Can students really use addition to subtract? I want to explore how students can use addition, something they are typically very comfortable with, to tackle subtraction. When students ask me if they can use an “out of the box” strategy to solve a math problem, my answer is always “Whatever works for you.”
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The Frustration With Subtraction As a Skill
A frustrating issue for teachers can be the time we spend on reteaching addition and subtraction, even as late as third and fourth grade. Usually students are more comfortable, more accurate, and more fluent with addition. When it comes to subtraction, we sometimes wonder if we should “cut our losses” and just move on?
For a classroom of students, many teachers see a majority of students can successfully subtract when there is no regrouping involved. A smaller number of students can accurately solve subtraction problems when regrouping is involved. An even smaller number of students can correctly solve a subtraction problem when there are multiple zeros in the minuend, or starting number.
How Do We Move Students To Accurately Solving Subtraction Problems?
If I have a majority of students in my class that are not successful in a skill that has been taught and practiced, I would call this a Problem of Practice. Meaning, I would examine what practices am I using, or have been used that are not getting my students where I want them to be. It is important to get clarity on what we are currently doing so we can examine small changes we can make to our practice, keeping the end goal in mind.
Well, what if we could reteach subtraction in a way that would:
- Give students many opportunities to build better number sense?
- Result in better accuracy?
- Move away from traditional algorithms?
- Teach students to build off of skills they already have?
If what we are doing has proven ineffective over time, let’s start doing something different. As scary, or uncomfortable as this might feel, the only way to figure out how to become more effective and efficient is by thinking of new ideas and trying new strategies. Don’t worry, it will become very clear very quickly whether we are on the right path!
Proclamation Day- We are Adding to Subtract!
Okay. We are going to announce to the class that any time they are being asked to find the difference between two numbers, they are going to count from the smaller number to the larger number. To learn more about why subtraction can be a difficult concept for students check out my blog article A Different Way To Teach Subtraction
Depending on your students’ experiences with subtraction, you may need to show them step-by-step what subtraction means and how it represents the length or amount between two numbers. The number line is a perfect way to illustrate this. I like to show students the set of subtraction problems below:
9-5=4
8-4=4
7-3=4
6-2=4
5-1=4
For each problem I show them what it represents on the number line. I want students to understand by adjusting both numbers by equivalent amounts with both numbers being larger or both numbers being smaller, the difference never changes.
Note: This is a perfect time to play around with questions like:
If I make the minuend only greater, what happens to the size, or quantity of the difference. Does the difference become greater or smaller?
What about if I make the minuend smaller? What happens to the difference?
Away We Go With Using Addition to Solve Subtraction
When introducing a new skill or concept, always start with easy numbers. Let them get their “feet wet” first before working with more complex numbers. It’s like learning to juggle. Start with two balls and just get the feel first before you start adding in more balls.
Use a problem like 19 – 16. Start with 16 and count up to 19. Easy peasy. I will even use my fingers to keep track at first. I try out quite a few where the difference is less than 10. Once students automatically start out with the subtrahend ( what you are actually taking away) and they have a method of keeping track as they count up.
Then move to a pair of numbers with a difference greater than 10. For example:
25 – 14
Students can solve this by moving from 14 to 15, then add on 10 more for a total of 11. I try to use problems where either the subtrahend or the minuend end in a 0 or 5. This gives students a familiar place to “land” when counting on. Once students are comfortable with adding on and moving by 5’s and 10’s, try problems that are a bit harder like:
88 – 51
There are definitely many ways to solve this, but most commonly I see students count on from 51 to 60. Then they add on from 60 to 80. Then they add on 8 more. What would be more efficient is adding on from 51 – 58 for a total of 7, then adding on from 58 to 88 for 30 which totals to 37.
The Benefits of Adding to Subtract
Wouldn’t it be great if students could seamlessly subtract without stopping to get a pencil and paper out? Well, once students practice a bit, they can do this mentally and quickly. What’s more is students become much more confident with their ability to work with numbers when they learn strategies like this. Need a resource for teaching K-1 students? Check out Origo’s blog post Making Subtraction Efficient – Just Think Addition
Envision asking your class to double check a subtraction problem on the board. You look across the room and see everyone looking off into the distance as they count by ones and tens to get from the subtrahend to the minuend. One student says they think the answer is wrong because they came up with a different number. He walks everyone through his thinking out loud. Another student points out he forgot to add on the last ten and counts it out loud. Talk about true collaboration!
