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Algebra GCF and LCM 7th grade – Mrs. DeGraaf
 * Subject **
 * Topic **
 * Grade Level **

Focus attention/motivation: 5 minutes Instructional input and modeling: 15 minutes Student engagement/practice: 15 minutes Closure: 10 minutes
 * Time Frame **

The overall goal of this lesson is to learn how to solve for GFC and LCM and how these concepts can be applied in everyday life.
 * Overall Goal/ Purpose **


 * State Standards: **
 * 6.B.3b ** Apply primes, factors, divisors, multiples, common factors and common multiples in solving problems.

The students will be able to find the greatest common factor between two or more numbers. Students will able to able to find the least common multiple between two or more numbers. 1. Smartboard 2. Post-it notes 3. Pg.z22
 * Instructional Objectives/Discoveries: **
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Materials **

**<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Focus Attention/Motivation: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> I will begin the lesson asking for a volunteer to share the DISCOVERY of yesterday’s assignment. We will review factoring. I will share with them that we are building on that knowledge. At the start of the class, I will also inform students that several of them are sitting on "HOT SEATS" and will be asked to answer questions related to the topic of study for the day.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Procedures **

I will review vocabulary with the students. The following words will be reviewed and the students will write these words in their notebooks: 1. Greatest common factor 2. Least common multiple 3. Common multiple
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Instructional Input & Modeling: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">

I will have the following steps on the smart board, and the students will write these notes in their algebra notebook: Finding the GCF by listing Factors Find the GFC of 45 and 81 45: 1, 3, 5, __9__, 15, 45 List the factors of each number. 81: 1, 3, __9__, 27, 81 Look for common factors. The GFC is 9. Identify the greatest common factor.

You can also find the GFC by first writing the prime factorization of each number. The GFC will be the product of all common prime factors.

<span style="font-family: 'Times New Roman','serif'; font-size: 14pt;">Finding the GCF by Prime Factorization <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Find the GFC of each set of numbers by using prime factorization.

140__: 2x2x7__x5 Write the prime factorization of each numbers. 112: __2x2x7__x2x2 2x2x7 Multiply the common factors. The GCF 28.

<span style="font-family: 'Times New Roman','serif'; font-size: 14pt;">Finding the LCM <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Find the LCM of 8 and12. Method 1 List the multiples of each number until you see the same multiple in each list Example: 8:8, 16 ,__24__, 32, 40, 48 12: 12, __24__, 36, 48, 60, 72 The LCM of 8 and 12 is 24. Method 2 Use prime factorization Write the prime factorization of each number. 8= 2x2x2 12=2x2x3 Write a product using each factor the greatest number of times it occurs in factorization. 2x2x2x3=24

Water boils at 100 degrees and ethanol boils at 79 degees. Find the GCF of 100 and 79. (Hint it is a small number!) Find the LCM of 100 and 79. (Hint it is a large number!) (cross-curricular with science)

If you weighed 90 pounds on the earth, your mass is 40 kilograms. Find the GCF of 90 and 40. Find the LCM of 90 and 40. (cross-curricular with science)

1. After the notes and teaching time, in teams of 4, they will solve these two real life situations: <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Situation 1. Oscar needs to ship 14 rock CDs, 12 classical CDs, and 8 pop CDs. He can pack only one type of CD in each box, and must pack the same number of CDs in each box. What is the greatest number of CDs Oscar can pack in each box? Explain.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Student Engagement/Practice: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">

Situation 2. The list shows the amounts of money the club leader collected from members for a camping trip. Each member paid the same amount. What is the most the camping trip could cost per member? Explain. List: Wednesday $36, Thursday $56, Friday $72.

After they solve these problems, I will discuss how we use GCF and LCM in everyday life.

2. Then the students will work on problems 1-18 on pg. z22 by themselves.

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> Closure: Students will be instructed to finish the worksheet at home. It will be graded the next day. I will review the need to know these concepts in life. We will the DISCOVERY of GCF and LCM. study (Greatest Common Factor). 1. Prior to the beginning of class, I will prepare questions related to the GCF and write them on sticky notes. See questions below. 2. I will place the sticky notes underneath student desks/chairs so that they are hidden from view. 4. I will have students check their desks/chairs for the sticky notes. 5. Students who have questions on sticky notes will then take turns reading the question and attempting to provide an answer. Sample Hot Seat Questions: 1. What are factors? 2. What is greatest common factor? 3. How do you find the greatest common factor between two or three numbers? 4. What are common factors? 5. How do you find the greatest common between 12 and 24? 6. What is the least common multiple. ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Before the class ends, we will do this “Hot Seat” activity: ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">In this activity, several students will be asked to sit in the "HOT SEAT" and answer questions related to the topic of

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">I will be using 3 different assessments in this lesson. I will use the predicting and asking the students if they remember doing these kinds of problems before as my pre-assessment in the beginning of the lesson to see where the students are at. I will use observations and examples on the smart board to see where students are at during the lesson. My final assessments will be when the students work in groups to solve the real life situations, “Hot Seat Activity,” and when the students work on pg. z22.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Assessment **

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The students who are having trouble will be grouped with me at the back table. I will work with them on the problems reviewing each of the steps.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Accommodations **

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;">The successful students will have the opportunity to create their own real life situations using the concepts taught in this lesson.