Common Core standard 4.OA.B.4 states that fourth graders should be able to “determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number.”
This standard can be a toughie. It should be no surprise that the task of learning multiples is made much easier when students are fluent with their multiplication facts. Multiplication fluency is supposed to be a third grade mastery skill, but as we know, many many students will still not know these facts going in to fourth grade. Learning to count multiples can be a great tool to help students who are struggling to learn these basic facts.
Despite the fact that many textbooks introduce multiplication in the first chapter, I usually begin this topic sometime in November because this will have given the kids a couple months to review and hopefully memorize those facts before we learn multiplication of greater numbers which I teach in December.
In my 30+ years of teaching 4th grade, these are some of the classroom-tested strategies I’ve employed that have helped my students master this difficult skill.
In my opinion, most fun and effective way I have found for students to memorize their multiples is through song. Play these songs a few times over consecutive days and you’ll be amazed how quickly they learn their multiples! Be warned, you will definitely find these songs ear-worming into your brain sometimes for days!
Here are my favorites:
Flocabulary. Flocabulary is hands-down the best and most effective site for educational music of all kinds, not just for math. Unfortunately, it is not free, but, if your building has a subscription to it, take advantage. You and your students will LOVE it. They have songs for each factor from 2-10, and they are all great. If you don’t have a subscription, you can always sign up for a free month to try it out.
Numberock. This is another amazing site of educational music, this one devoted just to math. The eight’s song is my (and my students’) favorite. Here’s a sampling. Check out their Youtube channel for other multiples songs. Oh yeah, they are free, too!
Schoolhouse Rock. If you are a veteran (read:old person) like me, then you remember these educational cartoons from Saturday morning cartoons. They were catchy and fun then, and guess what, they’re still great today. The Three is the Magic Number song is still my go-to for teaching the first ten multiples of three. Most of these can still be found on Youtube. Here are two of my favorites.
Sergeant Seven. I discovered this video recently, and it is a fun one to get the kids to recite their sevens multiples while marching around the room.
You can make a repetitious (and potentially boring) task like reciting multiples fun by incorporating movement. Have students chant multiples while marching, clapping, snapping, tapping, or hopping.Vary it by having one half of the class chant while the other listens. Girls chant then boys chant. Nine year olds then 10 year olds. Do it by table group. Increase speed and see who can recite them the fastest. Stand in a circle and march clockwise and then turn and march counterclockwise. Pass or toss a ball while each student says the next multiple. Be creative and your students will love counting numbers!
Here’s a fun movement activity that I use to practice the multiples of 7. Before school, make a hopscotch board on the floor with chalk or tape.
Before you start hopping, have your students practice chanting the multiples of seven at their seats. I use this handout in their math spiral for students to record and practice. Once most students have put them to memory, we continue chanting them while each student hops through the board on the carpet. Have students clap their hands or snap their fingers or march in place as you do this over and over to practice the multiples.
I use this poster to display the 7’s multiples in the classroom. I am always sure to make note to the students that similar tens are grouped together (21 & 28 and 42 & 49.)
Working for Kahoot in 2017, I created games that review all of the multiples listed below. Click the links below to check them out! They are free. Instead of an “exit ticket”, I use games like this as an “entrance ticket” to review the concept that we covered the day before. During the game we can review anything needed and correct any misunderstandings. It makes an engaging way to start my math lesson.
I have created many worksheetsand math notebook pagesthat give students opportunities to practice writing out their multiples of various numbers. Here is a small sampling of some of the pages included in my product A Multitude of Multiples Activities on Teachers Pay Teachers. Here’s a freebie of the multiples of 3.
These sheets included in Multitude of Multiples Activitiesare fun and independent practice of multiples that students can complete. As a teacher, they are super easy to checkand my students really looked forward to doing them.
Many mnemonic techniques have been developed over the years for learning multiplication facts. Once your students learn a few of these, you can just say something like, “the dancing fact” for 56 = 7 x 8 or “the score’s 7 to 7, Who’s playing?” for 7 x 7 = 49 to cue students to a fact they are stuck on. Of course there are a lot more. Here are a example posters from my product AMultitude of Multiples Activities.
First I’ll say, there’s no right or wrong order to teach the multiples, but to me it makes sense to teach them from easiest to hardest. I also group together similar multiples (such as 5’s and 10’s or 3’s and 6’s).
Another tip, don’t presume that all of your fourth graders can identify odd and even numbers. I’m not sure if this is because it is touched on less in the lower grades, but I have noticed that more and more students can not easily identify odd and even numbers. Take time to teach them the little rhyme listed above to help them remember.
I choose to teach the multiples in this order:
Day 1: Multiples of two (odds and evens), five, and ten (up to any place)
Day 2: Multiples of three (up to 30)
Day 3: Multiples of three (up to any place)
Day 4: Multiples of six (up to 60)
Day 5: Multiples of six (up to any place)
Day 6: Multiples of four
Day 7: Multiples of eight
Day 8: Multiples of seven
Day 9: Multiples of nine
Task cards are definitely my go-to for independent practice. Since this skill lends itself well for differentiation, I actually created two set of task cards to practice.
This first set just practice for multiples within the basic facts, so for example I did not include multiples of 3 higher than 3 x 10 = 30 or multiples of 9 higher than 9 x 10.
This set includes higher multiples of any digit 2-9 up to 100, as stated in the common core standard.
In my product A Multitude of Multiples Activities I included 4 pages of differentiated assessment to gauge each student’s learning of their multiples – level 1 is tests multiples of basic multiplication facts. Level 2 assesses multiples of 2-9 up to 100. Level 3 is assesses a student’s ability to apply divisibility rules to numbers beyond 100 and to factors of 11 and 12.
