Southern Luzon State University COLLEGE OF TEACHER EDUCATION Laboratory Elementary School Lucban, Quezon A Detailed Lesson Plan in Mathematics V (Finding Greatest Common Factor) Final Demonstration September 17, 2013 10:20am – 11:20am V-Gladiola Presented by: Ms. Marian Q. Padua Pre-Service Teacher, BEEd Gen. Ed. Noted by: Mrs. CECILE P. COSEJO Cooperating Teacher Approved by: Prof. LUCILA E. ABSULIO Supervisor, BEEd Gen. Ed Prof. MARISSA M. SACOPLA Chairman SLSU-Laboratory Elementary School Dr. HELENE D. DAYA, RGC Principal, SLSU-Laboratory Schools I. Objectives 1. Find the greatest common factor of a set of number. 2. Recognize the different ways of finding the greatest common factor of a set of number. 3. Apply the greatest common factor in solving word problem. 4. Improve the value of patient by following direction. II. Subject Matter Topic: Finding Greatest Common Factor and Applying GCF in Solving Word Problem. References: Math for Life pp. pp.98-99 Number Smart Quest for Excellence pp.119-121 Materials: Dora’s bag pack, envelope, tree, projector, box, Venn diagram. Value: Patience III. Procedure Teacher’s Activity A. Preparatory Activities 1. Prayer 2. Checking of Attendance 3. Energizer Class, before we proceed to our lesson for today, we will sing first. Chu…chu…chudo.. Gladiola Chu…chu…chudo.. Gladiola Chu…chu…chudo.. Gladiola Chu…chu…chudo.. Gladiola Common lets study Mathematics It’s fun to study this subject. Need my help and Dora’s bags pack. Where are we going? to Gladiola. Where are we going? to Gladiola.. 4. Drill ( The teacher will play an audio of the “ Dora the Explorer song” ) Children, I, Dora is looking for a treasure. I want you to help me find the treasure box. Did you see the treasure box? Let’s find out what is inside the treasure box. Pupil’s Activity Yes, we did! There are three mystery problems inside the treasure box, and you need to answer these problems: 1. 2×2 ×2×2= 2. 2×3= 3. 2×2×5= I want you to help me solve these problems: 1. 2×2 ×2×2= 2. 2×3= 3. 2×2×5= Very good! You did it! 5. Review Class, now that we solved the problem inside the treasure box, it’s time to go our next destination. There’s a note inside the treasure box. “Find the big tree and look for the two hanging fruits” Where are we going? Where are we going? This time, let’s answer the problem hanging in the big tree. 24 6 20 We’re going to the big tree! We’re going to the big tree! You will complete the present factorization of each number by building a factor tree. Very good! Now that you really understand the lesson about prime factorization. Will you dare to patient, listen, follow directions and wait for further direction? D. LESSON PROPER 1. Motivation Children, I have here a bag pack. My bag pack says she’s looking for her maps. Class, the three maps are our password to open the gate to our new destination. Three of you will hold the maps. The person holding the map will go in front and show to us the map you are holding. This time, kindly look at the back (The pupil’s will answer the factors of 36 and 42) Yes we did! 36 42 3 12 3 14 2 6 2 7 2 3 1 7 36 42 of the map. What does each letter stand for? You did it! 2. Presentation Welcome to Mathematics World! Class, I have here a Venn diagram. 24 18 Now, let’s have first number 24. Will you please tell me, what are the factors of 24? Very good! What are the factors of 18? ( The three pupils will show the maps) G stands for greatest C stands for common F stands for factor 24 18 The factors of 24 are: 1, 2, 3, 4, 6, 8,12, and 24 24 1 12 2 3 8 6 4 18 9 1 6 2 3 18 9 1 18 2 9 6 3 That’s right! Now, what did you notice to the factors of 24 and 18? 24 18 What are those numbers they have in common? Correct! What do you call to this numbers: 1, 2, 3, and 6? Very good! 24 18 These numbers at the center are common factors of 24 and 18. Now which of these numbers: 1, 2, 3, and 6 is the greatest common factor of 24 and 18? 