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# Lesson plan multiple and factors.ppt v 3

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Lesson plans for primary teachers to teach multiples and factors to grade 5 students

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### Lesson plan multiple and factors.ppt v 3

1. 1. Lesson plansHCF and LCMByKavita Grover1Class 5-Multiples &Factors, LCM &HCF
2. 2. LESSON PLAN BREAK-UPLessonplanSetting/time Slide # Topic1 Classroom/30 mins Multiples2 AV room/45 mins Composite and prime numbers3 Class room/60 mins Divisibility rules, factorization/4 AV room/45 mins Exponents and prime factorization5 Class rooom/45 mins Class test6 AV room/45 mins LCM7 AV room/45 mins LCM8 Class room/60 mins HCF9 AV room/45 mins HCF10 Class rooom/45 mins Class test
3. 3. Content• Learning objectives• Multiples• Prime and composite numbers• Test of divisibility• Factors• Factorization and index notation• LCMPrime FactorizationShort Division• HCFPrime FactorizationShort DivisionFactor tree Class 5-Multiples &Factors, LCM &HCF 3
4. 4. Learning ObjectivesThe student will be able to :• Differentiate between the terms factors and multiples composite and prime numbers LCM and HCF• Lists the multiples and factors of composite numbers• Express factors as index notations• Calculates the HCF and LCM of 2 or 3 digit numbers using Number trees Prime factorization Long division method Venn DiagramClass 5-Multiples &Factors, LCM &HCF 4
5. 5. Multiples• Multiples of a numbercan be made bymultiplying the numberby any whole number.• 1X12=12• 2X12 = 24• 3 X12 =36• 4X12=4812, 24, 36, 48, 60, 72, 84,96,108,120….aremultiples of 121 x 10 = 10,2 x 10 = 20,3 x 10 = 30,4 x 10 = 40,5 x 10 = 50,6 x 10 = 60,and so on ...5Class 5-Multiples &Factors, LCM &HCF
6. 6. Multiples• 5 10 15 20 25 30 35 40 45 50 556Class 5-Multiples &Factors, LCM &HCFA clock is set to ring at every 5thminute. Will itring 55 minutes later?
7. 7. Multiples• Is 12 a multiple of 3?If you multiply 3 by 4 you get 12, so 12 is a multipleof 3.• Is 15 a multiple of 3?3 x 5 = 15. So 15 is a multiple of 3, (and also of 5).• Is 21 a multiple of 6?21 is not a multiple of 6 because you cant make 21by multiplying 6 by any whole number.6 x 3 = 18 and 6 x 4 = 24 but there is no wholenumber between 3 and 4 that could give us ananswer of 21.
8. 8. What are the first five multiples of 13?13 x 1 =1313 x 2 = 2613 x 3 = 3913 x 4 = 5213 x 5 = 6513, 26, 39, 52, 6513, 26, 39, 52, 658Class 5-Multiples &Factors, LCM &HCF
9. 9. Find the Missing Multiples• 6, 12, 18, ____, ____• ___, 6, 9, 12, ____, ____, 21• ___, 24, 36, 48, 60, ____24 303 15 1812 729Class 5-Multiples &Factors, LCM &HCF
10. 10. Composite and Prime numbers10Class 5-Multiples &Factors, LCM &HCF1 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
11. 11. Prime Numbers• A prime number is a positive integer that has exactlytwo positive integer factors, 1 and itself.• For example, if we list the factors of 28, we have 1,2, 4, 7, 14, and 28. Thats six factors.• If we list the factors of 29, we only have 1 and 29.Thats two factors. So we say that 29 is a primenumber, but 28 isnt.11Class 5-Multiples &Factors, LCM &HCF
12. 12. Composite Numbers• A Composite Number can be divided evenly by numbersother than 1 or itself.• Example: is 6 a Prime Number or Composite Number?• 6 can be divided evenly by 2, or by 3, as well as by 1 or 6:• 6 = 1 × 66 = 2 × 3• So 6 is a Composite Number12Class 5-Multiples &Factors, LCM &HCF
13. 13. Factors• Factors are the numbers you multiplytogether to get a product or a factor is anumber that exactly divides another numberwithout leaving a remainder.• 12 can be written as the product of 2 x 6 or2 x 6 = 1213Class 5-Multiples &Factors, LCM &HCF2 and 6 arethe factorsof 1212 is themultiple of itsfactors 2 and6
14. 14. FACTORSThe factors of 12 are:– 1 x 12– 2 x 6– 3 x 4– 4 x 3– 6 x 2– 12 x 1• 12 can be divided evenly by 1, 2, 3, 4, 6 and 12:– 1 × 12 = 12– 2 × 6 = 12– 3 × 4 = 12• So 12 is a Composite Number• The factors of 12 are 1, 2, 3, 4, 6, and 12Class 5-Multiples &Factors, LCM &HCF 14
15. 15. Factors15Class 5-Multiples &Factors, LCM &HCF• For example, the product 24 has severalfactors.• 24 = 1 x 24• 24 = 2 x 12• 24 = 3 x 8• 24 = 4 x 6• So, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
16. 16. Divisibility rules• A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8.• A number is divisible by 3 if the sum of the digits is divisibleby 3.• A number is divisible by 4 if the number formed by the lasttwo digits is divisible by 4.• A number is divisible by 5 if the last digit is either 0 or 5.• A number is divisible by 10 if the last digit is 0.• A number is divisible by 8 if the number formed by the lastthree digits is divisible by 8.• A number is divisible by 9 if the sum of the digits is divisibleby 9.• A number is divisible by 6 if it is divisible by 2 AND it isdivisible by 3.16Class 5-Multiples &Factors,LCM &HCF
