I have decided that teaching factors and multiples is not for the faint of heart. In fact, I think it is one of the most challenging concept I teach.
However, we can’t skip those lessons. Hopefully as we teach factors and multiples, students will develop more efficient strategies for multiplying numbers and will continue to improve their memorization of multiplication facts. In this post, I’ve shared some of the lessons I use from my Multiplication Unit that help students learn factors and multiples.
What Are Multiples
In my factors and multiples lessons, students start by learning about multiples which was fairly easy for most students. During these lessons, a hundreds chart may be your best friend. You can use hundreds charts to have students highlight or color all the multiples of two, three, four, five, and six. During the lesson, have students look at the pattern on their hundreds chart and ask students to predict other numbers that are multiples of that number.
Multiples Booklet
For a little extra practice, I absolutely love this multiples booklet. It’s a big help for students as they begin to think about the multiples of one-digit numbers.
What Are Factors
Identifying factors is much more difficult for students. In our first activity, students used a stack of large index cards to create a number line from 0-100. I gave each student an index card, and on the index card they had to show all of the factors of that number. I gave students 1 cm and .5 cm grid paper to create arrays to represent their number. For instance, the student who had 12 would have created a 1×12, 2×6, and 3×4 array. Students also wrote the factor pairs for their numbers. Some students quickly recognized that some numbers had several factors, while other numbers (prime numbers) only had one factor pair. After students finished their first index card, they received a new index card and repeated the steps above until we had an index card for every number 1-100.
Once we had all 100 index cards ready, we taped the cards to the wall in the hallway to create a super long number line. Then, students were able to go on a number walk to identify all of the prime numbers through 100. This was such a meaningful activity for my students, and I felt like building the arrays and discovering which numbers were prime and which were composite made a pretty big impact on my students.
Factor Game
It’s important to not go too fast and leave students who need extra instruction behind. After I introduced factors, I wanted to take a day to work with students on an as needed-basis, so I introduced a fun factor game. While the majority of my students were playing the game, I met with those students who needed additional instruction.
Factors and Multiples Sort
I LOVE using a Venn-Diagram for a factors and multiples sort. This is an open sort so, students determine the criteria for each section. Students select two labels for the first sort and three labels for the second sort. I did require students to select criteria that would include at least one number in each section.
Prime and Composite Numbers
The Sieve of Eratosthenes is my absolute favorite way to teach prime and composite numbers. It’s actually pretty fascinating for me and my students!
Extra Practice
If you see that your students need a little extra practice, you might enjoy some of these extra practice pages that I included in the unit.
While this was a bit challenging, I do think that it required students to think in a way that would allow them to develop a better conceptual understanding of factors and multiples. You can download a free copy of the assignment here.
Additional Resources
I had my students enter a new notes and guided practice page in their interactive notebooks. Throughout the past two weeks, I have been impressed with how many times my students referred to these notes. 
Since this is such a challenging concept, I also added factors and multiples to my Number of the Day morning work. I think this regular reinforcement of factors and multiples (and MANY other skills) will be just what my students need to prevent them from forgetting the terms and concepts. If you already have my Number of the Day, you can download it again to have access to the updated versions.
Each day of the school year, introduce a new number. As a class, count by the multiples of that number through 100. Then, find all the factors for that number. After you finish a number, add it to a class banner and display in the classroom for student reference.
I print the prime numbers on teal paper, so they all look the same and really stand out. I print the composite numbers on white paper have students take turns decorating the composite numbers for the banner. This gives students a little more ownership of the banner. You can find the banner here.
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