24 18 The factors of 18 are: 1, 2, 3, 6, 9, d 18. There are numbers in common. The numbers they have in common are : 1, 2, 3, and 6. These numbers are called COMMON FACTOR. 24 1 12 2 3 8 6 4 24 12 8 4 Why is it 6? What are the common factors of 24 and 18? Very good! Now, what is GCF? It is the greatest number that can be divided. Children, there are different ways in finding the greatest common factor of a set of number. Let’s find out what are those. Now let’s find the GCF of 15 and 24. This time, I want you to list all the factors of these two n umbers. What are the factors of 15? Good, what about 14? Now, will you please encircle the factors of 15 and 24 that are common? Correct! What do you call these encircled numbers? Which of these numbers 1, 3, is greater? Therefore, the greatest common factor is 3. Based on the examples, how do we get the GCF? This time let’s try this example. The greatest common factor is 6. It is the greatest common factor. The common factors are: 1, 2, 3, and 6. GCF is the greatest divisor. 15 = 1, 3, 5 , 15 24 = 1, 2, 3, 4, 6, 8, 12, 24 15 = 1, 3, 5, 15 24 = 1, 2, 3, 4, 6, 8, 12, 24 Numbers 1, 3 is the common factors of 15 and 24. Number 3. We get the GCF by using the LISTING METHOD. Fifteen boys and twenty-four girls formed groups for a stamp collecting project. What is the greatest number of members in a group which has equal number of boys and girls? Now, what are the prime factors of 16? Good! What about 32? And now, what are the common prime factors of 16 and 32? Now, that you already get the prime factors of 16 and 32. The first step is to multiply the common prime factors to get the GCF. Now, you multiply these numbers: 2 x 2 x 2 x 2 = ____ Very good! Therefore, what is the GCF of 16 and 32? What is the quotient if you divide 32 by 16? How about dividing 16 by 16? 16 8 x 2 4 x 2 2 x 2 2 x 2 x 2 x 2 32 8 x 4 4 x 2 2 x 2 2 x 2 x 2 x 2 x 2 16 = 2 x 2 x 2 x 2 32 = 2 x 2 x 2 x 2 x 2 The common prime factors are 2 x 2 x 2 x 2. 16 The GCF of 16 and 32 is 16. 2 Arthur has 16 small shells and 32 big shells which he wants to arrange equally in boxes. Each box should have only one size of shell, either all small or all big. What is the greatest number of shells that can be in one box? Therefore, the GCF 16 can be divided into 16 and 32. 16 is the greatest divisor. What is the greatest number of shells that can in one box? What do we call to this method that we used? Very good! This time, we will enter to the second door of the cave. Let’s find out, what’s inside the second door. Children, there is a third problem in the second door. Let’s try it. What is the greatest number of books that can be place on each table? What are the given numbers of books in science and math? This time we are going to use the CONTINUOUS DIVISION METHOD. What is the possible lowest common divisor of 72 and 48? 1 The greatest number of shells that can be in one box is 16. The method that we used is Prime Factorization or Factor Tree Method. The given numbers of books are 72 and 48 for science and math respectively. The possible lowest common divisor The librarian needs to put 72 science books and 48 math books on some tables. She wants to put the Science and Math books in separate tables, with each table having same number of books. So this is how we are going to present it. 2 I_72____48_ I_36____24_ Who could explain the expression above? Very good! So who continue the process since 36 and 24 are not yet on their simplest form? Is quotient could still be factor? Then what is the next step of the method? Then who could continue this expression? Based from what we had done, what is the final step to get GCF? So, what is the product did you get? What do you call this number? Then, what is the greatest number of books that can be placed on each table? Very good! Is it clear to you class? 