No matter what grade students are in, subtraction seems to be frustrating for both students and teachers! Looking for an easier way to teach subtraction? Want students to rely on number sense more than a memorized, step-by-step algorithm, or method? Read on for different ways to approach subtraction that will open up new possibilities for your students.
Before we get started with the nitty-gritty teacher talk, if you are working on transforming your math classroom into a space where students actively engage in their learning to practice fluency and math concepts, grab my 10 Free Math Activities. No gimmicks, no sales, no nonsense. This freebie is just one way I can help make math hour the favorite part of the day for every student!
Why Is Subtraction So Hard For Students?
It seems like subtraction should carry the same challenges as addition. Isn’t subtraction just backwards addition? Well…not really. When you think about it, addition is the total or sum of two or more numbers. When we add, we are “putting together” numbers.
When we subtract, we are finding the difference between two numbers. Different models can show this. Using a number line a distance comparison.
Using a group of items can show you a size comparison.
Counting backwards for students seems to be particularly difficult for students. Have you ever asked a student to count backwards by 5’s starting at 100?
How Is Subtraction Traditionally Taught?
Traditionally, primary students tackle the skill and concept of subtraction as having a group and taking part of the group away to create a smaller group. They start with a group of items, count the number of items to take away, then count the remaining items in the group to get their answer. Students learn that subtraction is about taking something away from a group, which makes a smaller group.
Typically, the next step for students is to memorize subtraction facts within 20 and to start learning about place value as regrouping is necessary in the more standard algorithm. Not to get too technical here, but it is important to understand where to interrupt this learning progression to give students the ability to use subtraction with understanding.
Where Do Students Start To Have Trouble With Subtraction?
I’ve seen many students be able to answer subtraction problems with either a single digit from a single digit or a single digit from a double digit. Then they see this and it stops them in their tracks.
The other “trouble zone” they move into when subtracting happens when they struggle to remember the “rules” around the traditional method of subtraction. Do they take the top number away from the bottom or vice versa? What do they do when there are several zeros on the minuend?
Let’s Try A Different Way To Teach Subtraction
Since moving backwards is not ideal for students, why not focus on subtraction as the additional amount needed to reach the minuend, or the beginning quantity in a subtraction equation? Instead of counting backwards, why don’t we have students count forwards? Sometimes we call this counting on, or simply adding a small quantity to a number. This can also work for subtraction. Let’s see how this works with a simple problem first.
We are going to start with 5 and count forward until we reach 15.
What Skills Do Students Need To Subtract This Way?
Students will need some foundational, prerequisite skills to be able to count forward. They will need to be able to count by 5’s and 10’s. They will need to be able to add quantities. It will make it much easier if they know numbers that combine to make 10. As they get better at the skill, they can rely on mentally regrouping numbers as they add.
The best model to see this skill in action is the number line. It is a great tool to keep track of the “jumps” as they work their way up to the minuend, or beginning quantity. Which means, students will need to be familiar with segmenting number lines by ones, fives and tens.
Wait, How Do I Start Teaching Subtraction in a Different Way?
Great question! My first question to my class would be, “What if I showed you how to subtract in a way you’ve never seen before?” I would then hype it up even further and tell them it is going to blow their mind. I can visualize students right now start to “lean in”, literally, as I draw a number line on the board.
Underneath the number line I write 25 – 15. Then I demonstrate making jumps of 5 and recording it above. We add “the jumps” together and talk about how many spaces there are between our starting number and ending number. I use language like there are 10 spaces between 15 and 25. 25 is 10 more than 15. The difference between 15 and 25 is 10. 25 minus 15 is 10 and 25 minus 10 is 15. I point to the 10 and 15 noting how these two numbers added together equal 25.
When students are ready, we tackle a more difficult problem. 95 – 51.
What to Remember When Teaching a New Skill
Don’t forget, when we teach a student a new skill we want to use easy numbers. It is okay to start them with problems that they already know the answer. In fact, this is a good way for them to double check their accuracy when trying out a new way to compute.
One thing I try to always keep in mind; I encourage students to use the method they are most comfortable with, especially if they are successful with accuracy and efficiency. My role is to introduce and explore different ways to look at numbers, but it is the student who determines what methods and strategies they want to end up using.
Besides, even though they may not end up using the new computational strategy, it may be just the ticket to making a connection and having one of those “Aha” moments that marks a personal journey in math.
Now We Are Ready For the Fun
Okay, now that students have a good idea of what this new subtraction is all about, we are ready to have some fun. I pair up students and have them agree on who is “student A” and who is “student B”. Student A will solve the problem with the traditional method they already knew. Student B will solve the same problem counting up. If they both come up with the same answer, then they congratulate each other on a job well done. If they come up with differing answers, they must look at each other’s work to find the error.
How To Move Students To The Next Level
Okay, so once students are able to quickly use a number line to jump from one number to the next in increments of one, five and ten it is time to take them to the next level. Once you cover a skill, it is important to revisit it when you are teaching to remind and reaffirm a new skill. Students need to see it in “action” as a seamless part of problem solving.
Let’s pretend you are modeling a new problem on the board that involves subtracting at some point. I’m going to say, “Okay we need to subtract 18 from 98 here. I am going to start counting up and keep track on my paper.” I would proceed to talk out loud as I model it and write the increments I am counting by in a small column to the right.
The purpose of this is to lead students to being able to do as much mental math as possible. Every student is at a different place when it comes to working with numbers mentally. It takes a lot of practice to become fluent with this. For some students, they may need to use the number line model for a long time. Other students can use mental math to solve even more complex problems.
At this point, I would give students a practice sheet to lead them from problems easy to mentally compute to more challenging ones. Grab My Free Subtraction Worksheet Right Here.
A Rich Culture In The Math Classroom
Introducing new strategies and methods is illustrating how numbers work together. For a healthy math classroom culture and environment, you want each student to feel comfortable and confident in finding the strategies, and ways of thinking that are unique to them. Even though they may not end up using a new computational strategy, it may be just the ticket to making a rich connection and having one of those “Aha” moments that marks a personal journey in math.
Additional Resources
More about subtraction from one of my favorite Math authors, Marilyn Burns. Does Changing Subtraction to Addition Really Work?
Check out my Math Magic Problem that will delight and amaze them (while getting them to practice adding large quantities). The Magic Problem
Need a classroom activity for real life problem solving with addition and subtraction? 
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