CTK Insights

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04 Apr

Weekly report, the week of March 28, 2016

The present collection supplies a perfect illustration to the fact that even the most simplest of the problems may be looked at from various angles. I wish that the authors of school textbooks that often include only answers or "solutions to the odd-numbered problems" paid more attention to the possibility of alternative view points.

18 Jan

Kordemsky's Palindrome Problem

In his last book Mathematical Allurments (Matematicheskie Zavlekalki), published posthumously in 2000, he tells a story of a 7th grade girl who got tempted to solve that problem and found a solution, too. She informed Kordemsky that her solution was different from the one in the book. Kordemsky encouraged her to look further, for other solutions. Several of her classmates get involved in the search that eventually produced more than 120 solutions. I can imagine Kordemsky's delight in seeing his efforts at attracting young minds to mathematics being born fruit. The kids even came up with something unexpected: many of the numbers they came up lead to other solutions when some pairs of their digits get swapped.

17 Oct

Elementary Problems that Beg for Generalization

TweetIn a well known puzzle, a father willed to his three sons camels, with the proviso that of the inheritance should go to the oldest among them, with being due to the middle one and to the youngest. Shortly after the father's death, a wise man riding on his camel through the village noticed the […]

15 May

Fowl Photos for Subitizing

Subitizing is the ability to discern the number of object on a group without actually counting the objects. Even babies and animals do subitizing with small groups. The photos below present an opportunity for subitizing in increasing order of difficulty.

10 Jun

Dominoes and Chessboard Activities

Tiling a chessboard with dominoes is uniquely suitable as an entertaining and edifying activity even for young children. Both implements are widely available, while experimentation with them leads to a good number of problems. Some of the problems admit simple (albeit ingenious) proofs that I would classify as the "very first," in the sense that they require minimal (if any) knowledge of mathematics.

07 Jun

A Kindergarten Activity As a Problem for Adolescents

TweetTwelve kids stand in a circle, a kid per one of twelve marked spots. Every now and then one moves clockwise, another counterclockwise to an adjacent position (which may be occupied by more than one kid or be empty.) Is it possible that after a while all of them stand at the same spot? The […]

24 May

Three Checker Game on a One Row Board

TweetThe setup for the 2-players game described below consists of three checkers placed on a K×1 board: A move consists in picking one of the outside checkers and placing it anywhere between the other two. Here's a sequence of two successive moves. As usual, players take turns. The one who can't make a move loses […]

21 May

Engaging Math Activities for the Summer Break

TweetBelow is a growing collection of resources I designate as "Summer Math Activities". These deal with various (mostly non-computational) aspects of early mathematics and are suitable for young children. There is no good reason not to try these activities at any other time of the year. During summertime, with the kids out of school or […]