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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Multiples and LCM Factors and HCF Types of Numbers www.mathsrevision.com Prime numbers Prime Decomposition Squares, cubes and square roots 1

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Starter Questions www.mathsrevision.com 45 o 100 o 92 o 2

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Learning Intention Success Criteria 1.To be able to write out multiples 1.To explain that Multiples are the times tables 2.To explain how to find the Lowest Common Number. 2.Use sets of multiples to identify Lowest Common Multiples www.mathsrevision.com Types of Numbers Multiples 3

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Types of Numbers www.mathsrevision.com 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. 4

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Types of Numbers www.mathsrevision.com Lowest Common Multiple We need to write out multiples in order to find the Lowest Common Multiple. Lowest Common Multiple Smallest Same Number 5

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com 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 6

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Now try Exercise 1 Ch5 (page 28) www.mathsrevision.com Types of Numbers Revision of Level E 7

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Starter Questions www.mathsrevision.com 65 o 150 o 52 o 8

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Learning Intention Success Criteria 1.To identify factors using factor pairs 1.To explain that a factor divides into a number with no remainder 2.To explain how to find Highest Common Factors 2.Find HCF for two numbers by comparing factors. www.mathsrevision.com Types of Numbers Using Factors 9

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Types of Numbers www.mathsrevision.com 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 10

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Types of Numbers www.mathsrevision.com Highest Common Factor We need to write out all factor pairs in order to find the Highest Common Factor. Highest Common Factor Largest Same Number 11

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Types of Numbers www.mathsrevision.com Example :Find the HCF of 8 and 12. HCF = 4 F8 =1 and 8 2 4 F12 = 1 and 12 2 and 6 3 4 Highest Common Factor 12

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Now try Exercise 2 Ch5 (page 30) www.mathsrevision.com Types of Numbers Revision of Level E 13

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Starter Questions 5 cm www.mathsrevision.com 4 cm 14

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Learning Intention Success Criteria 1.To know the meaning of the term Prime Number. 1.To explain what a prime number is and to find all the prime numbers from 1 and 200. 2.Find all prime between 1 and 200. www.mathsrevision.com Types of Numbers Prime Numbers 15

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com 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 16

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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 Thursday, 06 August 2015 17Created by Mr. Lafferty @www.mathsrevision.com

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46 primes below 200 Use the method of Eratosthenes to find all primes below 200 What is the largest prime < 200? Thursday, 06 August 2015 18Created by Mr. Lafferty @www.mathsrevision.com

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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 PrimesRange ? Thursday, 06 August 2015 19Created by Mr. Lafferty @www.mathsrevision.com

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Strike the two’s, strike the three’s the Sieve of Eratosthenes when the multiples sublime, the numbers that remain are prime! Worksheet – www.mathsrevision.com Thursday, 06 August 2015 20Created by Mr. Lafferty @www.mathsrevision.com

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Strike the two’s, strike the three’s the Sieve of Eratosthenes when the multiples sublime, the numbers that remain are prime! Worksheet – www.mathsrevision.com Thursday, 06 August 2015 21Created by Mr. Lafferty @www.mathsrevision.com

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Now try Exercise 3 Ch5 (page 32) www.mathsrevision.com Types of Numbers Revision of Level E 22

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Starter Questions 8 cm www.mathsrevision.com 5 cm 119 o 23

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Learning Intention Success Criteria 1.To know the meaning of the term prime decomposition. 1.To explain what prime decomposition is and use it to decompose numbers into a product of prime numbers only. 2.Decompose numbers to a product of prime only. www.mathsrevision.com Types of Numbers Prime Decomposition 24

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Types of Numbers www.mathsrevision.com 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” Prime Decomposition Prime Factors are 2, 2, 3 12 6 3 1 2 2 3 25

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Types of Numbers www.mathsrevision.com Example :Express 660 as a “product of primes” Prime Decomposition Prime Factors are 2, 2, 3, 5, 11 660 330 165 55 2 2 3 11 5 1 26

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com Types 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. 27

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com Types 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 28

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Now try Exercise 9.1 Ch1 (page 15) www.mathsrevision.com Types of Numbers 29

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Starter Questions 10 cm www.mathsrevision.com 6 cm 114 o 30

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Learning Intention Success Criteria 1.To understand what a square, cube and square root of a number is. 1.To explain what a square, cube and square root of a number is. 2.Calculate the square, cube and square root of a number. www.mathsrevision.com Types of Numbers Prime Decomposition 31

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com Square, Cube and Square Root 32 When we multiply a number by itself we say we have squared the number. 2 4 2 3 3 4 We write above as 2 2 = 4 3 2 = 9 4 2 = 16

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com Square, Cube and Square Root 33 When we multiply a number by itself we say we have squared the number. Calculate 9 2 =10 2 = a 2 = a x a Read as a to the power 2 20 2 =81100400

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com Square, Cube and Square Root 34 When we cube a number we mean Calculate 3 3 = 4 3 = 5 3 = a 3 = a x a x a 2 3 = 2 x 2 x 2 = 8 2764125

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Now try Ex 10.1 Q1 to Q5 Ch1 (page 17) www.mathsrevision.com Types of Numbers 35

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com Square, Cube and Square Root 36 SQUARE ROOT “ A factor of a number that can be multiplied by itself to produce the original number “ because because

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com www.mathsrevision.com Square, Cube and Square Root 37 The square root of a number is another number than when you multiply it by itself the answer is the original number because Calculate 9 11

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Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Thursday, 06 August 2015Created by Mr. Lafferty @www.mathsrevision.com Now try Ex 10.1 Q6 to Q9 Ch1 (page 18) www.mathsrevision.com Types of Numbers 38

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