Fraction Sense

“I have this terrible fear of fractions,” Christina told him. … Also a fear of running out of popcorn. Nothing could be worse than going to a movie and they don’t have any popcorn, you know?”― Caroline B. CooneyFog

Why all the fuss about fractions? Here are several reasons:

  • Achievement in fractions on the National Assessment of Educational Progress has remained low for many years. In the forward of “Beyond Pizzas and Pies: 10 Essential Strategies for Supporting Fraction Sense” Skip Fennell, Professor of Education at McDaniel College and a past president of the National Council of Teachers of Mathematics gave the following examples: “only 24% of 13 and 17 year old students identified 2 as the estimated sum for 12/13 + 7/8, while a greater percentage identified 19 or 20 as the estimated sum (NAEP 1978)” and “only 50% of eighth grade students successfully arranged 2/7, 1/12, and 5/9 from least to greatest (NAEP 2004)”, and “only 29% of 17 year old students translated 0.029 as 29/1000 (NAEP 2004)”.
  • In the final report of the National Math Panel in 2008 the panel concluded, “Difficulty with fractions (including decimals and percent) is pervasive and is a major obstacle to further progress in mathematics, including algebra.”
  • In a study published in Psychological Science on October 2012, Seigler et. al. concluded that “elementary school students’ knowledge of fractions and division uniquely predict those students’ knowledge of algebra and overall mathematics achievement in high school, five or six years later…”

In order to achieve the end of all students understanding fractions and, therefore, being more likely to understand algebra,  the fraction learning progression in the Utah Core State Standards outlines a coherent approach to teaching and learning fractions. The progression document on fractions itself is available as the Draft 3-5 Progression for Number and Operations – Fractions. The progressions, though, are sometimes hard to read and understand. That doesn’t mean you shouldn’t read them, it just means they will take some study. That might be a great activity for a book study in faculty meetings or for your PLC meetings.

The fractions progression, however, has also been put into a very friendly learning module. It resides on the the  Illustrative Mathematics website and is called the Fractions Progression Module. I highly recommend it. By the way, Illustrative Mathematics has a wealth of information on all the standards. We will explore a great deal of that in future newsletters. For now, though, take a look at those Fractions Progressions.

For you fourth grade teachers who are or will be working on multiplying fractions by a whole number you might might want to take a look at this video from the Teaching Channel.

Next time we will focus a little on division of whole numbers.


Siegler, Duncan, Davis-Kean, Duckworth, Claessens, Engel, Susperreguy, and Chen; “Early Predictors of High School Mathematics Achievement”; prepublication paper retrieved 8/13/13 from

U.S. Department of Education, “Foundations for Success: The Final Report of the National Mathematics Advisory Panel; retrieved 8/13/13 from

McNamara and Shaughnessy; Beyond Pizzas and Pies: 10 Essential Strategies for Supporting Fraction Sense”; 2010; Math Solutions and Scholastic Inc., foreword


About MathDavidUtah

Husband of 1 gorgeous woman. Father to four intelligent boys. Father in law to three. Grampy to 7 (Charlie, Meili, Camden, Grayson, Marick, Diem, Remi)! Ham radio callsign K7CMG. Educational Leadership Specialist at the Utah State Board of Education.
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8 Responses to Fraction Sense

  1. Maria Gerber says:

    Will you be addressing specific grades in the future?


  2. Kate Thomas says:

    Great Link for the fraction progression! Thanks for including it! It would also help me to have links to applicable applications and videos as you approach the ideas. Great Job!


  3. Bill Hanvey says:

    I would choose fractions over public speaking…of course I’d probably convert them to decimals first. There is something far more familiar about decimals.
    -Bill Hanvey


  4. Darrin Johnson says:

    Thanks for putting this together. This will help our teachers.


  5. Terri McGuire says:

    Could you explain more clearly the point

    Doubles and halving (36 ÷ 4 = 72 ÷ 2 = 144 ÷ 1)— you double the dividend and halve the divisor to make a simpler problem

    These three expressions are not equivalent. What is the intent?


    • dsmith1953 says:

      You are absolutely correct. I chopped that from another source and obviously didn’t proof read closely enough. I will remove that error. Thanks for pointing it out.


  6. This will hopefully clear up a few misconceptions we have all had when teaching math. Good information about timed tests and knowing facts fluently. Thank you.


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