I’m sure everybody involved in making this video had the best of intentions, but it is riddled with issues that a strong math teacher could have helped them with:

The video is about understanding why the “keep change flip” method works for dividing fractions, a topic studied by eleven and twelve year-olds. They are

*much*too old to enjoy watching an explanation involving a cute puppet. Any one who shows this to their 6th or (eek) 7th Graders is going to get roasted.Their goal is to explain to students how 1 divided by 2/3 can be thought of as “how many times does 2/3 fit into 1.” This is an important way to understand division, but they should have chosen “1 divided by 1/5” or “1/2 divided by 1/8” to start with, since those go in more easily and make it easier to focus on the new idea.

In the video, Dr. Boaler first describes fitting into and then shows a visual illustrating her point. A student would likely forget the first explanation when they are quickly offered an attention-grabbing visual, and yet learning requires remembering her explanation while she shows the visual. This is sometimes called the

**split-attention effect**and it’s a useful thing to keep in mind while designing materials.Likewise, the visual itself doesn’t label any of the fractions—students have to remember that it represents 2/3.

A context might help here, because the visual makes no real attempt to

*represent the division*. Maybe we have a 2/3 cup scooper and need to measure out 1 cup of flour — how many scoops will we need?The original question was why keep-change-flip works, but this video provides no explanation of that. Instead it offers a completely different way of thinking about division, the fitting-into model. (Which, again, I like.)

If I were making this video, I would have done “1 divided by 1/5” and then “1 divided 2/3,” because students make better generalizations when they are given more than one example, as it helps one notice similarities and differences.

It is possible to use 1 divided by 1/5 to quickly give kids a sense that keep-change-flip works well with the “fitting into” idea—1 divided by 1/5 is 5, 2 divided by 1/3 is 6, etc. But you’d need simpler problems to develop this idea.

So, they probably should have asked someone who works with this age group to help out.

This gives me an excuse to share the fraction division materials I collected and wrote for BEAM, a wonderful non-profit that runs a math camp here in New York City.

The materials are based on a class I’ve taught during past years at the camp. They are a crash course in fraction visuals for students who have often seen a lot of algorithms and rules already.

The fourth lesson in the course is titled “Fitting In” and it covers the same territory as the Boaler video above—though, of course, because it’s designed for the classroom it can go much further. Might be useful to some of you, out there!

## Next Time Ask a Math Teacher for Help

I’m sitting on a break, on my iPhone, and conceptually, trying to break 1 up into 2/3 blocks is doing my head in. Agreed, start with 1/3 or 1/5 and it’s easy to see 1 is made up of 3 parts or 5 …but not 3/2 2/3rds parts. That’s whack.

2 divided by 2/3 would be better, but it’s still not a good starting point.

No no no. KFC. Keep Flip Change. Kids always remember KFC. “Did someone say KFC?” <local ad campaign>