Multiplication of fractions – a cool visual

As some of you know, I work part-time as a math paraeducator (a.k.a. “teacher’s helper”). In 6th grade, we have been studying multiplication of fractions. If your schooling was like mine, you probably were told, “This is how you multiply fractions,” then you were given a bunch of problems to do to get you used to the formula, and you never really UNDERSTOOD what multiplying a fraction times a fraction means, or why you end up with a smaller number as the answer.

I also know that some of you are home educators, so perhaps the following drawings will be useful to you in explaining this concept to your pupils.

This method, called the “brownie pan” method, uses visual aids, or manipulatives, drawn by the students. Here is how the student could illustrate the fraction 3/4:

brownie-pans1.jpg

Here is how the student could illustrate the fraction 2/3:

brownie-pans2.jpg

And, finally, this is how the student could illustrate the multiplication problem 2/3 of 3/4 OR 3/4 of 2/3 (Remember that the word “of” indicates the mathematical operation of multiplication.):

brownie-pans3.jpg

The sections of the brownie pan that are double-shaded show the numerator of the fraction product (How many pieces of the whole are we talking about?) and the total number of sections in the “brownie pan” shows the denominator of the fraction product (How many pieces total is the whole divided into?).

This is cool, is it not?

Do you have any questions, students?

4 Responses to “Multiplication of fractions – a cool visual”

  1. Marmee says:

    A gifted teacher, using her gifts, you are! I knew HOW to do this, like you said, but I never really understood how it worked. I will always think of you whenever we are multiplying fractions!

  2. kerri says:

    I’ll have to try this with my 11 yr old. She will be a real test. She’s been working on fractions for quite a while now and still does not get it…

  3. Joyce says:

    Thanks, Marmee, but REALLY, I just learned this neat way of picturing fraction multiplication this year, from the teachers whom I help!

    The entire program we use (I think it’s called Connected Mathematics) is based on the premise that students need to puzzle over some real life math problems, and understand WHY the math works, rather than just being told, “This is HOW to solve this type of problem.” I constantly need to hold myself back from helping too much.

    Anyhoo, it’s a nifty way to picture multiplication of fractions, eh?

    Hi, Kerri,

    I hope this helps your daughter. This is a difficult concept. Lots of 11 year olds have trouble with it!

  4. Kathie says:

    Cool! Just noticed that you changed the layout of your blog. It’s much more legible on my computer (Mac, with Firefox browser.)