I’ve been working on my next Playful Math Singles book, based on the popular Things to Do with a Hundred Chart post.
My hundred chart list began many years ago as seven ideas for playing with numbers. Over the years, it grew to its current 30+ activities.
Now, in preparing the new book, my list has become a monster. I’ve collected almost 70 ways to play with numbers, shapes, and logic from preschool to middle school. Just yesterday I added activities for fraction and decimal multiplication, and also tips for naming complex fractions. Wow!
Gonna have to edit that cover file…
In the “Advanced Patterns” chapter, I have a section on math debates. The point of a math debate isn’t that one answer is “right” while the other is “wrong.” You can choose either side of the question — the important thing is how well you support your argument.
Here’s activity #69 in the current book draft.
Have a Math Debate: Adding Fractions
When you add fractions, you face a problem that most people never think of. Namely, you have to decide exactly what you are talking about.
For instance, what is one-tenth plus one-tenth?
Well, you might say that:
of one hundred chart
+ of the same chart
= of that hundred chart
But, you might also say that:
of one chart
+ of another chart
= of the pair of charts
So what happens if you see this question on a math test:
+ = ?
If you write the answer “”, you know the teacher will mark it wrong.
Is that fair? Why, or why not?
CREDITS: Feature photo (above) by Thor/geishaboy500 via Flickr (CC BY 2.0). “One is one … or is it?” video by Christopher Danielson via TED-Ed. This math debate was suggested by Marilyn Burns’s blog post Can 1/3 + 1/3 = 2/6? It seemed so!
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