Fawn Nguyen, in her blog Finding Ways, posted a problem that she found in Don Steward’s blog. Both Fawn’s and Don’s blogs are way at the top of my go-to sites when I am looking for something creative to use in my work with math teachers. This problem is an example of why. It’s a simple problem that is accessible to middle school students, but turned around in such a way that makes it ripe for creating great learning opportunities for students.

The problem makes clear the importance of using units as tools for understanding. Fawn’s post discusses how she introduced the problem to her Grade 6 students and included their comments.

In order to make sense of the statements, student have to not only attach the labels, but also understand that labels are “acted upon” by operations. Another key understanding students need is that division translates in English to “per”.

If units are attached, 24000 g /150 g results in a naked number, 160, that is not grams. What unit is attached to the 160? If we are more specific with our units and write

We’re dividing a fraction by a fraction, so we invert the second fraction and multiply…even if the fractions are made up of words!

The answer of cakes per bag makes it clear what the question is.

Thanks, Fawn and Don, for providing us with this rich task!

That’s one way of looking at it. I suspect that the student with their feet on the ground might argue as follows:

There are 24000 grams in the bag and 150 grams needed for one cake, so I need to know how many 150’s I can get out of 24000. Ha ! Divide 24000 by 150 (thinking of division as repeated subtraction, something which the CCSSM doesn’t seem to recognize). Their answer will then have units of “cake”.