Visualizing Compensation

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

I was in a training today and they had us solve a Van de Walle problem called One Up, One Down.  It goes like this:

When you add 7 + 7, you get 14.  When you make the first number 1 more and the second number 1 less, you get the same answer. (Van de Walle, Karp, and Bay-Williams, 2013, pg 17)

Our challenge was to determine if this would always work for doubles and if it would work for situations where the addends are not the same.  We had to have a representation to show our thinking.  The different representations that people came up with were very cool!  Here are a few…


A ten-frame representation


Using counters as a model


An addition/subtraction chart


Yikes!  Big math!

Awesome activity, don’t you think?  Enjoy your weekend!


  1. Anonymous

    This one is cool! Thanks!

    • Donna Boucher

      I know! I thought it was pretty neat the different representations we came up with. A great problem to use with kiddos.

  2. Yasmine Laverne

    Hi Donna! Overtime I link to your site the images don’t appear. When I click on them a window pops up saying “page not found”.

    • Donna Boucher

      I don’t know, Yasmine. But thanks for letting me know. I’ve fixed this one.

  3. Cherry

    So cool! I love mathematic!


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