Friday, October 5, 2012

Addition with Regrouping

Math now a days is taught so differently than it was when I was a kid.  That sometimes is difficult for this brain of mine but when I really get into it, it makes so much more sense!  Here is one process that was different but "made so much more sense!"

Using base-10 blocks for adding large numbers.

First off, USE the base 10 blocks!  Visual/physical---perfect for those hands-on kids!
Step 1:  Use the base ten blocks to form the numbers.
+   300+40+9
(Teach place value and expanded form first!)
Step 2:  Teach to add from the ones place (right to left).
Combine the cubes in the ones place.
Step 3:  Can you regroup?  If yes, do so. 
These pictures showed the process in which I had the kids do it. 
Combine all the cubes, move the set of ten above the tens place and then exchange it for a ten rod.  This helps them to understand "carrying".
Step 4:  Add/combine the tens place, can you regroup?  Add/combine the hundreds place, can you regroup?
Then the children went on to use the place value "chart" along with their base 10 blocks and then without their base ten blocks.  Note that grayed area where they write their "carrying" number.  Awesome!  Perfect for visual learners!  (I'm sure you could create this chart pretty easy...I can't really share a copy of it since it's not my own original idea...just too good not to share!)
They moved on to...
no boxes.  Actually, by the time C. got to the checkpoint, he wasn't even writing the carrying down...he just did it all in his head.  Why?  Because that's what hands-on learning does for a kid!  :-)  They truly understand it vs. someone just telling them to carry one over and showing that if 7+3=10, there is only room for one digit so the 0 stays down and the 1 goes up.  LOL  Yeah, they may get the right answer doing that but do they really understand why they are doing that?
Anyway...I'm sure that this is something that some people have already done but this is the first time I've seen it taught this way...a definite improvement on how I learned.  :-)
 Happy days to you all!


  1. The 3 elementary schools that I have had contact with have taught math this way. We even get these models out in HS when kids either don't remember why they learned about carrying or are from other countries. It really does make a difference! In teaching algebra to ninth graders I often have them create balances to solve equations. They feel silly at first moving around blocks and such, but given a little time they seem to understand equality better. I was happy to see your post. :)

    1. Glad to hear. Perhaps they do touch on it at the school here...or maybe they use the technique for those that have a bit more issue with it but I haven't seen it be used nor did either of my kids have any background knowledge on how it was done. It is more time consuming and takes quite a bit of space with more than one kiddo doing it at once but it helps them understand quite well...especially with subtraction. We spent an extra session just on subtracting 3 digit numbers where we must regroup the ones place but the tens place has a zero. What do we do now? :-) I think we can move on now.