Math Arguments

Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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Which is bigger?

Which infinite sum is greater?

\(\frac{1}{2} + \frac{2}{4} + \frac{3}{8} + \frac{4}{16} + \frac{5}{32} + \frac{6}{64} + \frac{7}{128} ... \)

or

\(\frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \frac{8}{64} + \frac{13}{128} ...\)

What other mathematical aspects of this caught your attention? What do you wonder about the situation?

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Notice, Wonder
Matt Enlow
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Source: Matt Enlow

Quick, which infinite sum is greater? 1/2 + 2/4 + 3/8 + 4/16 + 5/32 + 6/64 + 7/128 ..., or 1/2 + 1/4 + 2/8 + 3/16 + 5/32 + 8/64 + 13/128 ... — Matt Enlow (@CmonMattTHINK) April 29, 2014

More Information:
Noticing and wondering is a tool to help students:
- Understand the story, the quantities, and the relationships in the problem.
- Understand what the problem is asking and what the answer will look like. Have some ideas to begin to solve the problem.
More Here at NCTM