A dear friend had this posted last night:
And to be honest, I had to look at the first problem (represented as a “tape diagram”) to figure out what they were asking. So my next blog will be about the difference between CCSS standards and how they are being implemented (often poorly). Today is to help out my friend…
So, back in the day we were given a set of procedures to follow step-by-step. We never really knew why (or at least I didn’t): just follow the magical steps in order and it will produce a number that your teacher will smile at and say you are smart. If you did not follow the steps correctly, then have fun with extra practice and staying in during lunch.
CCSS is reversing this. They are allowing students (through research-based strategies kids naturally use) to explore a variety of ways to solve problems. From there, in grade 4 they will generate the traditional algorithm. It hasn’t gone away; it is just the end of the journey.
Here are 3 of the most used strategies for kiddos in subtraction.
1. Count Up. Makes sense. We spend so much time teaching how to add. Why not use it? A subtraction problem is considered a “missing addend” problem.
One of the ways to represent counting up is on an open number line. This is the one the above pic shows on a tape diagram. So you are finding how far (the distance between) it is from one value to the next.
Typically, kids will add up to the nearest ten, then hundred, and jump until they get to the number they need. Add up all of the “hops” you did and that is the distance.
28 – 9
Think about it as, “What plus 9 makes 28?”
Or “How far must I go to get from 9 to 28?”
Think about it as “What plus 165 makes 400?”
Or “How far do I have to go to get from 165 to 400?”
This is my favorite strategy, because it takes the “borrowing” out of the math. (Why is it called “borrowing”? You will never give it back.)
2. Decompose the subtrahend. Name it what you want. You will break apart the second number in the subtraction problem to make it easier to subtract. This is typically shown by a number bond.
Break apart the 9 into 8 and 1. (9 = 8+1)
This allows the student to subtract the same amount of ones from ones first (8 – 8). The leftover ones (in this case, 1) can be taken away second. Again, a great strategy when the subtrahend (the second number in the subtraction problem) has a digit larger than the minuhend (the first number).
Break apart the 165 by place value (165 = 100+60+5).
This is typically a strategy that works well in your head, versus the complexity of seeing it written out mathematically. Trust me when I say that kids can do this quickly in their head; writing what they did is much harder (and much harder for us to figure out what the heck they did). You do have to know the ways to make 10’s and 100’s. So I have to know that 60 + 40 = 100 (or 6 tens + 4 tens = 10 tens = 100) to know that 300 – 60 = 240. This is the second grade standard; subtracting multiples of tens. (BTW: This is the one that gets blasted on Facebook. I have seen students use this strategy in their head time and time again. The minute we record their thinking mathematically, people get all out of whack. It is not more steps than the standard algorithm. The moves you make are written as equations using place value rather than little meaningless tick marks at the top of the problem.
3. Solve using place value. Similar to the second strategy, but you can break both numbers up as you choose.
Again, looks a lot scarier when I record it this way. Using a number bond is a great visual, and typically the student starts this process by just saying what they want to subtract verbally, rather than writing all of the notation down.
I am just showing one way to break apart the values. When I asked my son how he would do it, he said he would break up 400 into 100 + 100 + 200. That made sense to him, and in the end that is what we want. For students to use a strategy and make sense of it.
You will find that one strategy works with the numbers given better than another. For example, with the 400 – 165, I would use a counting up. With 28 – 9, I like the break up the subtrahend. The point of it all is for students to really understand what is happening when they subtract. Where is the “borrowing” or “regrouping” happening, so when they learn the traditional algorithm, it is an extension of their learning rather than some random tick mark step-by-step formula.
There are actually 5 Common Subtraction Strategies: Compensation and Constant Difference were not discussed here. If you would like information on those, comment below and I will make it an upcoming blog.
There are great (free!) teaching videos on Teaching Channel that you can watch as well. If you put any of these 5 strategies (or just, subtraction, grade __), they will pop up for you to watch. https://www.teachingchannel.org/videos/teaching-subtraction-methods