Common Multiples

5 min

Teacher Prep
Setup
Groups of 2. 1 minute of work think time to circle all the multiples. 1 minute partner discussion followed by a whole-group discussion.

Narrative

The purpose of this Warm-up is to review multiples, which will be useful when students find the least common multiple in a later activity. While students may notice and wonder many things about the circled numbers, the idea that some numbers are circled twice is the important discussion point.

Launch

Arrange students in groups of 2. Display the Task Statement for all to see. Ask students to circle all the multiples of 4 and 6 and then to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss with their partner the things they notice and wonder.

Student Task

Circle all the multiples of 4 in this list.

1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26

Circle all the multiples of 6 in this list.

1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26

What do you notice? What do you wonder?

Sample Response

Students may notice:

  • 4 and 6 have common multiples of 12 and 24.
  • 4 has multiples not in common with 6, like 8, 16, and 20.
  • 6 has multiples not in common with 4, like 6 and 18.
  • All of the common multiples of 4 and 6 are multiples of 12.

Students may wonder:

  • What other multiples would 4 and 6 have in common if we kept counting?
  • Why are all of the common multiples of 4 and 6 also multiples of 12?
  • Could we multiply 4 by any numbers to match all of the multiples of 6?
Activity Synthesis (Teacher Notes)

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the lists of numbers. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

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>

10 min

10 min

10 min