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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
Posted in Uncategorized
Tagged denominations, extending patterns, lookup, models, naming, recurrence relationship, sieve
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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
Posted in Uncategorized
Tagged denominations, extending patterns, lookup, naming, unlearning
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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
Posted in Uncategorized
Tagged extending patterns, math class, models, puzzle, unlearning
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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 thirtyfour 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
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
Posted in Uncategorized
Tagged education, math class, math in the comics, models, unlearning
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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 7letter curse word “algebra”. I submit most teachers have encountered some variation on student Jesse who … Continue reading
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
Notes on Notation – Division
In the course of normal school, students encounter various notations for division, and boy, are there many. We’ve got 15 / 5, and then there is also 15 ÷ 5 as well as . You may even have come across … Continue reading