This simple and efficient method will help your child build on what she knows about multiplication to become automatic and fluent with the division facts.
Wait, aren’t the division facts just backwards multiplication?
You might be wondering whether you really need to spend time on the division facts. After all, aren’t the division facts just the multiplication facts backwards? The truth is, some kids don’t need much practice with the division facts. These kids intuitively understand how to use their knowledge of multiplication to solve division problems and can easily apply their knowledge.
But, most kids need clear teaching to understand the connection between multiplication and division. And they need focused practice to become automatic with the division facts. After all, just because we know something “forwards” doesn’t automatically know we mean it “backwards.” (Try reciting the alphabet backwards to see for yourself!) In this article, you’ll learn a step-by-step plan for helping your kids become fluent with this final set of math facts.
Psst…want an all-in-one, open-and-go resource for teaching the division facts? I’ve put all this info together into one book for helping your kids master the division facts.
What are the division facts (or division tables)? Why are they so important?
The division facts are all of the division problems from 1 ÷ 1 = 1 up to 100 ÷ 10 = 10.
Can you imagine trying to find common denominators or equivalent fractions without knowing 24 ÷ 6? Or trying to do long division when you’re not quite sure what 35 ÷ 7 is? Without full mastery of the division facts, kids struggle as they start to tackle long division, fractions, and problems with larger numbers. They use so much of their working memory on simple calculations that they have little brain space left for understanding new concepts.
In what grade should my kids learn the division facts?
The second half of third grade or the first half of fourth grade is the best time for children to master the division facts. That way, they’re ready to tackle more difficult upper-elementary concepts, like fractions or long division. But if your child is beyond fourth grade, it’s still well worth your time to go back and help him solidify the division facts.
The easiest and best way to know whether your child needs more work with the division facts is to simply assess where she is at. I’ve put together a quick Division Facts Test you can use to figure out what your child needs to work on. You may even be pleasantly surprised to find that she knows them already! Or, she may know most of them by heart but just need some review with those challenging 6s, 7s, and 8s.
What do my children need to know before memorizing the division facts?
Before memorizing the division facts, your child should first learn the addition facts, subtraction facts, and multiplication facts. Each set of facts builds logically on the previous one, so it’s important that your child learn them in this order.
It’s especially important that your child know the multiplication facts well before starting the division facts, since he’ll use the multiplication facts to help master division.
How fast should my kids know the division facts?
Aim for no more than 3 seconds per fact, and faster if possible. But, it depends a lot on your child. Children who process information very quickly are quite capable of knowing each fact in less than 1 second, but children who are slower processors may always need a few seconds. You’re the parent and know your child best, so adjust your expectations to your individual child.
No matter how old your child, try to keep practice time relaxed and positive. Timed tests and drills aren’t necessary unless your child thrives on time pressure and finds it satisfying to beat the clock.
How to teach your child the division facts
The good news about the division facts is that if your child already knows the multiplication facts, he’ll probably learn the division facts pretty quickly. But, before he can use multiplication to solve division problems, he needs to fully understand the relationship between the two operations. Many children find this relationship hard to grasp without a visual model.
How to help your child SEE the multiplication/division connection
That’s why I use a simple grid of circles called a dot array to teach division. (It may look familiar if you’ve read my articles on multiplication!) Here’s what the dot array and L-cover look like.
With the dot array, you slide the L-shaped cover over the top of the array to easily show the relationship between multiplication and division problems.
For example, here’s how you can use the dot array to illustrate both 6 × 4 and 24 ÷ 4.
Looking at the same array for both problems helps make it clear that division is just the opposite of multiplication. When we multiply, we put together equal groups. When we divide, we take apart a quantity into equal groups.
Division as backwards multiplication
Once your child grasps the connection between multiplication and division, she’s ready to use the relationship to solve division problems. Take 24 ÷ 4 again. This problem means: “How many groups of 4 equals 24?” Or, in other words: “What times 4 equals 24?”
As your child practices these problems, this kind of thinking will become second nature. She’ll learn to look at problems like 54 ÷ 9 and think, “What times 9 equals 54?” to find the answer right away.
Once your child understands how to use multiplication to solve division problems, she’s ready to master the division facts for good. Now, all you need are some effective practice techniques to help your child become fully automatic with the multiplication facts.
How to practice division facts
Strategies and visuals on their own aren’t enough. If you stop there, it will still require a lot of effort for your child to figure out the division facts–and those long division problems will feel even loooooonger.
So, you also need to give your child lots of practice with the division facts to make them automatic. Here are my favorite ways to give your child this essential practice without the stress of timed drills or the tedium of flash cards.
Once your child has learned how to use multiplication to solve division problems, focus on just one specific division table for several days. Use a mix of practice techniques to give your child some variety and make the process fun. I like using a mix of recitation, games, and worksheets, so that kids speak, see, and write the facts.
Reciting the corresponding multiplication table refreshes your child’s memory on the multiplication facts he needs to have at his fingertips as he solves the related division facts. Start each division practice session with a quick recitation of the corresponding multiplication table. For example, before you start the ÷7 facts: “1 × 7 is 7. 2 × 7 is 14. 3 × 7 is 21…” Reciting the times tables is pretty old school, but saying the information aloud helps to cement it in your child’s memory.
Math games make math time fun and social. They also have a huge benefit: when you play a game with your child, you can monitor how well your child is using the strategies–and fix any mistakes before they become ingrained.
Worksheets aren’t the most exciting, but they’re an important practice component, since your child will often use division in his written work. Keep worksheets short and sweet so that your child stays alert and focused.
Once your child has mastered the new division table, mix up those facts with the facts she’s already mastered. Mixing them together provides cumulative review so that the facts are cemented in her long-term memory. Keep using recitation, games, and worksheets until your child has all 100 division facts memorized.
Teach Division Facts That STICK
You’re now well-equipped to teach your child the division facts (and not just give timed tests or drill stacks of flash cards.) You could spend hours planning out lessons, making up your own worksheets, and scouring Pinterest for cute division games. (And hey, if you like doing that kind of thing, go for it!) But, if you have other things to do, I’ve already done the work for you.
Division Facts That Stick is an open-and-go, all-in-one book for teaching your child the division facts. It gives you detailed lesson plans, fun games, and simple worksheets for every step of the process, so that you can teach your child division facts that truly stick.