Thursday, March 24, 2016

Fluency with Comparing Fractions

   I spend a lot of time in grades 3-5 working on developing strategies for comparing fractions.  I have written before about the 5 strategies my students use to compare fractions.  I also shared my favorite free computer game for kids who are working on fluency with comparing simple fractions.  Today I was working with an intervention group of fifth graders and had a few minutes at the end of our session.  I knew that I needed something quick and fun so I grabbed my regular old deck of playing cards.  
   We split the deck and each flipped two cards and made a fraction.  The first card flipped became the numerator and the second card the denominator.  This allowed us to make all kinds of fractions.   The person with the largest fraction won all of the cards.  Some of our fractions were less than one, some were equal to one and some were more than 1.  It was a great way for students to practice comparing fractions.  Out of the 5 strategies for comparing fractions, I saw students use comparing to a benchmark most frequently during this game.  It was a great way to reinforce the idea of one half, one whole and improper fractions.  I also saw students using common numerators to compare fractions and quite a bit of unit fraction reasoning.  My favorite use of unit fraction reasoning was when a student used the idea of unit fractions and the distance from one to compare 10/11 and 11/12.  "They are both missing one piece.  11/12 is missing 1/12 and 10/11 is missing 1/11.  Since 11/12 is missing a smaller piece, it is greater."         

     After a bit, we changed up the game and had each person flip 2 cards, use their smallest card as the numerator and their largest card as the denominator.  This made all our fractions less than or equal to one.  It made it so that the fractions were a bit closer together and required more critical thinking.  After a few minutes playing that way, we reversed it and had folks put their higher card as the numerator and the lower one as the denominator.  This was a great way to really reinforce the improper fraction, mixed number connection.  

This entire game took under 10 minutes and was a great way to reinforce some big fraction ideas!  I love how it requires no prep and is easy to differentiate!  By pulling out some of the cards in the deck, I could make this game based on friendlier fractions which would be great for third and fourth graders.

Book Study Launch

Looking for some motivation as the school year comes to a close?  Want to try a new structure for math class this spring and/or next school year?  Join us for a 5 part book study on Minds on Mathematics: Using Math Workshop to Develop Deep Understanding.  You can read all about it here!   


  1. I love no prep games like that one. It's definitely a winner!

  2. It must be the time of year for fractions! I just posted about how I increased the rigor of this comparing fractions game with my students over the past week. I LOVE using cards and dice to make math fun! :) I loved reading your take on the game and found a few conceptual understandings to add to my lessons! Here's my post if you want to check it out:


    1. Hi Tammy! Thanks for the great comment! Headed to check out your link now :)

  3. This is such a fun way to teach fractions. I look forward adding these to my curriculum. Games with cards and dice always seem to resinate with my students and they are always so excited about learning through play. Which even in fourth grade is so important!

  4. Hello, I really enjoyed looking at your blogs! They hold a lot of really awesome ideas along with fun and engaging lesson plan ideas! I am currently in school for my teaching license and could see myself using these ideas! I especially liked this game! It's easy and quite engaging for all students. It would also be very simple to modify for different grades and different ability levels. Within my math methods course, we discuss how hand-on activities will be the most meaningful because it gets the students moving and engaged without really even knowing it! Thank you for sharing your experiences and information!

  5. I really enjoyed reading your blogs and found this game to be especially useful! I am currently in school to obtain my teaching license as well and hope to incorporate many of your ideas into my future classroom. Recently, I work a lot with fourth grade students who are learning about fractions. Because this is such a challenging topic for many students, incorporating games such as this would be very fun and engaging for them! It is also a way for students to recognize that math is everywhere and can be found in every day objects, such as a deck of cards. Thanks so much for sharing!