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= Greatest Common Factor Lesson Plan =

Below is a 6th grade Greatest Common Factor Lesson plan that I designed. Writing techniques are integrated in this lesson as they build understanding of mathematical concepts and connections. The words in red are outlined specific writing techniques.

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__//**Overview: **//__ The Venn Factor lesson is designed to introduce 6th grade students to calculating the Greatest Common Factor of two whole numbers, while developing a definition for Greatest Common Factor. In addition, this lesson will introduce multiple representations for illustrating prime and composite factors of two whole numbers to students as they continue to develop understanding. This lesson is a part of the Factoring unit, which involves factoring of two or more whole numbers, while fully understanding what a GCF is. In this unit, once students construct their knowledge of these basic concepts, they will develop their own equations to represent two whole numbers based upon their understanding of factors and the GCF.

__//**Learning Objectives: **//__
 * Find prime factorization of various whole numbers
 * Organize prime and composite factors into a Venn diagram
 * Calculate the Greatest Common Factor
 * Develop a definition for Greatest Common Factor
 * Understand that the GCF is the multiplication of the common prime factorizations of various whole numbers.

**Common Core Standard 6.NS:** Compute fluently with multi-digit numbers and find common factors and multiples. __//**Instructional Plan: **//__
 * //__Standards Addressed: __//**
 * NYS Math Content Standards: **
 * 5.PS.10 || Work in collaboration with others to solve problems ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.PS.11 || <span style="font-family: Georgia,serif;">Translate from a picture/diagram to a number or symbolic expression ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.PS.16 || <span style="font-family: Georgia,serif;">Discuss with peers to understand a problem situation ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.CM.4 || <span style="font-family: Georgia,serif;">Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols in written and verbal form ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.CM.9 || <span style="font-family: Georgia,serif;">Increase their use of mathematical vocabulary and language when communicating with others ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.CM.10 || <span style="font-family: Georgia,serif;">Use appropriate vocabulary when describing objects, relationships, mathematical solutions, and rationale ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.CN.4 || <span style="font-family: Georgia,serif;">Understand multiple representations and how they are related ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.R.2 || <span style="font-family: Georgia,serif;">Explain, describe, and defend mathematical ideas using representations ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.R.6 || <span style="font-family: Georgia,serif;">Investigate relationships between different representations and their impact on a given problem ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.N.12 || <span style="font-family: Georgia,serif;">Recognize that some numbers are only divisible by one and themselves (prime) and others have multiple divisors (composite) ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.N.14 || <span style="font-family: Georgia,serif;">Identify the factors of a given number ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.N.15 || <span style="font-family: Georgia,serif;">Find the common factors and the greatest common factor of two numbers ||

__//**<span style="font-family: Georgia,serif;">a) Preparation/Anticipatory Set: **//__

<span style="font-family: Georgia,serif;">Once they have completed this activity and recorded their categories of information, I believe that their previous knowledge of factors in conjunction with this activity, have given them a good basis for the first activity in the lesson.
 * __**<span style="color: #ff0000; font-family: Georgia,serif;">List-Group-Label: **__<span style="font-family: Georgia,serif;"> Students will brainstorm associations related to their cue word: Factor. Students learned this term in their previous year of schooling and they have found factors of various numbers before this lesson, so they should all have a relative schema of this term already and how it relates to math. They will be limited to one page, 3 minute time and once they have their ideas on paper they will individually share their ideas with the class as I write them around the cue word on the board. (I will ask for clarification if needed.)Then students will work in cooperative teams of 2 while engaging in organizing the associations into groups of characteristics. Some associations will be broad like whole numbers, fractions and multiplication. Others might be examples of factors (because in math, most always students think of an application before a definition). Then students will categorize these associations with common characteristics by providing an appropriate label for each group. Once the students have grouped the associations into categories, they will share them with the class as well as their justification.

__//**<span style="font-family: Georgia,serif;">b) Procedures & Activities: **//__ <span style="font-family: Georgia,serif;">I will then review with the students what a Venn diagram represents (differences in the outer circles and similarities in the overlapping circles.) Students will then be given a blank Venn diagram paper. Students can then place the factor cards in the circle that they think is most appropriate. <span style="font-family: Georgia,serif;">As I circle the room I will prompt questions such as “How did you sort the cards?” and “Why did you sort the cards this way?” Then I will ask one group who is willing to go to the board and explain their Venn diagram to the class. <span style="font-family: Georgia,serif;">As a class, I will ask “What factors do the two numbers 18 and 24 have in common? [1, 2, 3, 6] Then I will follow up by asking which of these common factors is the greatest? [6] <span style="font-family: Georgia,serif;">Then I will ask students to pick two even numbers between 12 and 36 and construct a Venn diagram to find the GCF. During this activity I will go around the classroom and check for understanding. <span style="font-family: Georgia,serif;">Once the activity is completed, I will have them tell me how they would describe the GCF. //<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Components of this activity came from Illuminations: The Venn Factor //
 * <span style="font-family: Georgia,serif;">The Venn Factor: Students will be introduced to sorting factors through the use of Venn Diagrams rather than lists, which they are used to. I will first assign them partners to work with; then I will pass out baggies of cut out numbers to each group. The students will be instructed to find all factors of each 18 and 24 and then place the factors on the table in two different groups. (each factor will be on a card) Once the student’s cards have been checked, I will ask students to name the factors and I will write them on the board in the form of a list. Ex: 18 [1,2,3,6,9,18] and 24 [1,2,3,4,6,8,12,24].