3. Comparison and Exploration Class, since we’ve finished our adventure inside the cave, we need to ride on a boat for us to go to our destination. But we will need a ticket to ride on this boat, and for us to have a ticket we need to solve this problem using the three methods in finding GCF. of 72 and 48 is 2. We divide the numbers by a prime number which is two and we write the quotients below the dividends. 2 I_72____48_ 2 I_36____24_ I_18____12_ Yes it is. The next step is to continue the process until none of the numbers have common prime divisors. 2 _72____48_ 2 _36____24_ 2 _18____12_ 3 _ 9___ 6 _ 3 2 Multiply the all the prime divisors. 2 x 2 x 2 x 3 = 24 24 is the GCF of 72 and 48. The greatest number of books that can be place on each table is 48. Yes it is! Now solve the problem by finding the GCF using the three methods. What is the greatest number of foods that can be place on each tray? Very good! 4. Generalization Now, that you solved the problem, we can ride now to the boat going to our next destination. There at the cave we find the three methods in finding GCF. Now, what are the different methods in finding the greatest common factor? That’s right! What are the steps in finding the greatest common factor using the prime Listing Method 54= 1, 2, 3, 6, 9, 18, 27, 54 36= 1, 2, 3, 4, 6, 9, 12, 18, 36 GCF = 18 Factor Tree Method 54 36 18x3 18x 2 3 x 9 9 x 2 3 x 3 3 x 3 GCF= 18 Continuous Division 3 _54____36_ 2 _18____12_ 3 _9____ 6_ 3 2 GCF = 18 The greatest number of foods that can be place on each tray is 18. The methods in finding GCF are the listing method, prime factorization and continuous division method. Boots needs to put 54 bananas and 36 cupcakes on some trays. He wants to put the bananas and cupcakes in separated trays, with each trays having same number of foods. What is the greatest number of foods that can be place on each tray? factorization or factor tree method? Then, what is the next step? What will you do to the common prime factors? Very good! How about in Continuous division method? What will you do next? Very good! Is it understood? 5. Fixing Skills Children, I prepared three activities for you. Direction: Fill in the square The first step is to get the prime factors of a number. Identify the common prime factors. Multiply the common prime factors to get the GCF. The first step is: 1. Divide the numbers by a prime number and write the quotients below the dividends. 2. Continue the process until none of the numbers have common prime divisors. Then multiply the prime divisors to get the greatest common factor. Yes it is! Answers: 1. 5,2 GCF=3 2. 2, 14 GCF= 8 3. 2,3,4,4,5 GCF=4 1. 15= 3x___ 24= 2x2x___x3 GCF= _____ 2. 32 56 2 16 28 2 8 __ 4 7 GCF= ______ 3. 12=1, __, __, __, 6, 12 20=1, 2, __, __, 10, 20 GCF= ________ LISTING METHOD 6= 16= GCF 6. APPLICATION Now that you made it through the treasure box, you found the tree and the maps, and finally you passed the cave. It’s time for you to receive a reward for being patient in following the directions. Class I will group you into three (3). Then each group will receive one gift. Each gift box contains different set of problems. You are going to answer the problem assign to you. I will give you only three (3) minutes to answer. 7. Evaluation Direction: Find the GCF of the following set of numbers. 1. 24= CONTINUOS DIVISION 25 AND 75 GCF PRIME FACTORIZATION 14= 60= 40= GCF= 2. 20= 36= GCF= 3. 20= 30= GCF= 4. 15 28= GCF= 5. 18= 30= GCF= IV. Assignment Direction: Answer the following questions using the three methods. 1. What is the common factor of 14, 37 and 42? 2. Find the GCF of 18, 45 and 81 Answers: 1.6=1,2,3,6 16=1, ,2 ,4 ,8, 16 GCF= 2 2. 5 25, 75 5 5, 15 1 3 GCF= 25 3. 14= 2x7 60= 2x5x3x2 GCF= 2 Answers: 1. 8 2. 4 3. 10 4. 1 5. 6
Posted on: Mon, 24 Mar 2014 00:48:30 +0000
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