I have been getting so many questions from teachers about how to teach long division using partial quotients. Growing up, this wasn’t a strategy many of us were taught, but it is so helpful for a majority of students. However, I like to teach my students a couple of other strategies in case partial quotients isn’t one strategy that works for them.
How to Teach Long Division with Partial Quotients
The partial quotients strategy for how to teach long division was a serious game changer for so many of my students. This is a strategy that uses chunking to repeatedly subtract groups of the divisor in a more efficient way. My students that needed repeated subtraction when they were first learning their basic division facts really love this strategy because it’s a similar pattern to what they’re already used to.
However, I have my students write out their division facts prior to actually solving the division equation. When they are doing this, we usually do divisor times 1, 2, 5, 10, and 20 in order to come up with some of the numbers they may end up needing since long division is a much larger number for them to be working with. As the year goes on, they will move beyond needing these facts written out.
Step 1:
Write your multiplication facts (1s, 2s, and 5s). Then add your zeros for 10, 100, 20, 200, 50, and 500.
Step 2:
Start subtracting the largest numbers that you can from the number in the house.
Step 3:
When you can’t subtract any more from your multiplication facts, see if you can subtract the number outside of the house. When you can’t subtract any more, that is your remainder.
Step 4:
Add up the partial answers on the side to get your answer. Don’t forget your remainder!
How to Teach Long Division with the Box Method
The box method strategy for how to teach long division was new to me a few years ago and works best when the students are familiar with using this type of organizer when multiplying with partial products. This type of division strategy is similar to partial quotients but is organized in a different way.
Just like the regular partial quotients strategy, I have my students list out their multiplication facts so they have a starting point. They will draw a box and subtract the answer to the multiplication fact from the dividend, and write the factor they multiplied by the divisor on top of the box and the divisor on the left. When they subtract, they will continue the pattern until they can’t divide any further. What they are left with is their remainder, and they need to then add all of the numbers across the top to determine their quotient.
Tips for Any Strategy
When you are introducing new strategies I highly suggest using an engaging context or word problem. As you walk through the steps of the strategy, walk through what would be happening within the problem. If these strategies are completely new, spend a day (or more) with 1 digit divisors before moving on to 2 digit divisors. Make sure the students understand the purpose of listing out those multiplication facts if you choose to use this within the strategies. Also, make sure they understand what it means and how it works (it provides partial quotients that are ready-made for the students to choose from). Teach the students to check their answers with multiplication. That will help them to self-assess and will allow them to catch any small mistakes they may be making in subtraction or other computation errors.
Traditional Algorithm?
Since my state follows Common Core State Standards, I do not teach the traditional algorithm for division as part of my fifth grade curriculum. However, when state testing is finished, we do preview what they will learn in sixth grade math. The traditional algorithm is something I heavily teach them so that they are well prepared for the next year. Over the years, I have noticed that many of the sixth grade teachers expect students to already know the traditional algorithm, and I don’t want my students to be behind when they aren’t actually expected to know it yet.
Need some resources to help you with how to teach long division? Check it out below:
