Lesson Lesson Innovation Of Lcm Using Prime Number Factorization / Partitioning Method Mathematics Shape V

Lesson Plan of LCM Using Prime Factorization / Division Method

Mathematics Grade V

Students’ Learning Outcomes

·         Find LCM of 4 numbers, upwardly to 2 digits, using prime number factorization method.

·         Find LCM of 4 numbers, upwardly to 2 digits, using partitioning method.

Information for Teacher

·         Since the students conduct hold done both factorization together with partitioning method for finding H CF, thus they won’t detect this difficult.

·         First larn with iii numbers questions together with explicate both methods, together with thus private or grouping operate together with and thus hash out on 4 numbers questions.

·         When whatever release is used to multiply with the educate of natural numbers {1, 2, 3, ……}, the production of that release with each of the natural numbers is called multiples of that number, e.g. the multiples of iii are : 3(1), 3(2(, 3(3), 3(4(, …. Which are respectively equal to 3, 6, 9, 12……..

·         The number/multiple alongside the mutual multiples of 2 or to a greater extent than numbers is called the to the lowest degree mutual multiple.

·         Least mutual multiple is abbreviated every bit ‘LCM’.

·         Find LCM of 2 or to a greater extent than numbers through multiples.

·         In this method nosotros detect few multiples of all given numbers, together with thus write the mutual multiples separately together with the smallest of these mutual multiples is called LCM.

·         Find LCM of 6, 8 together with 12 past times finding multiples.

·         Find LCM of 2 or to a greater extent than numbers through prime number factorization.

·         In prime number factorization method the production of mutual together with uncommon factors is called LCM.

·         In this method, start write prime number factorization of each given number, together with thus inward each factorization, the factors repeating, write them inward exponential form.

·         Separate all highest ability factors from all factorizations.

·         Now the production of all factors is called LCM.

·         Find LCM of 72, 24, 96 together with 12 past times using prime number factorization.

·         LCM of the given numbers = inward all factorizations, production of all such prime number factors which having highest exponent.

·         Instead of writing factors inward exponential form, yous tin set all the mutual factors afterwards factorization of each number, together with and thus production of all mutual together with uncommon factors is called LCM.

·         To detect LCM piece writing the mutual factors, maintain inward hear that it is non necessary that mutual factors are mutual inward all given numbers, if they are mutual inward at to the lowest degree 2 of given numbers together with thus these are too consider inward mutual numbers.

LCM of given numbers = production of mutual factors (including factors mutual inward at to the lowest degree 2 numbers) together with uncommon factors.

=     2 x 2 x 2 x 3 x 2 x 2 x 3

                                         LCM    = 288 

·         Find the LCM of 2 or to a greater extent than numbers using partitioning method.

·         To detect LCM of 2 or to a greater extent than numbers using partitioning method, nosotros buy the farm on the partitioning procedure until below all numbers nosotros conduct hold 1’s every bit quotient.

·         The divisors may live prime number together with composite, but endeavor to carve upwardly with smallest number.

·         In this method the production of divisors of the numbers is called LCM.

·         Like finding H CF past times using partitioning method (Ladder method) it is non necessary that all the numbers volition carve upwardly with ane divisor. I.e. the release which is non divisible past times that divisor, together with thus merely write that release down.

·         Find LCM of 72, 24, 96 together with 12 using partitioning method.

·         During didactics the lesson, instructor should describe of piece of job concern with text book, when together with where necessary inward all steps.

Material / Resources

Board, marker/chalk, duster, text book

Worm upwardly activeness

·         Divide the students inward pairs.

·         Inform students that yous tin hash out with each other nigh factors of numbers together with prime number factorization for ane minute.

·         They volition need to select which pupil volition create down first.

·         Provide students with the iii or 4 questions to aid inward their discussion.

·         For give-and-take inward pairs, allocate fourth dimension 2 minute.

·         At ane minute, instruct students to switch. At this point, the other partner begins talking.

·         It is OK for the 2nd pupil to repeat approximately of the things the start pupil said.

·         However, they are encouraged to endeavor together with think of novel data to share.

Two infinitesimal sample questions:

o   What are factors?

o   Can yous say 2 things nigh factors?

o   What are prime number or composite factors?

o   How would yous detect the factors of a number?

o   What is meant past times factorization?

o   What is prime number factorization?

Development

Activity 1

·         Inform the students that the numbers carve upwardly whatever release precisely is called factors of this number. E.g. all possible factors of thirty are 1, 2, 3, 5, 6, 10, 15, 30.

·         In these factors 2, 3, v are prime number factors piece 6, 10, 15, thirty are composite factors.

·         Now say the students that to write whatever release every bit a production of its factors is called factorization. E.g. release thirty tin live expressed every bit a production of its factors inward unlike ways. I.e. next are the factorizations of 30, thirty = 1 x thirty or = 2 x fifteen or =3 x 10 or = v x six or = 2 x 3 x 5.

·         Similarly to limited whatever release every bit a production of its prime number factors is called prime number factorization. As according to inward a higher house example, prime number factorization of thirty = 2 x 3 x 5.

·         All possible factors of xviii are 1, 2, 3, 6, 9, together with 18.

·         In these factors 2, 3 are prime number factors while, 6, 9, xviii are composite factors.

·         Number xviii tin live expressed every bit a production of its factors inward unlike ways. I.e. next is the factorization of 18, xviii = 1 x xviii or =2 x nine or = 3 x 6.

·         Similarly prime number factorization of xviii = 2 x 3 x 3

·         A prime number factorization of a release tin live written inward the exponential form.

E.g. xviii = 2 x 3 x 3 = 2 x 3²

36 = 2 x 2 x 3 x 3 = 2² x 3²

Activity 2

·         Are yous create for something novel but every bit interesting every bit H CF was.

·         OK say what do nosotros hateful past times the tidings product?

·         Write 3, 4, together with six on board together with say the students nosotros are interested inward the smallest release that is divisible past times 3, 4 together with 6.

·         If nosotros should detect the production of all iii numbers i.e. nosotros multiply 3 x 4 x six = 72. It seems logical that 72 should live easily divisible past times 3, 4 together with six since 72 is the production of these numbers.

·         Ask the students, “Is 72 the smallest release that is divisible past times 3, 4 together with 6?”

·         After collecting response from students tells that the reply is “no”, since 36, which is half of 72, is too divisible past times 3, 4 together with 6.

·         Conclude that such a smallest release that is divisible past times all given numbers is called LCM.

Activity 3

·         Write on the board 42, 96 together with 24 or whatever other query from text book.

·         Ask the students to write the given numbers every bit production of prime number factors. E.g. 2 x 2 x 3 etc.

·         Now write inward exponential form, the numbers which are repeating ane time to a greater extent than together with ane time to a greater extent than inward each factorization.

·         After few minutes, instructor does them on the board every bit done inward the event given inward “information for teacher”.

·         Now inquire them to write the highest ability factors every bit product. E.g. 25 x 32.

·         Give few minutes to try, together with and thus inquire them to detect answer. Thumb upwardly who does it.

·         Now do it on the board together with explicate according to the method given inward “information for teacher”.

·         Conclude that nosotros detect LCM of these numbers using prime number factorization.

·         Repeat this concept with the aid of approximately other example.

·         If students experience hard to write inward exponential shape together with finding LCM, together with thus inquire them to write all the mutual factors together with uncommon factors every bit production together with and thus detect LCM.

·         Now say the students, how to solve the query according to this method.

·         For exercise laissez passer on students inward groups, ane or two-digit iii numbers than 4 numbers questions together with inquire them to detect LCM using prime number factorization.

Activity 4

·         Ask students, do yous shout out back the brusque cuts to banking concern check whether the release is divisible past times 2, 3, together with v or 10?

·         After taking their answer, say the divisibility seek rules to all.

·         Divisible past times 2 if the final digit (ones digit) is 0, 2, 4, six or 8 event 12345.

·         Divisible past times v if the amount of digits inward the release is divisible past times 3. Example 12345.

·         Divisible past times v if the final digit (ones digit) is 0 or v event 2345.

·         Divisible past times 10 if the final digit (ones digit) is ‘0’ event 99990

·         Tell them that this volition aid them piece doing LCM with partitioning method.

Activity 5

·         Write 3, 4 together with six on board together with solve with the aid of students.

·         Now start dividing each release past times the smallest release similar 3, write their reply (quotient) below these numbers.

·         If whatever of the numbers is non divisible past times 3, merely write that release down.

·         Again start dividing past times whatever smallest release similar 2 together with then, if whatever of the numbers is non divisible past times it, write that release down.

·         Continues this procedure until inward the final line, below each release nosotros conduct hold all 1’s every bit quotient.

·         Now past times multiplying all the divisors nosotros larn LCM.

·         Conclude that nosotros conduct hold institute the LCM of these numbers past times partitioning method.

·         Repeat this concept with the aid of approximately other example.

·         For exercise laissez passer on students inward groups, ane or two-digit iii numbers than 4 numbers questions together with inquire them to detect LCM using partitioning method.

Activity 6

·         Assign ane query to each pupil together with inquire to detect LCM past times using both methods.

·         Allocate time.

·         Ask students to banking concern check each other operate together with right the mistakes.

·         Guide the students inward query solving.

Sum upwardly / Conclusion

·         Least mutual multiple is abbreviated every bit ‘LCM’.

·         Recap the method of finding LCM using prime number factorization.

·         Recap the next method of finding LCM using division.

·         We write downwards the numbers horizontally.

·         We depict a vertical describe to the left of the numbers together with depict horizontal describe nether the numbers.

·         We than await for the smallest release that tin carve upwardly whatever of the numbers exactly.(try to select the prime number divisor)

·         If whatever of the numbers is divisible past times divisor, writing downwards the reply of that partitioning below line. Similarly if whatever of the numbers is non divisible past times divisor, write that release downwards below the line.

·         Then nosotros depict approximately other horizontal describe together with repeat this process.

·         When yous larn all 1’s every bit quotient inward a horizontal line, together with thus multiply all the divisors that are vertical, together with the production called LCM.

·         Solve query on board according to both methods.

Assessment

·         Find LCM of 48, 24, sixteen together with 72 past times using prime number factorization method.

·         Find LCM of 30, 18, 68, 8 past times using partitioning method.

Follow up

Questions	By using prime number factorization	By using division

·         Draw the inward a higher house said tabular array on board, write questions together with inquire students to detect LCM past times both methods.

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