Types of Numbers Multiples and LCM Factors and HCF Prime numbers www.mathsrevision.com Prime Decomposition 5-Apr-17 Created by Mr. Lafferty

Starter Questions www.mathsrevision.com Time Left : 5 7 8 4 6 1 3 2 mins Starter Questions 31o 100o 92o 45o www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Multiples Learning Intention Success Criteria We are learning that multiples are simply values in the times tables We are learning how to find the Lowest Common Multiple. Remember times tables and use them for multiples. Apply sets of multiples to identify Lowest Common Multiples www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Multiples Example 1 : Find the first seven multiples of 3. M3 = 3, 6 , 9, 12, 15, 18,21 www.mathsrevision.com Example 2 : Find the first five multiples of 4. M4 = 4, 8 , 12, 16, 20, ……… 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Lowest Common Multiple Lowest Smallest Same Number We need to write out multiples in order to find the Lowest Common Multiple. www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Lowest Common Multiple Example : Find the LCM of 3 and 4. M3 = 3, 6 , 9, 12, 15, ……… www.mathsrevision.com M4 = 4, 8 , 12, 16, 20, ……… LCM = 12 5-Apr-17 Created by Mr. Lafferty

Now try Exercise 1 Ch5 (page 28) Types of Numbers www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

Starter Questions www.mathsrevision.com 65o 52o 150o 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Using Factors Learning Intention Success Criteria We are learning that a factor divides into a number with no remainder We are learning how to find Highest Common Factors Identify factors using factor pairs Find HCF for two numbers by comparing factors. www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Highest Common Factor Example : Find the HCF of 8 and 12. F8 = 1 and 8 2 and 4 F12 = 1 and 12 2 and 6 3 and 4 www.mathsrevision.com HCF = 4 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Highest Common Factor Highest Largest Same Number We need to write out all factor pairs in order to find the Highest Common Factor. www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

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 www.mathsrevision.com 2 and 28 4 and 14 7 and 8 5-Apr-17 Created by Mr. Lafferty

Now try Exercise 2 Ch5 (page 30) Types of Numbers www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

Starter Questions www.mathsrevision.com 4 cm 5 cm 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Prime Numbers Learning Intention Success Criteria We are learning what a prime number is. understand the term Prime Number. Find all prime between 1 and 200. www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

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 www.mathsrevision.com Example : Is 10 a prime number. Explain? No, more than two factors 1,2,5,10 5-Apr-17 Created by Mr. Lafferty

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 Slides 5 and 6 give the resource sheets.

Use the method of Eratosthenes to find all primes below 200 What is the largest prime <200? 46 primes below 200

103 11 000 – 12 000 106 10 000 – 11 000 112 9000 – 10 000 110 8000 - 9000 107 7000 – 8000 117 6000 - 7000 114 5000 - 6000 119 4000 - 5000 120 3000 – 4000 127 2000 – 3000 135 1000 – 2000 168 0 – 1000 Number of Primes Range ?

Worksheet – www.mathsrevision.com Strike the two’s, strike the three’s the Sieve of Eratosthenes Worksheet – www.mathsrevision.com when the multiples sublime, the numbers that remain are prime!

Strike the two’s, strike the three’s the Sieve of Eratosthenes Worksheet – www.mathsrevision.com when the multiples sublime, the numbers that remain are prime!

Now try Exercise 3 Ch5 (page 32) Types of Numbers www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

Starter Questions www.mathsrevision.com 119o 5 cm 8 cm 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Prime Decomposition Learning Intention Success Criteria We are learning what prime decomposition is. Understand the term prime decomposition. Decompose numbers to a product of prime only. www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty

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” 12 = 3 x 4 = 3 x 2 x 2 www.mathsrevision.com 12 3 4 3 2 All Prime ! 5-Apr-17 Created by Mr. Lafferty

Types of Numbers www.mathsrevision.com Prime Decomposition Example : Express 18 as a “product of primes” 18 = 3 x 6 = 3 x 3 x 2 18 3 6 3 2 3 www.mathsrevision.com All Prime ! 5-Apr-17 Created by Mr. Lafferty

Now try Exercise 4 Ch5 (page 35) Types of Numbers www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty