Sunday, March 8, 2015

Using Expanded Notation to Regroup

Hi There! I’m Krista from The Knitted Apple and I am excited to be a guest blogger on Who’s Who!  

If you've ever taught regrouping to students, you know this is often a frustrating and complicated process.  Several years ago, before using flexible strategies, I looked with trepidation to the calendar as our second grade “regrouping unit” approached.  We used manipulatives, catchy songs, and rules to teach the standard algorithm for regrouping. No matter what we tried, students still struggled with this concept. 

Now I look forward to regrouping because the traditional algorithm is introduced only after a strong conceptual knowledge is established. We build that knowledge through the use of flexible strategies.  My favorite strategy to use for regrouping is expanded form, or expanded notation.  Students transition from concrete to pictorial, and then to the flexible strategy I'm showing you today. 

The advantages of using this strategy include:
  • Students have continued practice with expanded form
  • Students write the true value of each digit, maintaining place value
  • Students add on from a multiple of ten
Addition with regrouping using the expanded form is easy for students to remember because there are no tricks or rules.  It most closely matches how many of us would solve the problem using mental math.  We would add the combined value of the tens to the combined value of the ones.  Here is a visual of how students set up and solve a problem using this flexible strategy:

Subtraction with expanded form is a closer match to the traditional algorithm than addition, because students have to regroup in order to solve. The benefits I noted above still apply, but students do need to subtract beginning with the ones and moving to the hundreds, as in the traditional algorithm.  

I have students set up the problem differently than they do for addition.  Students can be confused by all the addition symbols used to separate the numbers in expanded notation.  Instead, students draw lines to separate the hundreds, tens, and ones.  It's similar to what they would see on a place value mat, but with numbers instead of pictures or manipulatives.

Finding practice pages for students is often tricky because there isn't enough space for students to work the problem. I created practice pages for students with this strategy in mind.  You can also use these pages for students already using the traditional algorithm, as it gives them practice lining the digits up correctly as they rewrite the problem vertically. 

The example shown above is from my St. Patrick's Day Math Sampler Pack.  To grab a copy of this freebie, just click here!

Happy Regrouping!



  1. I loved this strategy when I taught 2nd last year and refer to it a lot now that I'm teaching 3rd!

    Swinging for Success

  2. Thank you for the freebies! As a pre-service teacher, finding gems like these are so helpful!