## Angles in the Pentagon

Here’s a geometry challenge. A plane intersects a cube in such a way as to form a pentagon. If AL, FJ, and CM are all one-fourth of the side length of the cube, what are the angles in the pentagon?…

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Here’s a geometry challenge. A plane intersects a cube in such a way as to form a pentagon. If AL, FJ, and CM are all one-fourth of the side length of the cube, what are the angles in the pentagon?…

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Consumer math represents the most immediate and practical response to the student mantra, “When am I ever going to use this?” I was thinking about this yesterday during a late night run to Meijer to get some paper. They had…

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It is the habit among mathematics teachers, particularly at the elementary level, to present multiplication as repeated addition. The inimitable Keith Devlin, among others, has ranted about this, but it’s easy enough to see the temptation. When dealing with integers, multiplication…

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Several middle school math teachers have told me that there’s an important distinction between fractions and ratios that students don’t get. When I ask them what it is, the teachers can’t tell me; “it’s complicated”, they say. I’ve been troubled…

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First, a riddle… Q. How do you shoot a white elephant? A. With a white elephant gun. Q. How do you shoot a blue elephant? A. Paint him white, then shoot him with a white elephant gun. Back to Units…

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There are a lot of trite websites and apps available for teaching elementary education concepts. And then there are the occasional gems. Zip and Abby, from The Learning Chest, is one of the true gems. The goal of Zip and…

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This gem is timely to my thinking about ratios and units: It seems to have situated itself broadly enough across the Internet that I don’t know if it’s real or a fabrication, but it seems plausible enough. There are,…

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I’ve noticed that the teachers of fractions tend to make a strong distinction between division and ratios, but I haven’t entirely understood why. In my mind, ratios and division are intimately related, even inextricably so. However, my reflections on the…

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Background One of the thoughts I find myself returning to frequently is this: There is the belief shared among high school mathematics teachers that the struggle students have with algebra is that it’s the first time they’re exposed to abstraction….

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Abstract Unit, Arenas of mathematical mastery, Education, Mathematics

A common exercise that’s used to reinforce the concept that the tangent of a circle is perpendicular to its radius involves finding the radius of a circle given two measurements which are related to the tangent and the diameter secant:…

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Last night, as part of our learning-play, I asked my five-year-old son how to spell “night”. He told me “nitk”. That got me thinking about math education. English spelling is notorious for its quirks and oddities. In the case of…

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The lesser known of two math memes currently wandering around the Internet involves an interesting equation: \[\sqrt{2\frac{2}{3}} = 2\sqrt{\frac{2}{3}}\] This has spawned at least three discussions I’ve seen so far: What other values is this equation true for? Is this…

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