11 of 11 Items .... Source: Matt Enlow

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On a square lattice, a circle can pass through 2, 3, or 4 points, as in the diagram below. The original question asks for a circle that passes through 5 points, but can you define a circle that passes through other numbers of points? and explain how the circle was created?

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Sam Shah wrote:

Matt Enlow (math teacher in MA) posted a fascinating problem online today, one he thinks of when storing all those plastic bags from the grocery store. You shove them so they all lie in a single bag, and throw that bag under the sink. Here’s the question: how many different ways can you store these bags?

For 1 bag, there is only 1 way.
For 2 bags, there is still only 1 way.
For 3 bags, there are 2 ways.

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If it takes me 60 minutes to cook dinner by myself, and 90 minutes if one of my kids is "helping" me, how long would it take her to do it herself?

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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

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

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\(\frac{1}{4} + \frac{1}{8} + \frac{2}{16} + \frac{3}{32} + \frac{5}{64} + \frac{8}{128} + \frac{13}{256} + \frac{21}{512} + \frac{34}{1024} + ...\)

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Can complex numbers be categorized into rational and irrational, or is it only the real numbers that get divided that way? What do you think about this idea?

Must irrational numbers be real? If you think so, how do you reconcile the various definitions of irrational?

If you don't think so, why do we seem to perpetuate this idea with students that irrationals are composed entirely in the real number system...perhaps not by stating that directly, but by using representations such as the ones below?







This next is an extra credit project for a college teacher prep program ... these students obviously don't know their subject all that well and this "teacher" is no better. "Hands On Math: Burn The Textbooks, Shred The Worksheets, Teach Math." is the blog motto.


3

Are the visual organizers getting in the way of the understanding?

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Is this the largest parabolic segment that can fit in a square?



... You sure this one isn't just a little bit larger?

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In Algebra 2 Honors, we spent 45 minutes trying to fill out this table as much as we could. It was awesome. Left them with a nice cliffhanger to ponder over Thanksgiving: What are the zeros of \(x^4+1\)?

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How many quadratic trinomials \(q(x)\) can you find such that both \( q(x) \) and \( q(x) + 1\) are factorable into two binomials?

#WonderWithMe

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Spot the Error