How Do you Teach Regrouping with Understanding?

If kids aren’t building with base ten blocks to add and problem solve FOR WEEKS initially, they will get no where with their number sense understanding for regrouping.  Under common core standards, we are heading towards the understanding of the traditional algorithm in the 4th grade standard–not just being quick at a procedure of crossing out numbers and writing new ones above them.  Mistakenly 2 years ago we tried to rush the traditional algorithm with our second graders.  As a result they are still struggling with this in 4th grade. So here is the success story of what we did in second grade last year.  Nearing the end of the year, there were several skills that hadn’t been taught to the degree that they needed to be such as geometry etc.  I knew without the foundation of addition, counting, and problem solving we would be up against a wall again in 3rd grade, so we focused on these skills.  Throughout the year we spent a lot of time filling out number charts and discussing pattens on the hundreds chart above 100 using these:

Counting you ask?  Yes, we spent time counting and looking at patterns in numbers.  I know it is in the standard so that is part of why we counted, but counting is so much more important than teaching because it is the standard.  How can students reason about whether their answer makes sense if they can’t count?  Reasoning about math is in the mathematical practices several times.  Students who can’t count, can’t estimate and can’t round because they have NO idea about where the number comes in the whole sequence of numbers.

Second graders last year solved a CGI word problem each day while they were learning addition and subtraction.  Students spent several weeks using base ten blocks to solve their addition and subtraction regrouping problems.  When students weren’t permitted to use the actual blocks, we prompted them to draw illustrations of the blocks to help them solve their problems.  Even after students were shown how the traditional algorithm worked with their blocks, most of them tended towards drawing a picture of the blocks to solve the problem.  Most were successful doing this.  I was satisfied with this progress because I knew in 3rd and 4th grade that they would again have an opportunity to learn the traditional algorithm and other addition/subtraction strategies.

So here is how we are beginning with the kiddos in 3rd and 4th grades this year to teach addition regrouping.  The kids are still given the opportunity to use blocks if needed to formulate understanding.  Now I know that in showing them how to regroup the kids aren’t really “discovering” or “constructing” the algorithm themselves, but they are gaining an understanding.  I just don’t think we have enough time in the year for the kids to discover everything and they must be shown some things.  I haven’t arrived at that place yet where I think in CGI utopia…maybe I will get there someday??  (Don’t get me wrong, I find value in CGI)  For right now the kids are getting this method of teaching addition regrouping and making sense of it.  I’m happy and the kids are learning.

Traditional Algorithm Behind the Scenes

Now what I’m about to show you is the students’ first experience with regrouping like is pictured above.  It isn’t cute at all…not worthy of for sale anywhere…but it is real and handwritten.  To make it on a handwritten page was just so much faster than doing it on computer so it is what it is.  I wanted to create columns so the students wouldn’t get their numbers confused.  This worked well.  I didn’t have the kids put pluses between the numbers like true expanded form to keep them from confusion later on when we do subtraction regrouping similar to this.

We discovered that students had a difficult time in the hundreds column when they had a number regroup to the thousands place.  They weren’t used to putting two numbers together that weren’t zeros so this seemed to confuse them.  If we had three digit adding to do over, we would have the kids include a thousands column so that they could regroup their thousands there at first until they made the connection that they could put two digits other than zeros in the left hand column.  In other words, we would have them add one column more than the number of digits that there were in the number.  For example…

Later on last week, we taught the kids to regroup without the columns drawn and without the numbers being decomposed into hundreds, tens, and ones.  We continued to have the kids draw the arrows and to estimate their answer.  It was rocky at first and about half of the class got regrouping with numbers written in standard form (just normal).    They will be working on regrouping again early next week.