Group Lesson Plan Assignment Ranetta Goss & Santhi Prabahar Title of Lesson: Introducing Least Common Multiples (LCM) Topic: LCM Grade Level: 6 Georgia Performance Standards: M6N1. Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems. a. Apply factors and multiples. b. Decompose numbers into their prime factorization (Fundamental Theorem of Arithmetic). c. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers. M6P4. Students will make connections among mathematical ideas and to other disciplines. a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. c. Recognize and apply mathematics in contexts outside of mathematics. Class Overview: We have finished with greatest common factor (GCF). The students will spend the next 3 days on least common multiple (LCM) Materials Needed: None Technology and manipulatives (if applicable): We will play a game called Bizz Buzz. No materials are required. Students will learn to identify common multiples of two numbers. Specific Lesson Outcomes/Goals: We will start with a PowerPoint presentation to introduce Least Common Multiples (LCM). The students will be given a vocabulary sheet to follow along with the powerpoint. Once we are done with the powerpoint, the students will play a game called Bizz Buzz to get the students familiar with multiples. The game will focus on multiples of two numbers and introduce the concept of common multiples. Essential Question(s): When or why would it be useful to know the multiples of a number? Procedures: The entire LCM lesson is 3 days for 50 minute classes. Activating Strategy/Launch: 5-10 minutes Questions: Who can tell me what was the quiz about last Friday? (Answer: GCF) What is GCF? (Answer: Greatest common factor) Who can tell me what factors are? Give me an example. (Answers may vary: The factors of 9 are 1, 3, 9)
What are the factors of 15? (Answer: 1, 3, 5, 15) What are the factors of 30? (Answer: 1, 2, 3, 5, 10, 15, 30) Did any of your mom ask you to count by 2 or 5 in the car? Counting by 2: 2, 4, 6,8, 10,.. Count by 5: 5, 10, 15, 20, 25, Count by 10: 10, 20, 30, 40, 50, These are also called multiples. Multiples keep going never end. 1. Body of the Lesson: Investigation: (10-15 mins) Biz Buzz Game: 1) The students need to make a circle or semicircle behind the classroom or around the classroom. 2) The students will count the numbers from 1 to 50. 3) If they come across with factors of 3 they have to say BIZ( example 3,9 ) instead of the number. 4) If they come across with multiples of 5 (5, 10 ) then they have to say BUZZ. If they come across with both multiples of 3 and 5 then they have to say BIZ- BUZZ ( example: 15). 5) If they don t tell biz or buzz or BIZ- BUZZ then they are out. Also if they forget the next number then they are out. 6) They will keep playing until there is a winner. Whenever they say BIZ, BUZZ or BIZ- BUZZ I will start writing the numbers on the board. BIZ: 3, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, BUZZ: 5, 10, 15, 20, 25, 30, 35, 40, 45, BIZ- BUZZ: 15, 30, 45,. Once the game is over we will investigate what we did in the game by looking at the numbers on the board. I will ask questions,
What does the numbers in BIZ look like? (Answer: Multiple of 3) What does the numbers in BUZZ look like? (Answer: Multiples of 5) What does the BIZ BUZZ look like (Answer: multiples of 3 and 5) So, there are numbers that are multiples common to both3 and 5. What is the first or smallest number which is a multiple for both 3 and 5? We call this smallest number as Least Common Multiple. (LCM) Can someone tell me what kind method is this? Since we did listing and tree method in finding GCF, can you relate to one of them? They will come up with Listing Method. 2. Formative Assessment: I will be asking the following questions to assess the students understanding. 1) Can we play the game for any two numbers? Why? Why not? 2) What happens when you play for 6 and 10? 3) What is the Least common multiple you get for 6 and 10? 4) What happens if one number is a multiple of the other? Example: What is the LCM of 4 and 8? 3. Guided practice: (10mins) Now let s find the LCM of 4 and 9. Give me multiples of 4: 4, 8, 12, 16, 20, 24, 28, 36, Multiples of 9: 9, 18, 27, 36, 45, 54,... As soon as you see the common multiple, stop, and circle it. Now I want the students to work on a problem on their own: 1) Find the LCM of 12 and 15. Discuss the answer for any possibility of mistakes. 2) Find the LCM of 14 and 2 Problem Solving:
During a promotion, a music store gives a free CD to every fifteenth customer and a free DVD for every fortieth customer. Which customer will be the first to get both gifts? 1. Answer: 120 th customer. Closure: I will talk about the GCF and LCM and ask them to find the differences and similarities by making Tables. Greatest common Factor (GCF) Between two numbers List the factors of both the numbers Find all the common factors, Circle them together. Find the greatest common factor and circle them in different color. This method is listing Method Least Common Multiple (LCM) Between two numbers List the multiple of both the numbers Find all the common factors and circle them. Find the least common factor and circle them in different color. This method is listing Method Talk about confusing GCF and LCM for LCF and GCM. Tell them there is no need to find the least common factor because it is going to be 1 all the time for all the numbers. So, greatest common factor (GCF) makes sense.
Independent Practice/Homework: Find Least Common Multiple (LCM) for each number set. 1) 4 and 3 = lcm: 12 2) 7 and 4 = lcm: 28 3) 6 and 3 = lcm: 12 4) 5 and 15 = lcm: 15 5) 4 and 2 = lcm: 4 6) 4 and 7 = lcm: 28 7) 2 and 5 = lcm: 10 8) 20 and 5 = lcm: 20 9) 9 and 3 = lcm: 9 10) 12 and 3 = lcm: 12 Assessment: We will go over the homework each day to test students understanding of the material. At the end of the week the students will be given a quiz.