Category: Mathematics
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At a used bookstore today, I picked up the 1893 text Elements of Arithmetic: For Primary and Intermediate Classes in Public and Private Schools by Dr. William J. Milne. One thing that I noticed was that he is adamant that “and” is never to be used when naming integers: “In reading numbers expressed by three figures, the…
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(Edited 6/20/23: I lost the images for this post, and they’re in 3D. I haven’t reconstructed them, so there’s an additional challenge for you!) [mathjax]This is a challenging one: Given all the information at one corner of a tetrahedron (all three surface angles and all three edge lengths), what is the volume of the tetrahedron?…
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Problem [mathjax]You have just completed a game of 2048, and you want to know what percentage of initial tiles were fours. How can you do so? Rules First, the rules of 2048. In its basic form, this app consists of a 4×4 grid containing some tiles. On a turn, the user slides one of the…
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(Edited 6/20/23: I lost the images for this post, and they’re in 3D. I haven’t reconstructed them, so there’s an additional challenge for you!) [mathjax][Image lost, not reconstructed.]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…
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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 two options: A ream of 500 sheets for $4, or a ream of 750 sheets…
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[mathjax]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 and iterated addition will return the same numbers. Historically, it may be the case…
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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 by that response. For me, ratios and fractions both involve division, and they certainly look…
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[mathjax]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 In this TEDx Talk, Randy Palisoc argues that mathematics should be taught as a language. While…
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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 Abby is not to teach simple “math facts” or to drill on numbers as abstract…
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[mathjax]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, at least, lots of non-teachers who are equally convinced that the question is a trick because,…