Fraction Multiplication via Skip Counting!

Intended Audience:  Teachers, prospective teachers, and parents (public, private, homeschool).

In this video, 7-year-old Autumn uses skip counting to find $7 \times \frac{2}{3}$ as well as $4 \frac{4}{5}\div\frac{2}{5}$ in her head!

The first activity we do is just some skip counting by $\frac{2}{3}$ on the number line.  This is harder than it may seem, so it may help to look at this picture while Autumn is skip counting:

Autumn is including the whole number units as she skip counts, saying “One and two-thirds” instead of “four-thirds.”  Including the whole unit is initially harder for children, so you can scaffold up to it by just having them skip count “2 thirds, 4 thirds, 6 thirds, 8 thirds, …,” which is similar to skip counting by twos: 2 apples, 4 apples, 6 apples, 8 apples, etc.  However, including the whole unit is very important for helping your students understand the number line and building number sense; try to transition to including the whole units as smoothly as possible. You may want to watch our Skip Counting with Fractions video to get some ideas on how to do this.  (Eureka Math also has many great counting activities designed to help your students transition to skip counting with whole number units!)

In the next part of the video, Autumn and I remind the viewer about how to teach multiplication using skip counting in general.  We encourage you to watch our three videos mentioned in this video:

The big “win” for students is that nothing changes from working with whole numbers of the three videos to working with fractions in this video!  Multiplication continues to be “counting in a different unit.”

The second activity is a fraction multiplication using the ideas in the three videos above.  You may want to look at the following picture as Autumn shows how to multiply $7 \times \frac{2}{3}$:

Remember, the key that makes skip counting by a fraction work is that we are multiplying a whole number times a fraction.  Note that Autumn is not ready for “fraction times a fraction” yet, which will come later in her education.  You should not expect your students to jump to the fraction-times-fraction level without working on other prerequisites (which will be other videos).

In the third activity, Autumn shows that $4 \times \frac{2}{5} = 1 \frac{3}{5}$.  Again, it may be helpful to look at the following picture while she counts:

In the final activity, Autumn shows that division is just the opposite of multiplication. That is, if multiplication is the number reached by skip counting a number of $\frac{2}{5}$s, then division can be interpreted as how many $\frac{2}{5}$ units there are in $4 \frac{4}{5}$.  The result of the division,

$4 \frac{4}{5}\div\frac{2}{5}$,

is what Autumn finds by skip counting.  It may be helpful to look at this picture as she skip counts:

One final note: Autumn also does some multiplications and divisions like in this video  during our Growing up with Eureka Live video.  In fact, in that video is the first time we ever did calculations like those!  (We did skip counting by fractions, but never multiplication.) I highly encourage you watch her in this video–she shows you all sorts of great things to do with your students.

Hey, by the way, we found a female superhero T-shirt for me to wear in our videos! (Autumn is thrilled.)   Thanks goes to Chris Black and John Golden for the ideas.  If you have another great female superhero T-shirt to share with us, go to our Woman Superhero T-Shirt Challenge page and leave your idea in the comment section.  Thank you!

CHANNEL: Growing up with Eureka
© 2016 Autumn Baldridge and Scott Baldridge
Partially supported by NSF CAREER grant DMS-0748636