As a teacher of 4th grade for over 20 years, I can tell you that long division is easily the most challenging 4th grade math calculation your students will learn. It involves a complicated (sometimes confusing) algorithm that requires a strong fluency of basic facts for not just for division, but also multiplication, and subtraction, too. Mastering the steps for student requires a lot of practice, repetition, and perseverance. To teach it takes preparation and a lot of patience.
Here are some tips that will hopefully help your students become long division dynamo's in to time.
TIP #1 : Use T-charts
In the early going, I would recommend having students complete a t-chart for the facts for the divisor. This can be used to refer to as they search for the best multiples. It is especially helpful for those students who are weak on their multiplication facts.
I have included some free practice pages with problems including t-charts to help get students started using this strategy. You can download the FREE pages here. Look for a more full product like this on TPT very soon!
TIP #2 : Teach area models
To build on a skill learned with multiplication, I always teach my students how to relate area models to long division.
Here’s how the area model would look for a problem solved in this way:
This model can also be used to show problems that were completed using less efficient steps. Here’s the same problem in a different way.
To help students “see” the relationship between the two, I often draw the “division bar” over the area model to show them how everything remains in the same orientation and shows the same values.
TIP #3 - Teach the Flexibility of Partial Quotients
Show students that problems can be solved in multiple ways using this method and still be “right.”
In my opinion, this is really the secret sauce of why this method is so useful. Students who are not great with choosing the best multiples can still get to the correct answer - it will just take them more steps!
TIP #4 - Use Scaffolded Design
Keeping work neat is essential in doing math calculation, right? For this reason, I always use grids to help students both to keep their work neat and to guide the process in the early learning. As students gain confidence, I pull these scaffolds away and let students just work the problem in a blank space. Sometimes I even allow students to choose when they are ready to try the non-scaffold answer document!
By the way, if your principal happens to be evaluating you, you can remind him/her that this is great example of DIFFERENTIATION!
TIP #5 - Prepare for Parent Confusion
Of all of the work I send home for homework, this is the one that will most commonly come back with a parent note/e-mail asking, "What is this?" or saying, "I don't know how to help my child with this." I have even spotted Facebook posts from my parents with cynical comments about not understanding this new "common core math" and questioning why we aren't teaching it the "old-fashioned way", etc... I’d recommend against sending it as homework, at least until you are confident students can do it totally independently.
One way I try to help students (and parents) with this problem is by sending Learn Zillion assignments home. Learn Zillion is a wonderful series of online videos and lessons (similar to the more well known Khan Academy) that can be used to help teach topics in common core math or ELA. I'm a big fan of many of them.
Check out this link to see an excellent example of a video lesson using this method.
This is a tough skill. Go slow. If students are doing it along with you, they will often fool you into thinking, “they’ve got this,” but then when they start working independently, you discover quickly, “they don’t got this.” Do examples with them until you think they have it, and then do a few more. Trust me on this.
This is also a skill that requires lots and lots of review. I usually set aside at least 3-4 weeks to teach both the partial quotient and the standard algorithm. And after that, we still come back and review it a lot. I often tell my students this helpful axiom:
TIP #7 - Make it fun!
Learning (and teaching) long division can get tedious if you don’t break it up, so it is important to find a way to keep it fresh for you and your students. For example, at the start of each Math class I almost always play a Kahoot game to review what we learned the previous day.
It is a great way to engage students right at the start, and it acts as a great assessment tool for me to see whoneeds extra help. (See my Kahoot game links below.
I have also created many task card setsthat allow students to get up and move as well as to self-check. Students enjoy this, and I appreciate the fact that because they can self-check, I am freed up to help the students who need it.
The kids love solving the problems to reveal the jokes, and you'll love how easy it is to check for understanding.
In the end, teaching long division can be daunting and even exhausting. If you follow these tips, however, I think you’ll find that your students will really enjoy dividing in this way. As your students gain confidence and competency with the skill, you will feel a tremendous sense of pride from a job well done.
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 (which I never use) 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 20+ 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!
8 Times Table Song | Skip Counting by 8 Multiplication Song - YouTube
Skip Counting by 4 Rap Song | Dance the 4 Times Tables - YouTube
7 Times Table Song Rap: Skip Counting by 7 | Multiplication Song by NUMBEROCK - YouTube
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.
Schoolhouse Rock - 3 Is A Magic Number - YouTube
Multiplying by Fives School House Rock - YouTube
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 pages that 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 Activities are 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 coursem 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 Day 2: Multiples of three (to 30) Day 3: Multiples of three (to 99) Day 4: Multiples of six (to 60) Day 5: Multiples of six (to 96) 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.
Both task card sets are coded with fun jokes that makes it a breeze for you to check at a glance. The kids love the jokes, too!
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.
Also, just recently, I have made all of my Learn Zillion companion products absolutely FREE! Learn Zillion has removed many of the free videos and has moved them as part of a new paid version. Keeping up with their changes was getting exhausting, so I just made the video practice pages free across the board. Check them out here: