Comparing Fractions w/ Desmos

For the past few days, I’ve been hanging out with Mrs. Becker’s (Peytra) 6th grade exploratory class.  We both like experimenting with new strategies and often use her exploratory kiddos as guinea pigs.  Our recent experiment – Fractions.

Last year I started creating various fraction activity builders. These activity builders are slightly different than your average task for they don’t walk a student through a series of guided questions. I designed the slides so teachers and students have the flexibility to create their own problems.  It’s more of a general or open tool to be use as desired.

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That said, I’d like to highlight 2 moments from today…

Part 1 – Comparing Fractions

Directions:

1. Go to slide 2.
2. Shade 1/2 of the red square and 1/4 of the blue
3. Insert the appropriate comparison symbol
4.
5.                              Original Slide                                         After Directions

Eric’s Ah-ha Moment

Even though the blue 1/4 clearly looks smaller than the red 1/2, a handful of students used the less than sign.

• Me:  I noticed you used the less than sign, therefore saying 1/2 is smaller than 1/4. What’s your reasoning?
• Eric:  The denominator is bigger.  4 is bigger than 2.
• Isaac:  (Isaac joined the conversation) Look at the colors.
• Me:  What do the colors tell you?  Eric still wanted to say that 1/4 was bigger than 1/2.
• Isaac:  Which color is shaded more?
• Me:  (to Eric who is still hanging onto his belief that 1/4 is bigger than 1/2).  Do you see the blue dot?  Click on it and drag it over to the red 1/2.

Eric grabbed the move-able dot and dragged the blue 1/4 over to the red 1/2.  When Eric lined up the pictures, his face looked puzzled – he began doubting his first answer.  Time for a story…

• Me:  Let’s say I baked your favorite type of cake.  Which would you prefer:  The red 1/2 piece or the blue 1/4 piece?
• Eric and Isaac:  (eyes wide picturing yummy cake) The 1/2!
• Me:  Why? (to Eric)
• Eric:  I’d get more.
• Me: OK.  Let’s go back to the denominator.  When the denominator gets bigger, what happens to the piece of cake?
• Eric:  The piece gets smaller.
• Me:  Would you repeat that statement?
• Eric:  When the denominator gets bigger, the piece of cake gets smaller.

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Part 2: Equivalent Fractions

Directions:

1. We now know that 1/2 is greater than 1/4.
2. Change 1/4 to represent a shaded region that is equal to 1/2.  You are not allowed to use 1/2.

Aiden’s Ah-ha Moment

After class, Peytra shared that one table had a great ah-ha moment.  I pressed for details!

Peytra:  Aiden had no idea how to start. He stared at the screen for a bit.  I watched him drag the blue and place it on the red.  He then began making adjustments (to the fraction) until the blue and red matched. He figured out how to find the equivalent fraction on his own!!!

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Desmos & the Whole Class Discussion

The Teacher Dashboard can be used to facilitate whole class discussions.  Pictured below is the dashboard.  The blue column on the right houses all the names.  The Anonymous Icon (the person) switches student names to famous mathematicians. When the person is hanging out in the white circle, the Anonymous Icon is in play.

To view student progress, click on the desired slide. When the word Responses, is in blue text and underlined then you’re on the student response page. On this page, teachers can view all student responses and decide which ones to highlight. Simply click on the student’s individual response to enlarge.

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Closing Thoughts

Peytra and I are well aware that comparing and finding equivalent fractions are not 6th grade standards.  We also know that there are many students who don’t understand fractions conceptually. While some students immediately created an equivalent fraction for 1/2, others struggled. The conversations were insightful and supported our desire to integrate more opportunities for fraction exploration and sense making.

The Activity Builder:  Exploring, Comparing & Finding Equivalent Fractions

If you use this activity builder, I’d love to hear about your experience!

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