Subtraction Strategies (Besides Traditional Algorithm)
Double digit subtraction - the most common frustration in early elementary math. I’ve never met a teacher who doesn’t say that this unit frustrates them and kids, and I’ve never had a full group of kids love it either.
If you’ve ever taught double digit subtraction, I bet you will tell me that most kids make mistakes - usually the same mistakes - every time. And it usually results in us beating our head against the wall, screaming the steps for the 100th time and making everyone anxious.
Math anxiety starts here.
So I set out to find strategies that
Maintain place value - place value takes a long time, developmentally, with kids still developing meaning into 5th grade.
Elicit a lot of thinking - not just following steps (that often leads to frustration)
Both of these strategies worked with my students and they really understood and loved them.
I’m going to walk through the first (and usually the most favorite one) with pictures. This strategy is similar to partial sums for addition, and maintains place value.
There aren’t so much steps to this, as there are levels of understanding.
Start with:
Understanding “negative” or minus numbers. This will help students later on (ever heard, why were we always told you can’t subtract 7 from 4?") avoid that misconception altogether. (tip: Build a vertical number line for this!)
Understanding the parts of numbers (also known as expanded form) (practice every day!)
Understanding how to subtract a 1 vs. a 10 or 100 from a number.
Rather than focusing on a step and subtracting only numbers 1-9, students are actually dealing with the full scope of numbers. This strategy will not only get them an answer, but also have them thinking about large number relationships and place value.
And eventually…it’s an algorithm just like any other. Steps that work every time.
But usually elicits less mistakes.
The next strategy is a good old fashioned number line.
But before you have an opinion, a full blown out number line should only be used in the beginning for understanding. If students want to use “addition to subtract” they should eventually develop a shorthand (more efficient way) to do it mentally. If not, they can always use another strategy. I’ve noticed some kids really grab onto this and some ditch it for the strategy above - that is perfectly fine!
I’m not here to argue about what algorithm is the end-all-be-all, but that algorithmic teaching itself is what leads to frustration.
These strategies don’t involve more steps - they involve more deep thinking. And if that is something you want, try them out.
