As a Math Coach, I have to admit that I get a bit frustrated from time to time. It happened again the other day…

I went into a 3rd grade classroom and while the teacher was doing a number talk with the students, I walked around their desks and looked over a study guide that she had given them the night before as homework.

I came to the quick conclusion that number 7: **703 – 258**, was by far and away the most missed problem on the worksheet. Not only that, I saw so many different answers….why? Why was this particular problem the cause of so many mistakes?

I know the answer to that because I know what goes on in that classroom. The make up of the class contains a group of highly motivated math students who many times will grasp concept quickly, and because of that the teacher doesn’t see a need to use concrete representation to introduce skills such as regrouping. BUT, later that evening I received an email from the very same teacher asking that we spend her Math Lab day reteaching regrouping in subtraction. She had decided to test the students after their review of the study guide because she felt that the answers the students shouted showed that they ALL were ready to be tested. While grading the test she found that this regrouping is where her class still needed the most help. I have to say that while the email made me happy, because she reached out to me, it also made me sad…because this could have been avoided!

We were all taught the standard algorithm when we were younger, but I don’t recall my teacher ever asking this:

Most of us couldn’t answer this now, but if students are allowed to use base ten blocks to make the original number, then rearrange to create the same value, an answer to this question becomes very clear!

They are exactly the same value! So when we regroup, we are basically making trades with our base ten blocks to make it easier to “take away” **WITHOUT** losing the value of the original number!

Which one is easier to take 147 from? The second image of course!!!

Students see this and it won’t take long for them to eventually move on from the base ten blocks! Soon they’ll be masters at regrouping!

Had the teacher began this skill with concrete modeling, I believe that the student errors would have been avoided. Not only that, but a deeper understanding of what is happening when they regroup would have permeated her class.

One thing to note: students should be given the opportunity to use manipulatives ALL the time! It is the students’ knowledge of the skill and the context of the problem that determines whether or not they will choose to use the manipulatives. Teachers should **NOT** make this choice for them…

Here is a great post/video from Math Coaches Corner that speaks to my last statement:

Connecting Concrete and Abstract Learning

What do you think? Have you used this to a good result in your lab? Comment below.