Division. Need I say more? What about upper elementary division? I know what you’re thinking. It’s hard. It can be hard to teach division and most definitely sometimes hard for students to learn. There are many reasons why the concept of division is difficult for students. It can trace all the way back to a lack of number sense in the primary grades or a lack of multiplication fluency in the previous grade. It doesn’t matter which “piece” students are missing, the smallest thing can throw a division problem completely off. So, what’s the solution? No pun intended. Ok, maybe it was totally intended. Let’s talk about a few ways to help support you and your students with division.
I know this necessarily doesn’t hop right into division but division and subtraction have a very strong relationship. What I’ve noticed with multiple students that I’ve worked with throughout the years is that even when they know the process of how to divide, they make errors when subtracting out groups. If you know a division unit is coming up, prep students before by reviewing subtraction. You can put subtraction work in centers with my subtraction task cards or assign lessons on the computer. Strong subtraction = more accurate division.
If I could shout this from the roof tops, I would. And just maybe I will. Students have to be fluent in basic multiplication facts no matter which strategy is used to teach division. Practice these also before teaching upper level division. If students still struggle, allow them to use a multiplication chart for a certain amount of time but let them know that they will not always be able to use it.
Manipulatives are still very important for upper elementary division. Model problems using base ten blocks or place value chips. Start small with problems like 84/4. See if students can build the number 84 in base ten blocks and rearrange them into 4 equal groups. The end result should be 2 tens and 1 one left in each group.
When introducing upper elementary division, use graph paper. This is a game changer to keep students’ numbers in the right places and lined up with the right place values to subtract. It’s also a great visual to correlate with the area model of multiplication and division so students can physically see rows/columns, if needed. Eventually, once students get comfortable enough with division strategies, the scaffold of the graph paper can be removed, but it is a life saver in the beginning.
Partial quotients made it so much easier to teach division after I had built up their foundation of basic multiplication and division facts. Partial quotients is a strategy that allows students to repeatedly subtract groups away from the dividend. Students can multiply the divisor by a factor that they know and subtract that group away from the dividend. If students struggle with a starting point, I like to get them benchmarks numbers to multiply by. For example, if the divisor is five, can you multiply that number by a ten? What about a hundred? I try to teach students to multiply to get as close to the dividend as they can, sometimes they have to subtract out way smaller groups and that is ok. They will learn to become more efficient as they go. Giving students benchmark numbers that are friendly is helpful to those who are not fluent yet with their facts.
Just like students can be taught to check subtraction problems with addition, this very same principle can be used when helping check division. If students aren’t sure if their answer is correct, they can multiply the divisor by the quotient and get the dividend. Students could even be taught to check with a calculator. However, if they try to be sneaky and re-do their division problem with the calculator, ask them to show where their mistake was when originally dividing. Error analysis is a higher level skill, hooray! One more thing with this one: if you teach students how to multiply to check their work, don’t forget about remainders. Students should know that after they multiply the divisor by the quotient, then they need ADD the remainder (if there is one) to get the total.
I hope some of these tips and tricks help you to find the solution for you and your students when you teach division. Yes, pun still intended. Take a deep breath and build those foundational skills. I promise it will pay off!
Looking for resources to help students learn about division while still having fun? Check out my Math Escape Rooms! While available in various grades and topics, I’ve picked out a few for this topic below.
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