<span style="font-family: Georgia,serif;">Then I will prompt the following questions to the class as a whole: <span style="font-family: Georgia,serif;">What is the prime factorization of 18? [2*3*3] <span style="font-family: Georgia,serif;">How do you know it is the prime factorization? [2 and 3 are both prime numbers] <span style="font-family: Georgia,serif;">What is the prime factorization of 24? [2*2*2*3] <span style="font-family: Georgia,serif;">What prime factors do 18 and 24 have in common? [Both 18 and 24 share one 2 and one 3] <span style="font-family: Georgia,serif;">Now, I will instruct the students to multiply the common prime factors and see the result. The result in this case is 6. The students will recognize that the GCF is the same as the GCF that they found yesterday. With this connection, I can explain to the students that the GCF of two whole numbers is the multiplication of the numbers common prime factors. <span style="font-family: Georgia,serif;">I will walk around the classroom to observe and make sure that students understand the material. If they need to, they can find the GCF of two more whole numbers of their choice if they are having difficulty. <span style="font-family: Georgia,serif;">Once students have completed this activity, they are ready to move onto the next activity, bringing with them the knowledge they now retain. //<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Components of this activity came from Illuminations: Venn Factor. //
 * <span style="font-family: Georgia,serif;">Factor Tree: Students will be introduced to a new method for finding the greatest common factor, using a factor tree. We will do this activity first as a class. I will ask students for two factors that have a product of 18. I will then ask students if the factors that they gave me are prime or composite. Then I will explain to students that if a factor is prime, they are done factoring that number. If the number is composite, they will continue to factor it until it results in two prime numbers. Then, we will do the same for the number 24. Once students have found the prime factors for each number, they will sort them into a Venn diagram like they did yesterday. Note: this time they are only organizing prime factors of the numbers rather than prime and composite factors.
 * <span style="font-family: Georgia,serif;">Once the students understand this concept, I will ask them to find the GCF of 14 and 72 using any strategy.
 * <span style="font-family: Georgia,serif;">Venn diagram strategy with prime and composite numbers.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">OR **
 * <span style="font-family: Georgia,serif;">Factor Tree with prime numbers.


 * **__<span style="color: #ff0000; font-family: Georgia,serif;">Triple Entry Form __**<span style="font-family: Georgia,serif;">: Students will be given the following mathematical terms: factor, product, prime number, composite number, greatest common factor and prime factorization. They will work individually as they create a triple entry form for these terms in the following format:

<span style="font-family: Georgia,serif;">The idea for this writing strategy came from Daniels, Zemelman & Steineke.
 * <span style="font-family: Georgia,serif;">Word || <span style="font-family: Georgia,serif;"> The students definition in their own words || <span style="font-family: Georgia,serif;"> Examples ||
 * <span style="font-family: Georgia,serif;">Since students just participated in constructive conversation on these terms in previous activities, these concepts should come rather easy to them.
 * <span style="font-family: Georgia,serif;">As students do this individually, I will also construct my own.
 * <span style="font-family: Georgia,serif;">I will collect their entries and look over them before the next time we meet.
 * <span style="font-family: Georgia,serif;"> Then I will hand them back and I will share my entry with the class to uncover any misconceptions. They will also be given an opportunity to share their thoughts and examples.

__//**<span style="font-family: Georgia,serif;">c) Differentiation: **//__
 * <span style="font-family: Georgia,serif;">Students will have prior knowledge with factors from their 5th grade class experiences that will impact this lesson. Adaptations that I could use to help support diverse learners are:
 * <span style="font-family: Georgia,serif;">Having each student record their personal interests on a piece of paper, and then have them pair with a partner and form a Venn diagram illustrating their interests (both common and uncommon.) As students do this I will ask them why they put their interests in that specific spot on the diagram. Using this before using a Venn diagram to illustrate factors is beneficial because it gives students a visual example of how to properly use a Venn diagram before using a Venn diagram in a math context.
 * <span style="font-family: Georgia,serif;"> Adding written directions on the Venn diagram worksheet for those who would rather have visual representation to look back to and if students have difficulty focusing in on verbal directions.
 * <span style="font-family: Georgia,serif;">Give the students an organized worksheet to perform their work on rather than in their notebook. It provides direction and it keeps the information organized.
 * <span style="font-family: Georgia,serif;">If students are struggling with the transition of representations of factors Venn diagram and tree diagram, rather than a list, I will show them that they can still find the GCF of two numbers by the lists that they create. (this is what they are used to from last year) However, I believe that these representations will be easier for them rather than a list.


 * //__<span style="font-family: Georgia,serif;">Materials &Resources: __//**
 * <span style="font-family: Georgia,serif;">Scissors
 * <span style="font-family: Georgia,serif;">Ziploc bags
 * <span style="font-family: Georgia,serif;">Paper and pencil
 * <span style="font-family: Georgia,serif;">Personal journals
 * <span style="font-family: Georgia,serif;">The Venn Factor cards
 * <span style="font-family: Georgia,serif;">Papers with blank Venn diagram

__//**<span style="font-family: Georgia,serif;">Assessment: **//__ <span style="font-family: Georgia,serif;">Then the second question would be to find the GCF of two whole numbers using one of the strategies we learned in class and to explain why that number is the greatest common factor.
 * <span style="font-family: Georgia,serif;">Part of my assessment will be the triple entry form that the students created in their journal. When I look over their entry, I will keep note of how well they have grasped the concepts. However, I will not give the journal entries a grade; they are more like a check for understanding.
 * <span style="font-family: Georgia,serif;">I will also give a quiz shortly after this lesson to make sure that they understand the different strategies they can use to find the GCF. My first question on the quiz would be: What is a greatest common factor?