Desmos Graph: Adding Positive & Negative Fractions w/ Dynamic Labels


A picture of the mixed number 5 thirds

For the past 15 months, I’ve been working on fraction models.  When I brought the models to students, the resulting conversations were great.  Just what I was hoping for.  The downside stemmed from the behind the scenes “coding”.  My original design coupled with the need to import multiple images required lots of conditional statements and therefore caused the program to run slowly.  A picture of the mixed number 5 thirds

Recently, Desmos released their newest feature – Dynamic Labels!!  This feature is a game changer.  I no longer need to import number images.  I also abandoned my need to separate the parts of the mixed number for a more streamlined look influenced by @Klockmath  and  @nathankraft1 ‘s work.  The two changes reduced both the lines of “code” and the number of conditional statements thereby creating a tool with more usability.  You can find the graph here.


Positive and Negative Fraction Model

Now, it’s time to update all my old fraction models.  A task, I happily accept.   I began with a graph that visually represents adding positive and negative fractions.  Positive fractions are blue.  Negative fractions are red.  Use the black sliders to toggle between positive and negatives.

Positive fractions are blue      Negatives fractions are red

One fraction is stationary and the other moveable.  Use the moveable fraction to estimate the answer.


Toggle off and on the common denominator feature.
Toggle off and on the common denominator feature************************************************************************************

For the second picture, I copied the image onto a Google slide and inserted lines to represent the elimination of zeros pairs. Then used the scribble feature to circle the answer of 5/6.

Example 1:  4/3 + (-1/2) = 5/6

Positive 4 thirds added to negative one halfScreen Shot 2017-07-07 at 8.27.41 AM


Example 2:  -4/3 + (-1/2) = -11/6    aka        -1 1/3 + (-1/2) = -1 5/6

negative 4 thirds added to negative one half              Negative 4/3 added to negative 1/2


Closing Thoughts

I love summer. It’s my time to recharge, spend quality time with my family and work on projects too time consuming to complete during the school year.  That said, I’m excited to for the school year to begin.  Honestly, I can’t wait to get this fraction model into the hands of teachers and students.  Let the fraction talk begin!!




About jgvadnais

Instructional Technology Coach. Desmos Fellow. Google Level 1 Certified. SoCal transplant. New Englander at heart. Lover of yoga, dogs, green smoothies and coffee creamer
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