Recently I received an email asking me, “what is the BEST way to teach subtraction?”. My response was, “I’m kind of the wrong person to ask because I don’t think we should teach subtraction strategies.”
In this vlog, I explain that statement and talk about the best way to teach subtraction in our quest to build our math minds so we can build the math minds of our students.
We Should Not Teach Subtraction Strategies
I don’t believe that it’s our job to directly teach subtraction strategies to students. I believe in what is known as Cognitively Guided Instruction or CGI. The general premise of CGI is that we give students mathematical problems in a context and then just let them solve it, see how they’re solving it and then we use that to try to make their strategies a bit more efficient and to help them become more flexible with their strategies.
Early on with fact fluency, when kids are doing 6+7, they will start out needing to model “one, two, three, four, five, six,” then “one, two, three, four, five, six, seven,” and then go back and count everything. However, as they start to learn more about numbers they start to come up with different strategies based upon their understanding of how numbers work. So, it’s not so much of teaching strategies to kids whether it’s for addition or subtraction, it’s about developing their understanding of how numbers work that leads to them developing these strategies.
Move towards more flexible, accurate, & efficient strategies through developing key understandings
If we’re just going to start with a story problem, look at how they’re solving it, then move to more efficient strategies, what are those strategies when it comes to subtraction? Again, it’s not the strategies. I’m going to talk about three key understandings that kids need to be showing to develop some cool strategies for subtraction. However, it’s not just strategies, it’s the concepts around subtraction that is the byproduct of what they will have strategies based upon those.
Key Understanding 1
The first key understanding kids need to develop is place value understanding. When they understand how numbers break apart into ones, tens and hundreds, they can use that to help them when they are subtracting. It essentially makes the problem ‘nicer.’ They have such cool understandings around how numbers work and around place value, that then leads to that strategy. If kids have already built an understanding of place value, We don’t have to teach that strategy directly. It will come more naturally to them.
Key Understanding 2
The second key understanding that I want you to be building for your kids, is helping them understand the relationship between addition and subtraction. Once I learned that you can add to subtract, I never went back. That was mind-blowing to me because addition is just so much easier, and sometimes trying to do subtraction in your head becomes super difficult. So, if I can think of it as addition it makes subtraction so much nicer. For example, “What do I need to add to get to a particular amount?.” So, it’s about knowing how to use addition to help them with subtraction. The foundation of that is understanding how addition and subtraction are related.
Key Understanding 3
The third key understanding that I want you to be looking for, is the ability to break apart numbers to make the problem nicer. This starts early on with subtraction with their facts. So, if I’m doing 16-7, most of the time what you’ll see kids doing is counting one by one by one to subtract it. However, if they could break seven into a six and a one, taking away 6 from 16 is so much nicer because it gets me to that friendly number of 10. Then just take one more away. That also works as we move into more complex problems around subtraction. It’s not just for whole numbers either. It’s for decimals and fractions as well and it’s a very powerful strategy. The idea at its foundation, is being able to understand that I can break apart numbers to make the problem friendlier.
Conclusion
So again, there is no best way we should teach subtraction. The best strategy is to have kids build the three key ideas about mathematics that we talked about today. They will start developing the strategies on their own if they have a grasp on those key understandings.
If you want to see strategies based on these concepts, I’ve included a download here that will show you each of them. I even show you what it looks like as they move into multi-digit subtraction, decimals, fractions, and even subtraction that normally would require borrowing or regrouping. Subtraction is subtraction is subtraction. It doesn’t matter if we’re subtracting whole numbers, decimals, fractions, or even as they start subtracting polynomials. Subtraction strategies and the foundation of these ideas still apply.
I hope this helped you build your math mind so that you can go out there and build the math minds of your students and don’t forget click below to get the download.