Using Common Multiples and Common Factors

5 min

Teacher Prep
Setup
Tell half the class to clap every other beat, and the other half to say "yeah!" on every third beat. If time, repeat for 3 and 4, 2 and 4, and 2 and 6. Follow with a whole-class discussion.

Narrative

In this Warm-up, students explore the concept of least common multiples using rhythm.

Launch

Tell students they will be establishing a steady beat as a class. Use a visual hand motion or display a visual timer to set the beat. Tell one half of the class to clap on every other beat, and tell the other half to stomp their feet on every third beat. If time allows, repeat this activity for the following intervals: every 3rd and 4th beat, every other and every 4th beat, every 4th and 6th beat. Follow with a whole-class discussion. 

Student Task

Your teacher will give you instructions to create a class rhythm. As you participate, think about these questions:

  • When will the two sounds happen at the same time?
  • How does this game relate to common factors or common multiples?

Sample Response

Sample response: When claps happen every 2 beats and stomps happen every 3 beats, they happen at the same time after 6, 12, 18, and 24 beats. These are all common multiples of 2 and 3. The first time it happens is the least common multiple, which is after 6 beats.

Activity Synthesis (Teacher Notes)

The purpose of this discussion is for students to share their thinking on how this activity is related to common multiples or common factors. Invite students to explain what they noticed. If not mentioned by students, make sure they understand that students clapping on every other beat is like finding multiples of 2, and students stomping on every 3rd beat is like finding multiples of 3. When the two things happen at the same time, it is like a common multiple.

Standards
Addressing
  • 6.NS.4·Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. <em>For example, express 36 + 8 as 4 (9 + 2).</em>
  • 6.NS.B.4·Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.<span> For example, express <span class="math">\(36 + 8\)</span> as <span class="math">\(4 (9 + 2)\)</span>.</span>

25 min