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Types of Numbers

Types of Numbers. Multiples and LCM. Factors and HCF. Prime numbers. www.mathsrevision.com. Prime Decomposition. Squares, cubes and square roots. 92 o. 100 o. 45 o. Starter Questions. www.mathsrevision.com. Types of Numbers. Multiples. Learning Intention. Success Criteria.

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Types of Numbers

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

  2. 92o 100o 45o Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

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

  4. Types of Numbers Multiples 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. www.mathsrevision.com M4 = 4, 8 , 12, 16, 20, ……… Created by Mr. Lafferty @www.mathsrevision.com

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

  6. Types of Numbers 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 Created by Mr. Lafferty @www.mathsrevision.com

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

  8. 52o 150o 65o Starter Questions www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

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

  10. Types of Numbers 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 Created by Mr. Lafferty @www.mathsrevision.com

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

  12. Types of Numbers 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 Created by Mr. Lafferty @www.mathsrevision.com

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

  14. Starter Questions 4 cm 5 cm www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

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

  16. Types of Numbers 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 Created by Mr. Lafferty @www.mathsrevision.com

  17. Strike the two’s, strike the three’s the Sieve of Eratosthenes 25 primes Below 100 when the multiples sublime, the numbers that remain areprime! Created by Mr. Lafferty @www.mathsrevision.com

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

  19. Range Number of Primes 0 – 1000 168 1000 – 2000 135 2000 – 3000 127 3000 – 4000 120 4000 - 5000 119 5000 - 6000 114 6000 - 7000 117 7000 – 8000 107 8000 - 9000 110 9000 – 10 000 112 ? 10 000 – 11 000 106 11 000 – 12 000 103 Created by Mr. Lafferty @www.mathsrevision.com

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

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

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

  23. 119o Starter Questions 5 cm 8 cm www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

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

  25. Types of Numbers Prime Decomposition A number is either Prime or Composite. (except for 0) If it is composite, like 12, it canalways be expressed as a “product of primes” Example : Express 12 as a “product of primes” 2 12 www.mathsrevision.com 6 2 3 3 1 Prime Factors are 2, 2, 3 Created by Mr. Lafferty @www.mathsrevision.com

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

  27. Types of Numbers Some words to learn The Sum is what you get when numbers are added together The Difference between two numbers is found by subtracting one number from the other www.mathsrevision.com The Product is what you get when numbers are multiplied together The Quotient is what you get when one number is divided by another. Created by Mr. Lafferty @www.mathsrevision.com

  28. Types of Numbers Examples 17 The Sum of 3, 5 and 9 is 25 The Difference between 45 and 20 is www.mathsrevision.com 60 The Product of 2,5 and 6 is 6 The Quotient when 30 is divided by 5 is Created by Mr. Lafferty @www.mathsrevision.com

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

  30. 114o Starter Questions 6 cm 10 cm www.mathsrevision.com Created by Mr. Lafferty @www.mathsrevision.com

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

  32. Square, Cube and Square Root When we multiply a number by itself we say we have squared the number. 4 3 2 2 www.mathsrevision.com 3 4 We write above as 32 = 9 42 = 16 22 = 4 Created by Mr. Lafferty @www.mathsrevision.com

  33. Square, Cube and Square Root When we multiply a number by itself we say we have squared the number. Read as a to the power 2 a2 = a x a Calculate www.mathsrevision.com 92 = 81 102 = 100 202 = 400 Created by Mr. Lafferty @www.mathsrevision.com

  34. Square, Cube and Square Root When we cube a number we mean a3 = a x a x a 23 = 2 x 2 x 2 = 8 www.mathsrevision.com Calculate 43 = 27 64 125 53 = 33 = Created by Mr. Lafferty @www.mathsrevision.com

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

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

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

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

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