Goodbye Pizza Pies (Hello Number Lines)

pizza

Students in the U.S. have an enormous deficit in their understanding of fractions. For instance, half of the eighth graders in this country are not able to correctly order 3 fractions, even though this is a 4th grade standard. Let that sink in for a moment. This is content they should have learned four years earlier. Even worse, only 24% of eighth graders were able to figure out that the sum of  ⅞ and 12/13 is close to 2. What’s the take home lesson from all of this? The strategies we have traditionally used to teach fractions do not work. We need to take a different approach.

How have fractions been taught?

Just think back to your childhood. You’re in your 3rd grade classroom and you are starting a new unit called fractions. What are the images that come to mind? Pieces of a pie? Pizza?

But guess what? Leading researchers and mathematics experts, including Dr. Nancy Jordan from the University of Delaware and Dr. Hung-Hsi Wu from Berkeley strongly recommend against the pie model. They have recommended using the number line as a better way to teach fractions because it offers a more extendible understanding of fractions. The length model also lends itself to more real world applications (construction, architecture, sewing, manufacturing).

The pie model tends to reinforce the common misconception that a fraction is usually less than one. In reality, a fraction can be almost any point on a number line: 6/1, 24 ½ , 0/2, -¾ etc. Another enduring problem with the pie metaphor is that it makes fractions seem fundamentally different from other numbers. If students’ mental images of a fraction are wedge-shaped, what does it then mean to add, subtract, multiply and divide that wedge by other wedges? What is ½ of a pie divided by ¼? There are very few practical applications of fractions operations that involve circular shapes.

It’s much more useful to think about fractions on a number line. Take the tricky concept of dividing by a fraction. Using the measurement model of division with whole numbers, you can think about 16  ÷  4 as how many 4s you can fit in the length 16. Using that same model of division with fractions, ½ ÷ ¼ , you can think of how many ¼-length pieces fit inside ½. You can probably even think of a circumstance in real life when you’d need to divide by a fraction. If you have a ½ foot wood board and you need to divide it evenly into ¼ foot pieces, how many pieces could you make?

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To address the deficit in fractions knowledge, we applied for and received grants from the National Science Foundation to develop a suite of fractions apps that focus on the number line model. We recently released our first fractions app, Fractions Boost EDU. To pilot it for free,  click here.   

 

Read our blog post about Teachley: Fractions Boost EDU here. )

Introducing Fractions Boost!

Are your students confused by fractions?

If so, you are not alone. Fractions is one of the most difficult math topics for elementary students, yet couldn’t be more important. Research shows that developing a strong understanding of fractions is the foundation for future math success. For this reason, the National Science Foundation recently awarded Teachley a grant to develop a series of fractions games. We are extremely excited to announce the beta launch of our first game, Teachley: Fractions Boost EDU, now available for Teachley premium subscribers. Not a premium user? Sign up to pilot here.

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To download for FREE on your iPad, go to bit.ly/TeachleyApps.

Or, if using Apple’s VPP, bit.ly/BoostVPP

 

 

 

Teachley: Fractions Boost EDU is the school version of an exciting 3D racing game that helps 3rd-5th grade students gain conceptual understanding of fractions and represent them on a number line. Students race through a futuristic game world, driving through number line checkpoints and fraction tunnels.

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Students drive through racing checkpoints, estimating where fractions fall on a 0 to 1 number line. If they need help, their dashboard provides a series of supportive hints and scaffolds that help students develop an understanding of the meaning of the numerator and denominator. For example, for the fraction ⅔, students are prompted to “tap 3 times” to split the number bar into 3 equal segments and then “move 2 segments” to find the solution. This engaging game covers all 3rd grade fractions standards, and students learn to compare fractions with the same denominator or the same numerator and determine equivalence.

 

Fractions Boost also motivates students through social engagement. Students design and build tracks to challenge their classmates. In order to a share a track with the class, you must first pass that level yourself.

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Beta launch:
We decided to launch a Beta version of the app for our premium school customers as soon as possible so we could gather more feedback on the game before launching a full commercial version (expected later this spring). We’d love to hear how your students learn from the game, how we can enhance their understanding, and any other suggestions for improvement before we finalize the game design and professional audio recording. Not a premium customer but want to try it out? Sign up here to pilot Fractions Boost and our other math games for free.