math, Number Sense & Numeration, Number Strings, Number Talks

Subtract

I know it’s only Tuesday, but I’m in a “celebrate the little things” frame of mind.  It’s helping me cope, which is pretty important for teachers under stress.  And other humans of course.

This week, only 2 days old, I am teaching area and perimeter.  But I like to continue with Number Talks even when we’ve moved away from the computation portion of our work. Yesterday I started with one from Sherry Parish’s “Number Talks: Whole Number Computation” book. I chose one from the grade 2 section:  20-19, 20-14, 20-12.  We talked about how we could use all of our strategies from the math wall, but that counting up seems to work better than counting down.  We used the math racks for this activity, and I celebrated my own ability to say “subtract” every time instead of reading the problem as 20 TAKE AWAY 14.

Then today, we started with 20-19 (because one thing I have definitely learned from Cathy Fosnot and her Number String work is that starting with a helper problem is very important – this is not part of the Number Talks book work.)  Everyone remembered or quickly figured out that the answer is 1.  Then I wrote 30-19.  They weren’t so sure at first.  It took us a while to get to 11.  Some kids wanted to count all the way down (their go-to strategy).  Some wanted a math rack so I pointed out it doesn’t have 30 beads so what would they do, they didn’t have a plan. Some made random guesses AS ONE DOES!  We started to talk about our potential answers.  I purposely called on a student that I knew had the right answer AND that I knew could explain the thinking to share.  This child did a great job of noting that the helper problem was helpful.  If we think about how 30 is just 10 more than 20, but we still subtracted 19 then the answer should be 11, or 10 more than 1. I pulled out the math racks. I showed them 30-19 using a 20 rack and a 10 rack.  This way I could show how I added 10 more in but didn’t remove any more than I had the first time, leaving 10 more remaining after I “took away” or “removed” the 19 beads on the rack. After we did 40-19, someone noticed a pattern.  This is honestly the thing that makes me happiest sometimes.  Some groups of kids will notice patterns right away and then stop puzzling over the math because they have found the short cut.  But this class always takes a bit longer to see the pattern.  It’s fine with me, because we have a lot of good conversations along the way.  But I’m also glad when the pattern becomes part of our conversation too.  Even after this child thoroughly explained the pattern, some were skeptical.

Along the way I was drawing the number lines.  I decided to draw a new one each time because I wanted them to clearly see how each time the 19 didn’t change, but our starting and ending point did.  I also wanted to highlight the iterated units.

We talked about each of our strategies:  does it make sense to count up?  to count down?  to try and “take away” something?  to think of an addition problem that would help?

Two weeks ago I blogged about a moment when everyone was working independently.  It has rarely happened since. But it is happening, throughout our day.  Slowly but surely we are edging forward, and today’s math was a reminder to me that we are indeed doing good work. Not every day is easy.  In fact, today wasn’t that easy.  But this was my shining moment.

We’ll continue on with this tomorrow, but I will use some other number besides 19.  I am also going to write out today’s work on a chart paper because I think it will help us going forward and, therefore, deserves a spot on the math wall.