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.
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?