# Monthly Archives: January 2009

## Powerful Sunglasses

This is a puzzle. Imagine I own a pair of sunglasses that reliably blocks ultraviolet rays so that, out of any ten rays that shine on it, only one of them gets through.  So, if 40 rays shine on them, … Continue reading

## Notes on Divisibility – Eratosthenes and Euclid

You will want to read the Notes on Divisibility post first. In the figure below, I’ve shown the first 22 mile markers, and the red marks on each.  Skip counting by twos leads to the red “2” marks, skip counting … Continue reading

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## Notes On Divisibility

Imagine the numbers 1, 2, 3, … laid out in a regular linear sequence, like mile markers on a long road. The markers don’t need to be a mile apart, you can put them closer if you like, but you … Continue reading

## Half a pizza and half a balloon

This is a puzzle If you’ve ever actually tried to divide a pizza into 15 equal pieces – and I mean the kind of dividing that uses a knife or a cutter or piano wire – you’ll find that knowing … Continue reading

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## Making Change – A Sam Lloyd puzzle

This is a puzzle, taken from the famous puzzle producer Sam Lloyd, complete with original illustration.  This puzzle is old: A lady bought a boquet at the florists for thirty-four cents and had a one dollar bill, a three cent … Continue reading

## Notes on Notation – Equality

The humble little equal sign, , is called on to do a large number of different tasks.  As teachers, we often assume that kids will keep these tasks straight.  To an amazing extent, kids actually do.  And I suggest this … Continue reading

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## Math in the Comics – part 1

I saw a poignant comic strip in the newspaper today, and thought it was illustrative to mention here: Paige has no clue what to do with and or how to solve that set of equations.  Her brother then asks her … Continue reading

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## Notes on Notation – Variables

Variables have often been seen as the big bugaboo of the middle school math curriculum and beyond.  They have become inextricably identified with that 7-letter curse word “algebra”.  I submit most teachers have encountered some variation on student Jesse who … Continue reading

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## The Lewis Carroll problem

This is a puzzle. Lewis Carroll, the author of Alice in Wonderland, was also a mathematician. In his diary for 1890, he wrote the following statement: is always the sum of two squares where x and y are a pair … Continue reading