Summary: In this lesson (adapted from NCTM), students use Lucidchart's Venn diagram templates to sort prime factors of two (and then three) positive integers as a strategy to determine prime factorization. Students develop a definition of greatest common factor based on their exploration. Essential Questions: What is a factor? What is a prime number? What is prime factorization and how do you find it? What is the greatest common factor?
Objectives
Christie Madsen is a former elementary and middle school classroom teacher. She has spent the last five years supporting the meaningful implementation of education technologies in schools and districts nationally and internationally.
CCSS 4.OA.B4 6.NS.B4 ISTE 5B, 5C, 6C
Students will be able to... Find prime factorizations of various positive integers. Organize prime factors into a Venn diagram. Calculate the Greatest Common Factor. Develop a definition for Greatest Common Factor.
Preparation
Greatest common factor
Lesson Overview
School Name
2016/17
Standards
Grade Level: 4-6 Subject: Math Time: Two 50-minute sessions
Materials: Student devices (Chromebooks, iPads, or Lab Setting), All About Venn Diagrams Venn Diagram Templates Create a Document
Engage: Draw a blank Venn diagram with two circles on the board. Organize the class into pairs and ask them to discuss their interests/hobbies. Have one student make a list while the other draws a Venn diagram, like the one on the board. Together, have the students sort their interests onto the diagram to reveal what interests they have in common. After five minutes, pull the class back together to pose the following questions: 1. What did you list in the space of the individual circle? Unique interests or interests that students did not have in common. 2. What did you list in the overlapping section of the Venn diagram? Interests that students share. Tell students they will be using Venn diagrams to find factors that various numbers share or have in common. Review key vocabulary: Factor: numbers we can multiply to get another number Product: the result of multiplying two or more numbers Prime number: numbers that have exactly two factors, one and the number. Composite numbers: numbers that have more than two factors
Learning Plan
Explore: Tell students to list all factors of 18 and 24. After 5 minutes, call students back together to name factors of 18 (1, 2, 3, 6, 9, 18) and 24 (1, 2, 3, 4, 6, 8, 12, 24). Have students log in to their Lucidchart accounts and open the 2-circle Venn diagram template. Students then sort factors into the Venn diagram with their partner. After students have finished sorting the factors, pose the following questions to the class: 1. How did you sort the factors? 1, 2, 3, and 6 are in the overlapping circle, 9 and 18 are only in the 18 circle, and 8, 12, and 24 are only in the 24 circle. 2. Why did you sort the factors this way? 3. What factors do the two numbers have in common? 1, 2, 3, and 6. 4. What is the greatest common factor? 6. Have students change the text color or the GCF to red. Ensure that students label their Venn diagram for future reference - "18/24 Factor Diagram - Student Name" Students choose two of their own numbers and repeat individually to find the GCF. Practice as many times as needed to build student confidence in using this strategy. Circulate and offer assistance as needed. -This is a good time to end session 1.-
Evaluate: Review key vocabulary in discussion format before passing out and independent exit ticket. Review: factor, prime number, prime factorization and how you find it, greatest common factor and how you find it.
Explore (continued): Review factors of both 18 and 24 from the Venn diagram activity. Explain to students that they'll be learning a new strategy for factoring, called a factor tree. Ask students for two factors that have a product of 18. Record their answer on the board as the beginning of the factor tree. Ask students whether the factors are prime or composite. Explain: a factor is prime if they are done factoring that number; a factor is composite if they can continue to factor it using the factor tree. Continue until all factors are prime. Repeat this process with 24. Once students have found the prime factorization for 18 and 24, sort them into a new Lucidchart 2-circle Venn diagram. Ask students how this Venn diagram is different from the one they created in the previous activity (they may reference if needed). Lead them to conclude that this Venn diagram has all prime numbers. Pose the following questions: 1. What is the prime factorization of 18? 2×3×3 2. How do you know it is the prime factorization? 2 and 3 are both prime numbers because they only have factors of 1 and itself and if you multiply all three numbers the product is 18 3. What is the prime factorization of 24? 2×2×2×3 4. What prime factors do 18 and 24 have in common? 18 and 24 share one 2 and one 3 Tell students to multiply the common prime factors. The result is six. This is the same greatest common factor they found in the previous activity. Ask students to identify the greatest common factor of 18 and 24.
Elaborate: Tell students to find the greatest common factor of 14 and 72 using any strategy. As students are working, circulate to groups and ask the following questions: How did you find the greatest common factor? How do you know it is the greatest common factor?
Explain: Review two strategies to find the the GCF: 1. Factor two numbers using a Factor Tree or Venn diagram. 2. Look for the GCF in the overlapping space of the Venn diagram. If Factor Tree strategy was chosen, place prime factors in Venn diagram. Multiply the common prime factors to determine the GCF.
Have students use a Venn diagram to compare three numbers, using Lucidchart's 3-circle Venn diagram template. Repeat the same activity finding the greatest common factor of 36, 48, and 60. After they have identified, have the confirm that this is the GCF by finding the common prime factors and multiplying them. Example here.
Extensions
Teacher Reflections
Technology Integration
Assessment
Rather than a traditional paper/pencil Venn diagram, students will leverage Lucidchart's free educational offering to gain real-world, relevant experience with a best-of-breed diagramming application. Lucidchart encourages students to gain and practice digital literacy skills and provides an opportunity to create a powerful visual aids to support the explanation of a complex process.
Use the attached Greatest Common Factor Exit Ticket for independent practice. Collect on the way out the door and assess student work to offer differentiated instruction based on results.
Student Name:
3. Sort the prime factors of 20 and 35 into the Venn diagram.
2. Use a factor tree to find the prime factorization of 20 and 35.
35
exit Ticket - Greatest Common Factor
20
1. What is the greatest common factor?
Date:
4. What is the greatest common factor of 20 and 35?
