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?

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. )