Minus…subtraction…take-away. Do these all mean the same thing? They are certainly all represented by the same symbol.
Last week the math coordinator was in my class for a few days. (Here name is Melissa and she blogs here!) After watching me do a number string related to subtraction, she encouraged me to always say “subtract” when I am reading the problem to the class, rather than “take-away.” Some kids will actually do some adding to solve these types of problems, and by always saying “take-away” I would be restricting their thinking and maybe even imply that they need to use a certain strategy, namely that they need to remove.
I know that there are different ways to solve a subtraction problem: add on, count back, think of it as a part of a fact family and figure out the addition problem. But I hadn’t really been intentional about my language when discussing subtraction with the class. I was more focused on the answer! (I’m hanging my head in shame!) (not really…but you know what I mean!)
On Thursday and Friday we had bus cancellations, so I didn’t really get a chance to try this out until today. We were working a Number String from Cathy Fosnot’s mini-lesson book. We talked about 14+1, then 14-1 (Did you read that 14 subtract 1? or 14 minus 1?) Then I gave them 14-13. You can’t see them in this picture, but I had the maths.ca relational rods going in the background, and had build 14+1, and 14-1, and those were still visible to the students. I saw lots of kids with their fingers out counting back. It’s an okay way to get correct answer, but very inefficient. However, I then asked my favourite student (my daughter!!) to tell me how she solved it. I’d seen her working away on those fingers, and I know that if she spent a tiny bit of time thinking before she started that, the answer would have been obvious to her. Knowing this, I had to ask her about her strategy. “Well, I thought about having 14 cookies, and then I ate 13 of them, so yeah…one is left.” This is not totally unreasonable for her (don’t judge my parenting!) especially if they are Viva Puffs! I annotated her thinking like this:
I pointed out to everyone that CC was thinking of subtraction as “taking away” something. And then asked others what they thought about when they saw a subtraction sign. Someone else said, “Well, I knew you would only need one more to get from 13 to 14, so I knew it would be 1.” I talked about how that child was thinking about the difference between 14 and 13, which was different from CC’s but they both still got the same answer. Then we did 2 more problems from the string, and talked about the “take-away” strategy and the “find the difference” strategy.
Someone even mentioned that they thought about 9+2=11, which is a great connection to some work we did a week or so ago, so that was awesome too.
It’s funny how being intentional about how I was reading that symbol to the class changed the strategies they used. This wasn’t truly the goal of the Number String, but “m delighted by the results. I am hoping the forecasted 25-35 cm of snow (and 80 Km/h winds!) hold off until late on Tuesday so we can work on this again tomorrow. I feel like we are developing a really big understanding about subtraction!