Minus/Subtraction/Take-Away

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!