Do you recognize any of these strange phrases?
- Does McDonalds Sell Cheese Burgers Raw?
- Dad, Mom, Sister, Brother, Rover
- Dirty monkeys smell bad
If so, you may be a 4th or 5th grade teacher who teaches long division. If you aren’t aware, these weird sentences are mnemonic devices commonly used to teach the multiple steps used in long division. Using the standard algorithm, I teach these steps:
- Divide
- Multiply
- Subtract
- Check (that your difference is less than the divisor)
- Bring down
- Repeat or Remainder (if no digits can be brought down)
As a teacher of fourth grade for over 30 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 (often confusing) algorithm and requires a strong fluency of basic facts for not just for division, but also multiplication, and subtraction, too. To master the steps requires a lot of practice and repetition.
Here is a short Q & A with wisdom I have gained from teaching long division for 30+ years:
I have heard of different ways to teach long division. What are they?
The methods I have taught to my students over the years include:
- the standard algorithm (AKA, the old fashioned way)
- the partial quotient method (sometimes called the “The Big 7 method”)
- the box method (a variation of the standard method)
- area model (In my opinion, an essential technique for understanding but not a commonly used as a solving method)
Which long division method would work best for my students?
Not being evasive, but I would say, it really does depend on your students.
The Case for Teaching Using the Standard Algorithm: Ask yourself, are the majority my students fast and fluent with their basic multiplication and division facts? If so, I would recommend teaching the standard algorithm. It is the fastest and is easiest to learn, in my experience. It is also the most commonly used so it will likely be familiar to family members who might try to help at home. Read this blog post if you want to learn in great detail about how I teach using this method.
The Case for Teaching Using the Partial Quotient (sometimes called the “Big 7”) Algorithm: If your students are not fluent in their facts yet, I would recommend the partial quotient method, because it is the most forgiving as it allows for many different ways to solve correctly (see image below). Another plus of this method is it give kids practice with multiplying by tens, hundreds, and thousands (a 4th grade standard) while also transitioning much more easily into the tough 5th grade standard of two-digit divisors. Another plus of this method is that it best demonstrates what you are actually doing when you divide, that is, repeatedly subtracting. Read this blog post if you want to learn in great detail about how I teach this method.
The Case for Teaching Using the Box Method. This method is perfect for students who know their facts well enough, and can memorize the steps in the standard algorithm, but struggle with the organizational part of the standard method. I have even used this method side by side with the standard method, allowing students to choose which they prefer. Many teachers swear by this method.
The Case for Teaching Using the Area Model. In my opinion, whatever method you use you should always bring it back to its most concrete representation, which is in this case the area model. This model works really nicely with the partial quotient method because it can help show how multiple ways to solve can lead to the same quotient. (See below.)
How long should I spend teaching long division?
This again will depend on your students, but I will tell you that I teach in a high achieving school, and I spend at least 3 weeks on the skill. Usually once we’ve gotten to 4-digit dividends, I only spend about half of my 70 minute math period reviewing the algorithm and the rest on another topic (I like to introduce shape and number patterns or another more hands on skill during this time.) Later in the year, be sure to come back and review because your kids will get rusty.
What Mnemonic device do you use?
I teach my students Does McDonalds Sell Cheese Burgers Raw to stand for (Divide, Multiply, Subtract, Check, Bring down, and Repeat/Remainder). I like this mnemonic because it includes an often missed step by students: to check. That is, students should always ask themselves after they subtract, “Is my difference less than my divisor?”
What do you use to practice long division with your students daily?
If you’re looking for tools to make long division less daunting for your students, I’d love to share these resources with you.
Here are some products for the Partial Quotient (Big 7) Method, Word Problems, and Division Math Facts.
Long division can be kind of boring to teach after a while. How can I make it fun?
I review daily using these Kahoot games for each step in our learning process. Click the link below to see the games I have for this.
Also, I have students do daily practice with their basic facts using these fun Boom cards.
Take the fun level to 11 with this end of unit escape game for long division!
What is your preferred way of teaching long division? Let me know in the comments.