17. 17. Writing facorsThe factors of 48 are1 x 482 x 243 x 164 x 126 x 8Another way of writing factors is:Write your first pair of factors with areasonable space between them, thenmove on to the next pair until youhave them all.This way, when you get to the 6,8 pair,you can stop because 7 is not a factorand you already have 8 in your list.17Class 5-Multiples &Factors, LCM &HCF
18. 18. Exponential Notation or IndexNotation• 4cm x 3cm= 12 cm square• When a number is multiplied by itself severaltimes, we express the product in the givenform:• 3x3=32= three raised to the power 2• 4 x 4 x4 x 4 x 4= 4 5= 4 raised to the power 5• 8 7= 8 x 8 x 8 x 8 x 8 x 8 x 8• 2 x 2 x 2 x 4 x 4 = (2 x 2 x 2) x (3 x 3) =23x 42Class 5-Multiples &Factors, LCM &HCF 18
19. 19. Exercise 11) Write in the exponential form.a) 5 x 5 x 5=b) 10 x 10 x 10 x 10=c) 6 x 6 x 6 x 6 x 6=d) 2 x 2 x 3 x 3=e) 8 x 8 x 8 x 4 x 4 x 4 x 41) Write in the product form.a) 8 7=b) 6 3x 11 4=Class 5-Multiples &Factors, LCM &HCF 19
20. 20. Factorization & Exponents• 60=1x6060=2x3060=3x2060=4x1560=5x1260=6x1020Class 5-Multiples &Factors, LCM &HCF60
21. 21. Factorization & Prime Factorization• The factorpairs for 60 are• 60=1x6060=2x3060=3x2060=4x1560=5x1260=6x10602 30Compositenumber3 10Compositenumber2 560 is written as the product of its prime factors60 = 2 x2 x 3 x 5
22. 22. FACTOR TREE• 60=4x15=2x2 x3 x5604 153 522
23. 23. Prime factorization through shortdivision6030152235 51The prime factors of 60 are2x2x3x52, 3, and 5 are all prime numbers,so we have prime factored 60. Allwe have to do now is neaten ouranswer up a bit. It is customary towrite prime factorizations inincreasing order, that is with thesmallest numbers first.
24. 24. Prime Factorization24Class 5-Multiples &Factors, LCM &HCFSo the prime factorization of 910 is 2x5x7x13• Now let us try another example: 910
25. 25. Least common Multiple-LCM• A cold drink truck visits Ritas neighbourhoodevery 4 days and Amul ice cream truck visitsher neighborhood every 5 days. For themonth of June on which day will both thetrucks visit on the same day?25Class 5-Multiples &Factors, LCM &HCF1 2 3 4 5 6 78 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30
26. 26. Least common Multiple-LCM• In the given problem we have to first find the multiples ofboth the numbers.• Cross out the multiples that are common. (20 and 40)• Which multiple is the least-20• Both the trucks will visit the neighbour hood on 20 June orafter 20 days.Truck Days of visit1 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44,...2 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,...26Class 5-Multiples &Factors, LCM &HCF
27. 27. Exercise -Find the LCM of 18 and 24.Multiples of 18 18, 36, 54, 72, 90, 108, 126, 144,…Multiples of 24 24, 48, 72, 96, 120,144, ….• Common multiples of 18 and 24 are 72 and 144• The least common multiple of 18 and 24 is 72.• LCM = 72
28. 28. Highest Common Factor-HCFFind the HCF of 60 and 72,1815260 ,7230 ,365 ,623 ,1815260 ,7230 ,365 ,623The common factors of 60and 72 are 2 x 2 x 3The HCF of 60 and 72 =2x2x3=12Uncommonfactors
29. 29. HCF by prime factorizationFactors of60Factors of72
30. 30. LCM of 60 and 72• To find the LCM of 60and 72 we multiplyall the factors.• 2x2 x3x5x6 = 336• So the HCF of 60 and72 is 12 and• LCM is 336,1815260 ,7230 ,365 ,623
31. 31. Find the HCF of 56 and 48– Prime Factor Tree for 56 • Prime Factor Tree for 48562228142 756 is all the prime numbers2 x 2 x 2 x 7 multipliedtogether482224122 62 348 is the prime numbers2 x 2 x 2 x 2 x 3multiplied together
32. 32. Look for common factors in both treesMultiply them together =xx482224122 62 3562228142 722288 is the biggest number that goes into both 56 and 48So it is the Highest Common FactorFinding the Highest Common Factor
33. 33. HCF through Prime Factorization• The prime factors of :56 = 2 x 2 x 2 x 748 = 2 x 2 x 2 x 2 x 3The prime numbers that are common are:2x2x 2= 8So the HCF of 56 and 48 is 8
34. 34. HCF & LCM as a diagram22 273535Write the common primefactors of both 504 and700 here .The HCF =2X 2 X 7=28Write the other PRIMEFACTORS of 504 in the504 circleWrite the other PRIMEFACTORS of 700 in the700 circle504 700The LCM is found by multiplying all the numbers from the circles504 = 2 x 2 x 2 x 3 x 3 x 7700 = 2 x 2 x 5 x 5 x 7
35. 35. The four different ways to find the HCF50422 273535700,1815260 ,7230 ,365 ,623The prime factors of :56 = 2 x 2 x 2 x 748 = 2 x 2 x 2 x 2 x 3The prime numbers that are common are:2x2x 2= 8So the HCF of 56 and 48 is 8xx482224122 62 3562228142 72228