Visualizing Compensation

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!

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

  1. 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”.

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