Determining the Greatest Common Factor With "Who Is...The Greatest?"

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

6

Overview

In this action-packed math lesson, students will embark on an exciting adventure. The students will be introduced to a thrilling comic strip where brave heroes face off against a formidable foe, using their knowledge of the greatest common factor (GCF) and the least common multiple (LCM) as a weapon. Through interactive activities and challenges, students will reinforce their understanding of GCF and LCM while enjoying an engaging storyline.

This learning activity was created as a result of the ALEX - Alabama Virtual Library (AVL) Resource Development Summit.

Phase

During/Explore/Explain
Mathematics (2019) Grade(s): 6

MA19.6.8

Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

UP:MA19.6.8

Vocabulary

  • Greatest common factor
  • Least common multiple
  • Exponential Form
  • Prime Factorization
  • Factors
  • Multiples
  • Prime
  • Relatively Prime
  • Composite

Knowledge

Students know:
  • Strategies for determining the greatest common factor of two or more numbers,
  • Strategies for determining the least common multiple of two or more numbers,
  • Strategies for determining the prime factorization of a number.

Skills

Students are able to:
  • Apply strategies for determining greatest common factors and least common multiples.
  • Apply strategies for determining the product of a number's prime factors in multiple forms which include exponential form and standard form.

Understanding

Students understand that:
  • Determining when two numbers have no common factors other than one means they are considered relatively prime.
  • Composing and decomposing numbers provides insights into relationships among numbers.

Learning Objectives

Students will be able to find the greatest common factor (GCF) and the least common multiple (LCM) in two or more whole numbers.

Activity Details

1. Display the "Who Is...The Greatest" comic strip to the students by opening the PDF in the left margin of the article. Introduce the characters and storyline to pique students' interest.

2. Review the concepts of the greatest common factor and the least common multiple with the class. Display the instructions provided by the comic strip and explain the steps to find the GCF and the LCM using examples. Some strategies include:

When finding the greatest common factor (GCF) and the least common multiple (LCM) of numbers, students can use several strategies. Here are some strategies they can employ specifically when given factor pairs:

  • Listing Method: Students list all the factors of the given numbers and identify the common factors to find the GCF. To find the LCM, they can list the multiples of the numbers until they find a common multiple.
  • Prime Factorization Method: Students can use prime factorization to find the GCF. They can break down each number into its prime factors and then identify the common factors for the GCF and multiply the highest powers of the common and uncommon prime factors to find the LCM. 
  • Venn Diagram Method: Students can draw a Venn diagram with two circles and write the factor pairs of each number in the respective circles. They can then identify the common factors in the overlapping region to find the GCF. For the LCM, they can multiply the factors in both circles, including the factors in the overlapping region.
  • Division Method: Students can use the division method to find the GCF. They can divide the larger number by the smaller number and continue dividing the remainder by the smaller number until the remainder is zero. The last divisor used is the GCF. To find the LCM, they can divide the product of the two numbers by the GCF and multiply the result by the smaller number.
  • Using a Calculator: Students can use a calculator with GCF and LCM functions, if available, to find the GCF and LCM quickly. They input the numbers and use the respective functions to obtain the results.

Encourage students to choose the strategy that works best for them and practice using different methods to develop a deeper understanding of GCF and LCM concepts.

3. Divide the students into pairs or small groups. Provide each group with the comic strip containing battle challenges. The comic strip will have pairs of numbers representing the attacks and blocks. Explain that the comic strip presents a challenge related to the greatest common factor of GCF and LCM concepts.

4. In their groups, students will solve each battle challenge by finding the GCF and LCM of the given numbers. They will use the comic strip context to understand attacks and blocks.

5. Pause at key moments in the dialogue to ask students comprehension questions, such as:

  • What are the challenges presented by the stranger?
  • What does the stranger ask Booker about?
  • Why are the GCF and LCM important in this challenge?

 

6. Facilitate a class discussion to explore students' initial understanding of the GCF and LCM and its relevance in solving problems.

7. After the group work, facilitate an interactive class discussion. Solve each challenge together on the whiteboard, allowing students to share their solutions and strategies. 

8. Conclude the lesson by showing the continuation of the comic strip on page 2. Let students speculate on what might happen next and how GCF and LCM could play a role in the story. Students will complete page 2 as the assessment. 

Assessment Strategies

The students will be assessed on the correct GCF and LCM calculations from the comic strip problems. 

Acceleration

1. Advanced Problem-Solving: For students who grasp the concept of finding the greatest common factor (GCF) quickly, provide them with more challenging numbers to work with. Use larger numbers or numbers with more factors to increase the complexity of the problems.

2. Extension Activities: Offer extension activities for students who finish the comic strip activity early. These activities can include finding the GCF of larger numbers, solving word problems that involve the GCF, or exploring real-life applications of the GCF concept.

3. Group Work: Encourage students who excel in finding the GCF to work collaboratively with their peers who may be struggling. They can serve as peer tutors, explaining the process and providing guidance to their classmates.

Intervention

  1. Guided Practice: For students who need more support, provide guided practice before they attempt the problems independently. Review the steps for finding the GCF and work through a few examples together as a class. Then, gradually release responsibility by providing scaffolded practice problems with increasing difficulty.

  2. Visual Representations: Use visual representations, such as factor trees or Venn diagrams, to help students visualize the factors and identify common factors between numbers. This can assist students who struggle with abstract concepts.

  3. Differentiated Practice: Provide differentiated practice problems based on students' individual needs. Offer simpler problems with smaller numbers for those who require more foundational practice, and gradually increase the difficulty as their understanding improves.

Background / Preparation

For Student: Before engaging in the activity, students should have a basic understanding of multiplication and factors. They should be familiar with the concept of finding factors of whole numbers and be able to identify factors of given numbers. Students should also have some exposure to the terms "greatest common factor (GCF)" and "least common multiple (LCM)" and understand how to find GCF and LCM when given factor pairs.

For Teacher: To effectively facilitate the activity, teachers should familiarize themselves with the concept of finding factor pairs, GCF, and LCM. They need to review and understand the provided article to gain a clear understanding of how it connects to the concept of finding the GCF. The teacher should prepare the necessary materials, including copies of the comic strip, or provide digital access through a learning management system (LMS) and pencils or pens for students.

Learning Activity (Before)

Determining the Greatest Common Factor With "Hockey's Youngest Star"

Total Duration

46 to 60 Minutes

Learning Activity (During)

Determining the Greatest Common Factor With "Who Is...The Greatest?"

Learning Activity (After)

Determining the Greatest Common Factor With "Jason's the Greatest"

Materials and Resources

  1. Copies of the comic strip "Who Is...The Greatest" or provide digital access through a learning management system (LMS).
  2. Pen or pencil
  3. Interactive Whiteboard to project the comic strip
  4. internet-connected devices for each student or group of students. 
EBSCO Discovery Service: Middle School
https://search.ebscohost.com/login.aspx?direct=true&db=mih&AN=35249059&site=eho…

Approved Date

Owner (Author)

mgsaboyd
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