Top Posts
 Notes on Representation  Tally Marks
 Notes on Divisibility  Common Divisors
 A Multiplication Nomograph
 Groupings, Shopping Lists, and Vectors: The Series
 Mathematical Notation and Schools  10
 The Lewis Carroll problem
 Notes on Representation  Tally Marks, Tully Marks
 Notes on Deferred Computation  the Pythagorean Spiral
 Math in the Comics  part 5
 Quantity  Different Kinds of Numbers: Notations

Recent Posts
 Mathematical Notations and Schools – 15
 Mathematical Notation and Schools – 14
 Mathematical Notation and Schools – 13
 Mathematical Notation and Schools – 12
 Mathematical Notation and Schools – 11
 Mathematical Notation and Schools – 10
 Mathematical Notation and Schools – 9
 Mathematical Notation and Schools – 8
 Mathematical Notations and Schools – 7
 Mathematical Notations and Schools – 6
 Mathematical Notation and Schools – 5
 Mathematical Notation and Schools – 4
 Mathematical Notation and Schools – 3
 Mathematical Notation and Schools – 2
 Mathematical Notation and Schools: The Series
Blogroll
 attribution black box deferred computation denominations discoverable education embedding equivalence extending patterns gauntlet graded hurdles invariants lookup math class math in the comics matrix multiplication models naming notation puzzle recurrence relationship representational proof representations reverse engineering selection series on math learning sieve sorting standing on nothing state unlearning whole vs. parts
Archives
 July 2011
 June 2011
 May 2011
 April 2011
 February 2011
 January 2011
 December 2010
 November 2010
 October 2010
 September 2010
 August 2010
 July 2010
 May 2010
 April 2010
 March 2010
 February 2010
 January 2010
 December 2009
 September 2009
 August 2009
 July 2009
 June 2009
 May 2009
 April 2009
 March 2009
 February 2009
 January 2009
 December 2008
Tag Archives: puzzle
What is Multiplication – part X
Yesterday, in the supermarket, a customer dumped a whole basket full of power bars on the counter. The checkout counter person started to scan them in, one by one. After seeing about seven of them scanned, with a lot more … Continue reading
Posted in Uncategorized
Tagged denominations, math class, models, puzzle, representations, reverse engineering, unlearning
2 Comments
Math in the Comics – part 10
From last week’s Foxtrot comic, another take at the cultural background conversation of math. Who is bad at math? At one level, a puzzle. The top part, the part that starts with “1611135″ is not a subtraction problem. It is … Continue reading
Posted in Uncategorized
Tagged gauntlet, graded hurdles, math class, math in the comics, puzzle, selection
2 Comments
A CollatzInspired Puzzle
This is a puzzle. In prior posts, I used the Collatz Problem, restated here: Each counting number n past 1 is assigned a successor number, as follows: The number “1″ is considered home, and when you’re home, you stop. If … Continue reading
Posted in Uncategorized
Tagged models, puzzle, recurrence relationship, representations, reverse engineering
Leave a comment
Mathematical Puzzle – Hinges
This is a puzzle. Imagine I have three rods of length 1 each, and they are connected together with perfect hinges. Together, they form a somewhat flexible shape ABCD (with AB=1, BC=1 and CD=1), even if I fix the two … Continue reading
Math in the Comics – part 2
Today, Bill Amend has another comic strip with math in it: It plays on the Fibonacci series, which these two geeks obviously know well. The starting numbers of the Fibonacci series are 1, 1, 2, 3, 5, 8, … and … Continue reading
Posted in Uncategorized
Tagged extending patterns, math in the comics, puzzle, recurrence relationship, reverse engineering
2 Comments
Notes on Divisibility – Common Divisors
In an earlier post I introduced the notion of a divisor without relying on division, instead thinking of it as a mark that was left during skip counting. This is a very old notion, dating at least to the times … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, lookup, models, naming, puzzle, reverse engineering
Leave a comment
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
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
4 Comments
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
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