## Friday, November 29, 2013

### Student Generated Strategies for 3 digit Addition

I have spent a lot of time over the last few years thinking about how to develop lessons and problem strings to help students construct their own knowledge about multi-digit addition and subtraction rather than teaching them "how to do it."  I have written about some of my struggles, triumphs and amazing moments but I always find more I can talk about with teachers and students around teaching kids to think about math rather than just doing it.

Today I want to share with you 3 different solutions to a three digit addition problem that I posed this week to a group of third graders who are a bit behind where they should be but are working hard to construct their own knowledge about addition.

 This idea is one I see many second and third graders try out.  It works on every problem and is fairly efficient.  They are adding numbers by place value and it is a strategy many students invent for themselves.
 This student used a strategy that is VERY efficient for this problem because 299 is so close to a VERY friendly number.  It is the idea of compensation or taking from one and giving to the other.  It is a great strategy for kids to have in their toolbox and it leads to a strong ability to calculate mentally.

 This student did something similar to the last student but instead of compensating before doing the problem, he compensated after finding the sum.  He "pretended 299 was 300 and added 548 to it.  Then I took away 1 because I added one more than I had to."
I have been using problem strings to lead kids to making some of these big discoveries about multi-digit computation for the last few years with great success.  I have also read and applied much of what I have learned from reading this book which has really helped me out.  They really focus on the idea of students constructing their own knowledge and number sense.

I was surprised to learn a few weeks ago that another book by the same author existed that I did not know about.  I saw this book on a colleagues shelf and knew I had to have it.  It has a WEALTH of mini lessons for working on addition and subtraction and had I had this book a few years ago it would have made my journey to being a better math teacher much smoother!

What opportunities are you providing for your students' to develop their number sense?