Lafferty
Starter Questions
Level 2
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)
17-Jul-15
-16 -12 - 6
(b) (-9) x (5)
Created by Mr. Lafferty
(c) (-22) x (-11)  2
Types of Numbers
Prime Decomposition
www.mathsrevision.com
Level 2
Learning Intention
Success Criteria
1. We are learning what
prime decomposition is.
1. Understand the term prime
decomposition.
2. Decompose numbers to a
product of prime only.
17-Jul-15
Created by Mr. Lafferty
Types of Numbers
Prime Decomposition
www.mathsrevision.com
Level 2
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”
12
12
3
All Prime !
17-Jul-15
3
=3x4
4
2
2
Created by Mr. Lafferty
=3x2x2
Types of Numbers
Prime Decomposition
Level 2
www.mathsrevision.com
Example :
Express 18 as a “product of primes”
18
18
3
All Prime !
17-Jul-15
3
=3x6
6
3
2
Created by Mr. Lafferty
=3x3x2
Types of Numbers
www.mathsrevision.com
Level 2
Now try Exercise 4
Ch5 (page 35)
17-Jul-15
Created by Mr. Lafferty