Tuesday, January 15, 2013

Addition and Subtraction Strategies

I was so excited to work with Amy from Teaching In Blue Jeans for a guest blog spot! Amy, I was so thankful for the opportunity and enjoyed having you over for a Blog Swap as well!  If you haven't seen Amy's guest blog about sight words, be sure to catch it here...
Also, don't forget to stop by Amy's blog...she is full of great ideas :)

Teaching In Blue Jeans
What I discussed on Amy's blog was some of the math strategies that I have been using this year with my second graders.  I am inspired to share this little blog post with you as I just completed a very large packet on Subtraction Strategies for Common Core Math Instruction.  You can find it at both of your favorite teacher shops!
 TPT... Click Below:

or Teachers Notebook...Click Below:

     I’ll let you in on a little secret...I grew up NOT loving math so much. Not loving the memorizing, not loving the formulas or algorithms, not loving the feeling that everyone else seemed to understand this cut and dry subject while my mind was trying to make sense of it in different ways. Sadly, this was pretty much my sentiment throughout high school as well.  Don’t get me wrong, I worked and I worked (and even got tutored at times), but I would have chosen to write an essay over solving for Pi any day! 

Fast forward 10...Fast forward 15... Fast forward to now (there is enough math in this article without having to calculate ages)...Here I am, a multiage teacher and math is perhaps ONE OF MY FAVORITE subjects to teach.  I have a classroom of first and second graders.  For the past 5 years,  I taught both grades in the same classroom.  This year, as per our district (and new standards, curriculum demands and testing) we are splitting the grade levels for math.  I teach the 2nd graders and my colleague in multiage is teaching our first graders.

Our district is currently in the process of choosing a new math program, which I am very excited about! There are a few possibilities on the table, but I definitely have a few favorites in mind.
In the meanwhile, in order to meet the new Common Core Standards for math, I have been supplementing with plenty of Singapore Math Strategies.  For Singapore math, I scoured the internet over the summer and taught myself mostly about their strategies for decomposing numbers (part, part, whole) and bar modeling for problem solving.  Using these strategies has helped to make a big difference in my students’ number sense and in the way they approach word problems.
      Another resource I am loving this year is written by the one and only Marilyn Burns and her team of “Math Solutions” teachers.  Burns and her team wrote a series for Scholastic called, “Do the Math.”  The series I am using focuses on “Numbers and Operations” and has excellent lessons on number sense, computation and problem solving.
You can find out more about Marilyn Burns’ Math Solutions at http://www.mathsolutions.com.


You can find out more about the Do The Math Series at http://teacher.scholastic.com/products/dothemath/

       Part of the reason I love this series is because of the strategies that are presented for addition and subtraction.  Burns does not focus on algorithms, rather, there is a heavy emphasis on “Splitting” and the use of the “Open Number Line.”  
I’d love to go into all of the different methods I have been using, but I will save them for other blog entries!  For now, I want to focus on the Open Number Line Strategy.  As a precursor for using this strategy, I have to stress the importance of students being able to count forward and backward by ones and by multiples of ten.  Plenty of time should be spent early in the year working specifically with the 100s chart.   Students should then begin counting forward and backward with numbers from 100-1,000.  I spent a lot of time with my students doing “warm-ups” of 1 more/1 less, 10 more/10 less, 100 more/100 less.  
     After that, they were ready to tackle these number lines (and I was ready to say goodbye to the torturous old way of teaching addition and subtraction with regrouping algorithms!)  It is important to note, that parents should be informed of how to use these new strategies as well.  I’ve been making an effort this year to create a handout for each new strategy I teach, this way the students get the reinforcement at home as well!

So here we go...let’s take a look at how to do it.  Below you will find one of my parent hand-outs.  As a thank you to Amy and her followers, I pulled it out of my packet and am giving it to you as a freebie :) You can the click on picture below to grab it as a Google document:
     As far as subtraction goes, I have taught my class to use the Open Number Line in two ways. First, we worked on the “Counting Back” Method (seen in the graphic below). 

     Currently, we are “Comparing” by counting up from the subtrahend to the minuend.  The comparing method for subtraction is generally my students’ preferred method, because it is much easier for them to count forward rather than backward on a number line.
Recently, during my adventures with the Open Number Line Strategy, I introduced my students to a game I made called, “Deep Sea Dive to Zero.” Throughout the game, students have the opportunity to use subtraction with an open number line.  This game is especially good  during the earliest  "Open Number Line" lessons. You can get it for free right here:
     Let me tell you, the kids went WILD about this game.  When I introduced it, we played “them against me,” and oh, boy, did they ever love that!  After that, I left the game out during the week for them to play during Guided Math Workshop.  It was a big hit and they got quite good at counting backwards by multiples of 10 on an Open Number Line!
This is a funny story...as I am sitting here writing this blog post, I just received notification that I got an email from one of my second grade students.  I CANNOT believe the coincidence of this timing!!!!!  Here is what the email said (on a Sunday morning no less!):

"I love the new math strategies. I taught my parents and they like it better then old fashion math. My favorite is open number line. I started with not being very good at subtraction and then the open number line helped me learn it."

     I cannot express how this made me feel!  A very far cry from what my feelings used to be about math...
...and really, I owe it to the Common Core changes and to math strategies that go beyond the “cut and dry.”   At the heart of it all, of course, are my eager little learners...the real reason why math is a bright spot in my day!


  1. Awesome! I'm a math coach and I'm impressed!!

  2. Hello There,
    I just wanted to see if you were currently interested in additional guest bloggers for your blog site.
    I see that you've accepted some guest posters in the past - are there any specific guidelines you need me to follow while making submissions?
    If you're open to submissions, whom would I need to send them to?
    I'm eager to send some contributions to your blog and think that I can cover some interesting topics.
    Thanks for your time,

    1. Hi Tess, I would love to talk to you more about that...what is your blog?

  3. This comment has been removed by a blog administrator.

  4. Thank you for sharing your strategies Tracey! I already enrolled my kid to MSA-math tutorial.


Notes For the Teacher