5 Captivating Ideas for Teaching Factors & Multiples

If DNA is the building blocks of life, then factors and multiples are the building blocks of math. Everything from algebra to trigonometry to geometry will use some variation of factors or multiples. In order to ensure your student is successful for years to come after they leave your classroom, you need to lay a strong foundation now for them to build upon.

After all, the best time to plant a tree is yesterday. The second best time… Is now! To get those seeds started, check out these efficient, engaging ideas to make teaching factors and multiples a breeze in your classroom.

1. Math Workshop

Yes, yes, I know. Math workshop is all I ever talk about! I can’t help it… Have you seen how diverse, effective, and engaging it is? Math workshops are truly the whole package, and are extremely time-efficient, to boot. If you’ve never used the math workshop model before, never fear: I have you covered! Learn all about math workshop here, and then check out my other blog posts to learn how to absolutely rock it! In addition, you can find dozens of math workshop lesson plan units in my store.

Essentially, math workshop is a combination of many different engaging learning techniques bundled into one. From math centers to craftivities, and assessments to practice worksheets, the math workshop model has it all. It begins each day with a mini-lesson, where you would model whichever segment of factors and multiples you’re working on, then moves on to an active engagement segment. This is where students receive hands-on practice. Finally, the lesson finishes with independent practice and a closer.

Math workshop may sound intimidating, but it’s really just a normal lesson compartmentalized into organized, easy-to-understand segments that allow students to seamlessly transition from observing to learning to practicing. For something as multi-faceted as factors and multiples, I cannot stress enough how helpful the nuances of the math workshop model are.

Of course, if you’re looking for something a little smaller rather than the whole meal that is math workshop, you have plenty of other choices for teaching factors and multiples. For instance…

2. Math Centers

Chances are, you can turn just about anything into a math center, and factors and multiples are no exception. Students are engaged when they’re up and moving, and for a subject like this, engagement is exactly what you need so they retain the information rather than just memorize it!

As an example, divide students up into groups and set up several different stations throughout the room. At each station, set up a different multiple (preferably a larger number). Have students work together in their groups to determine all the possible factors of that number. After a certain amount of time, have students rotate stations until they’ve gone through them all.

Another idea is to set out bingo cards at each station. Create several different laminated bingo cards with a variety of multiples (one in each square) and have students work in groups (so they can check the multiples together) at each station. Call out random factors (e.g., “Mark any multiples on your bingo sheet that belong to the number 3!”) and continue until a group gets bingo. Then, have students wipe off their cards and rotate stations, so they have a different card each time.

Of course, these are just two ideas–there are a plethora of math centers you could create! For more engaging center ideas, check out my blog post about it.

3. Math Games

Games in math… Crazy, right? Not if you want high levels of engagement and to create a memorable, positive learning experience for your kiddos!

One of my favorite games is the math relay. Creating a relay for factors and multiples is easy, too! First, you’ll need twelve popsicle sticks. Use a marker to label them 1-12. If you don’t have popsicle sticks, that’s fine! You can also just use slips of paper labeled the same way. Then, divide students into two (or more!) teams and have them line up, like in a relay race.

The rules of the relay are as follows: you will write a number (multiple) on the board. It is up to you whether students are allowed to confer with their team to decide what factors go into that number, and whether you will give a time limit. Once they know, then the first student in all the lines will come up to grab the popsicle stick(s) labeled with the correct factor(s). Whichever team grabs the correct factors gets a point, then that student will go to the back of the line and the relay starts over with a new number.

Relays are a fast-paced, engaging game, but they do require a bit of prep work on your part. If you’re looking for something with a little less prep time involved, you can always check out this list for more game ideas.

4. Mysteries

Oh, mysteries, my beloved! Now, I love mysteries, and you can totally use them for factors and multiples, too! If you want to liven things up a bit, try something a bit different, like this factors mystery activity or multiples mystery activity I created for teaching factors and multiples!

In these activities, students are given a clue sheet (like the one shown below) and move around the room reading the clue cards. They have to solve the problem on the clue card to get their clue. For instance, the card may say, “Which number is NOT a factor of 32.” Then students determine which number is the answer. In this case the answer is 12, so they would read the clue under the number 12. “The thief did not drink cola with them.” Then the student would place a checkmark next to cola on the drinks section of the clue sheet. As the student moves through all 27 cards eliminating the suspects, drinks, and locations one-by-one the answers to the mystery becomes more clear on who stole the cupcakes, where the suspect went to eat them, and what the suspect drank while eating them.

This is an engaging activity that will definitely have your students invested and in love with math!

5. Assessments

Now, of course testing is important, but there are a plethora of reasons why over-testing is an issue. Students shudder at the mere mention of a test, but they’re a vital part of your career. After all, you need to be checking for understanding!

Thankfully, there are many ways to check for understanding besides your boring old tests. A personal favorite of mine are tickets out the door. They’re quick, easy, simple as all-get-out, and here’s the kicker: most students don’t even realize they’re being tested! All you need are sticky notes or a small scrap of paper. At the end of your lesson, right before transitioning to a different subject, ask students a simple question. Something like “Alright, kiddos, let’s wrap things up. Grab a scrap piece of paper real quick. Now, what are the factors of 16? Write them down and hand them to me as you leave!” would be great!

If you use a number with more than two factors, such as 16, it’s easy to tell which students are fully grasping the material and who may still need a bit more intervention (or are just plain rushing).

There are an innumerable amount of other simple assessment ideas out there, of course. For more information, check out my A-Z list of informal assessment ideas! Ultimately, each time you hit a significant point in your lesson, you’ll want to be checking for understanding. Your students’ responses will be a good indicator of whether it’s time to move on or if you need to backtrack over some of the more challenging spots.

Regardless of whether you look forward to teaching all about factors and multiples, these easy-to-implement ideas will make your life a whole lot easier when you reach that segment in your math classroom. Who doesn’t love an easy work day? And, hey, the easier things are for you, the easier things will be for your students. They need a positive learning environment, and when you’re relaxed and ready for the day, they will be too!

Happy teaching!

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