Distinguishing Between Factors & Multiples


While reading through the new state standards, I was reminded of another frequent question I am asked by math educators: How to teach the difference between factors and multiples? The fourth grade standard indicates “gain familiarity with factors and multiples.” For years this puzzled me as well, but the real key is to understand that factors are a Whole-Part relationship, and multiples are about Sequencing. Hmm. . . .do you hear Thinking Maps on their way? I certainly do!

A Brace Map shows students to clearly SEE what Factors are. Products are comprised of Factors.

The product of 24 has several factors.

After building several Brace Maps to show the products of a number, we then add a Frame of Reference and ask students to write a clarifying statement to demonstrate their understanding.

Brace Map Math Factors and Products

When I teach multiples to students they need to see this as a sequence. It is almost like skip counting, if you will. What are the multiples of 4? What are the multiples of 24?

What are the Multiples of 4?

Once students have a firm understanding of factors and multiples, it is easy to see how a Compare/Contrast Map is in order to help solidify the concepts in their mind. A wise Thinking Maps consultant once told me that the real key to comparing/contrasting concepts and ideas is to determine ahead of time if the concepts are considered more alike or different in the students’ minds. Based upon that decision, determine where to focus their attention on the Map. Most math educators tell me that this concept is confusing for students (and sometimes educators) because they think they are the same. Let’s focus on the differences to help clarify concepts.

Through careful thought, planning, and mapping we can help ALL students to SEE and understand Factors and Multiples.

Share some feedback. What has worked for you?

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Posted in Math
7 comments on “Distinguishing Between Factors & Multiples
  1. Glenda Walker says:

    James, once again you have helped me have an aha-aha moment in my quest for deeper math understanding. This makes it so simple and understandable. You are the best!

  2. James Dean says:

    Glenda, so glad that I could assist in making Mathematical THINKING visible! The Maps are great tools for helping students move from the Concrete to the Abstract by literally giving them a MAP to get there!

  3. Gail Sansome says:

    James, What a great connection! This truly makes sense! Thanks for sharing!

  4. James Dean says:

    Thank you, Gail. I appreciate the comment and glad that it makes sense.

  5. Shannon says:

    I just finished lessons on multiples and factors in my fourth grade classroom. I was trying to figure which TM I should use. I will use this one before we begin fractions after holiday break. Thank you for the awesome map! My kiddos love the maps. We use them to take notes on a regular basis!

  6. James Dean says:

    Shannon, just navigating back through my blogs and somehow missed your comment on this. So glad that you found value in the information shared here. The MAPS are powerful tools for both the teaching and learning process and particularly beneficial in MATH to SEE what are students are THINKING! Let us know how that fraction lesson went.

  7. DONOTY says:

    Thank you this helped me

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