ALEX Learning Activity

  

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

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  This learning activity provided by:  
Author: Ginger Boyd
System:Geneva County
School:Samson Middle School
  General Activity Information  
Activity ID: 3054
Title:
Determining the Greatest Common Factor With "Jason's the Greatest"
Digital Tool/Resource:
Explora for Middle Schools
Web Address – URL:
Overview:

In this engaging activity, students will combine the world of mathematics and pop culture by delving into interesting facts about the talented singer, songwriter, and dancer Jason Derülo. Through an interactive activity featured in the Alabama Virtual Library, students will have the opportunity to reinforce their understanding of important mathematical concepts while simultaneously piquing their interest in music and pop culture. Through this interactive approach, students will gain confidence in applying the greatest common factor (GCF) and the least common multiple (LCM) concepts to practical situations while enhancing their problem-solving skills.

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

  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 6
8. Find the greatest common factor (GCF) and least common multiple (LCM) of two or more whole numbers.

a. Use factors and multiples to determine prime factorization.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given any two or more whole numbers,
  • Strategically select and apply strategies for finding the greatest common factor of the two numbers and justify that the strategy used does produce the correct value for the greatest common factor.
  • Strategically select and apply strategies for finding the least common multiple of the two numbers and justify that the strategy used does produce the correct value for the least common multiple.
  • Use the relationship between factors and multiples to determine prime factorization.
Teacher 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.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.6.8.1: Identify the least common multiple of a given set of numbers, with or without the use of a calculator.
M.6.8.2: List multiples of any given whole number, with or without the use of a calculator.
M.6.8.3: Identify the greatest common factors of a given set of numbers, with or without the use of a calculator.
M.6.8.4: Define prime factorization.
M.6.8.5: List common factors of given whole numbers, with or without the use of a calculator.
M.6.8.6: Identify the prime factorization of a single digit number, with or without the use of a calculator.
M.6.8.7: Identify the prime factorization of any two digit whole number, with or without the use of a calculator.

Prior Knowledge Skills:
  • Define Multiple.
  • Name the first ten multiples of each one-digit natural number.
  • Name the first 10 multiples of each one-digit natural number.
    Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.
  • Count within 1000; skip-count by 5s, 10s, and 100s.
  • Recall basic multiplication facts.
  • Name the first ten multiples of each one-digit natural number.
  • Identify all factor pairs for a whole number in the range 1-20.
  • Apply properties of operations as strategies to multiply and divide.
  • Define factors, prime number, and composite number.
Learning Objectives:

Students will be able to find the greatest common factor (GCF) and least common multiples (LCM) of number pairs.

  Strategies, Preparations and Variations  
Phase:
After/Explain/Elaborate
Activity:

  1. Introduction and Review(10 minutes): The teacher will begin the activity by reviewing the concepts of greatest common factors and least common multiples. They will provide clear explanations and examples to ensure students have a solid grasp of these mathematical ideas.

  2. Students will be given the article, Jason's The Greatest, which includes various interesting facts about Jason Derülo, each associated with a GCF problem. They will solve each problem by finding the greatest common factor of two given numbers. Students will circle the correct answer, which will complete the statement about Jason. This activity will allow students to practice their GCF skills while having fun discovering facts about the artist.

  3. After completing the GCF skills of the article, students will embark on a "Least Common Multiples Challenge." They will be provided with a new set of numbers (the teacher can just make these numbers up and project them on the interactive whiteboard) and tasked with finding the least common multiple (LCM) of each pair. Students will work individually or in pairs to solve the LCM problems and compare their answers with their peers.

  4. The teacher will lead a whole-class discussion, reviewing the GCF and LCM problems and providing explanations for each. This time will also be used to share interesting facts about Jason Derülo discovered through the activity.

Assessment Strategies:

The assessment for this activity will involve two components:

  1. The teacher will review the completed article, "Jason's The Greatest" (including the Least Common Multiple Challenge), to gauge students' understanding of these concepts. They will provide feedback and support as needed.

  2. Class Participation and Engagement: Throughout the activity, the teacher will observe students' participation and engagement, looking for struggling students.


Advanced Preparation:

Approximate Duration: The activity can be completed within one class period, which typically lasts around 45 to 60 minutes. However, the duration may vary depending on the pace of student engagement, class discussions, and the inclusion of additional extension activities or assessments. Teachers can adapt the activity to fit their specific instructional time constraints and student needs.

Background Knowledge/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 article and pencils or pens for students.

By adequately preparing and having a solid understanding of the concepts and materials involved in the activity, teachers can effectively guide students in exploring and applying the concept of finding the greatest common factor (GCF) while using engaging and relevant resources such as the provided article.

Print copies of the article Jason's The Greatest, or students can access it through an LMS or directly through the Alabama Virtual Library

Materials:

  1. Print copies of the article or provide access to Jason's The Greatest through a learning management platform for student access. 
  2. Internet-connected devices for the students.
  3. Projector or Interactive Whiteboard
  4. Pencils or pens
Variation Tips (optional):

Acceleration: 

For students who grasp the concepts quickly, the teacher can provide more challenging GCF and LCM problems or introduce additional real-life applications. These students can also be encouraged to create their own GCF and LCM problems for their peers to solve.

Intervention:

Students who struggle with GCF and LCM can receive additional support through one-on-one or small-group interventions. The teacher can use manipulatives or provide extra practice worksheets to reinforce the concepts. Additionally, peer tutoring can be utilized to help struggling students catch up with the rest of the class.

By implementing these acceleration and intervention strategies, teachers can cater to the diverse needs of students and ensure that each student is appropriately challenged or supported in their understanding of factor pairs and related concepts.

Notes or Recommendations (optional):

This activity is preceded by Determining the Greatest Common Factor with "Hockey’s Youngest Star" and Determining the Greatest Common Factor with "Who Is...The Greatest?" 

  Keywords and Search Tags  
Keywords and Search Tags: Facts, GCF, greatest common factor, LCM, least common multiples, number pairs