Greatest Common Divisor: Extending the Definition

Having just talked about definition issues in geometry, I thought a recent, short question related to a definition would be of interest. We know what the Greatest Common Divisor (GCD, also called the Greatest Common Factor, GCF, or the Highest Common Factor, HCF) of two numbers is; or do we? Negative GCD? Here is the …

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More on Faces, Edges, and Vertices: The Euler Polyhedral Formula

Last time we looked at how to count the parts of a polyhedron, and a mention was made of Euler’s Formula (also called the Descartes-Euler Polyhedral Formula), which says that for any polyhedron, with V vertices, E edges, and F faces, V – E + F = 2. We should take a close look at that simple, yet amazing, …

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Three Meanings of “Percentile”

(An archive problem of the week) Having just discussed quartiles, I want to look at related issues concerning percentiles. There, I briefly mentioned different perspectives on the concept of quartile, and focused on differences in the details of the calculations; here I will focus mostly on the different perspectives, and then touch on variations in …

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The Many Meanings of “Quartile”

Some time ago I discussed various issues pertaining to the concept of median in statistics. The same issues, and more, affect the concept of quartile (the median being the second quartile), so much so that different statistical software packages produce many different answers for quartiles. I have seen this affect students, who are taught one …

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What is Multiplication? How (Not) to Teach It

Last time we looked at the roles of multiplier and multiplicand from several perspectives. This time, I want to focus on one extended discussion about how children should be taught to think of multiplication.

What is Multiplication? Multiplicand and Multiplier

We have received many questions over the years about the meaning of multiplication. When we multiply , what are we really doing? This can confuse not only students and their parents, but also teachers. The next couple posts will deal with various aspects of this question.