Skip Counting with Fractions

Intended Audience:  Grades 3-6 math teachers, prospective teachers, and parents (public, private, homeschool).

In this video, 6-year-old Autumn skip counts by fractions 1/2, 1/3, and 1/5.  There are a number of ways to skip count by a fraction.  Here are some of them used in Eureka Math/EngageNY:

  1. 1/4   2/4   3/4   4/4   5/4   6/4   7/4   8/4   9/4 …
  2. 1/4   2/4   3/4   1   1 1/4   1 2/4   1 3/4   2   2 1/4 …
  3. 1/4   1/2   3/4   1   1 1/4   1 1/2   1 3/4   2   2 1/4 …
  4. 1/4   1/2   3/4   1   5/4   3/2   7/4   2   9/4 …

Autumn is doing the second skip counting technique above (the fourth is the hardest, which is why it shows up in later grades—try it with 1/6).  The beauty of the second skip counting technique is that

  • it emphasizes the whole unit “…, 3 fourths, ONE, ONE and 1 fourth, ONE and 2 fourths, …”
  • it emphasizes the repeating pattern of important fractional units (1/4, 2/4, 3/4)  between each whole unit.

That doesn’t mean the other skip counting techniques are not important! They all have a role to play in a curriculum.  For example, the first skip counting technique emphasizes that counting fractions is just like counting whole numbers but in a different unit.  That is, “1 fourth, 2 fourths, 3 fourths, 4 fourths, 5 fourths,…” is just like “1 apple, 2 apples, 3 apples, 4 apples, 5 apples…”

Obviously, Autumn already knows a lot about fractions.  I apologize for not showing how to develop the concept of a fraction (maybe another video?).  This process takes a long time and is carefully developed in the Eureka Math/EngageNY curriculum.  You can find out more about how we do this in the curriculum by reading Chapter 6 of “Elementary Mathematics for Teachers” that I co-authored with Thomas Parker.

Regardless, there are many things that parents can (and often already do!) with their children to help them get ready for fractions.  These things include very sensible activities like using a tape measure or cooking cups where the notion of fraction just naturally manifests itself, “Honey, measure out 1/3 cup of sugar please.”  Early on, “1/3” is basically only an adjective modifying the noun “cup;” it references a particular measuring cup, but even so it does bring up a nice way to have a discussion about meaning of those fractions with your children.  Tape measures are also great, “What are those marks between 1 inch and 2 inches on the ruler? Between 5 inches and 6 inches? What could they mean?”

Surprisingly to me, one of the main paths that Autumn came to understand fractions was from reading to her.  Here’s the story:  I started reading full-length novels to her starting when she was 2 years old (stories like Narnia, Lord of the Rings, Harry Potter, Watership Down, etc.).  These are thick books that are close-to or over 1000 pages each.  As we read each book, I started (rather by accident) to discuss with her the fraction of the book that we had read, “Look, honey, we are 2 thirds of the way through!”  An unanticipated-but-nice feature of thick books is that it is very easy to split the book’s pages into thirds, fourths, fifths, sixths by separating the pages with your fingers.  Since the books were all of different thicknesses, over time Autumn came to see the main issues in defining fractions:  to establish the whole unit and the relationship of the fractional unit to that whole unit (cf. how fractions are developed in grade 3 of the CCSS).

As always, comments are welcomed!

Skip Counting with Fractions

CHANNEL: Growing up with Eureka
© 2015 Autumn Baldridge and Scott Baldridge
Partially supported by NSF CAREER grant DMS-0748636

About Scott Baldridge

Distinguished Professor of Mathematics, LSU. Geometric topologist: gauge theory, exotic 4-manifolds, knot theory. Author: Elementary Mathematics for Teachers.
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1 Response to Skip Counting with Fractions

  1. kvbutler says:

    Students who think like this (skip-counting fractions) have much more accuracy and flexibility when measuring with a standard ruler. Some of my 7th grade pre-engineering students were still struggling to measure correctly with fourths and eighths . . . let’s not talk about sixteenths yet. We even took time to break down a unit into halves, fourths, eighths, and finally sixteenths. Next year I will try these kinds of skip counting for fourths and eighths with them!
    THANKS! smile emoticon

    Liked by 1 person

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