CTK Insights

Every book carries an ISBN or EAN-13 or both numbers. ISBN or EAN-13 are two ways to encode information that would allow to identify a book on the market. ISBN contains 10 digits EAN-13 thirteen. All but the last digit encode country, manufacturer (publisher), and product (book) information. The last digit serves as a safeguard [...]

What's the task? The task is to combine several 3- and 4-pyramids into larger 3- and 4-pyramids. What's the setup? You'll need 4 tetrahedra and 6 square pyramids. Having 8 tetrahedra and 8 square pyramids will allow to complete 3- and 4-pyramids simultaneously. For your convenience, here are the maps of the pyramids. Just cut, [...]

What is the setup? You'll need a set of cards with numbers 1, ..., N written one per card; N not too small and not too big. Say, for N = 8: How to start? Shuffle the cards somehow and place them in a row: What is the activity? Look at the number on the [...]

Today's activity is based on a problem by Vyacheslav Proizvolov offered at the 1985 All-Union Soviet Math Olympiad. What do you need? Strictly speaking, that activity needs nothing beyond a piece of paper and a pencil. However, it may be convenient to have numbers, say, 1 through 20, written on small paper pieces: What is [...]

The two activities described below require nothing beyond a paper and a pencil. Both activities consist of carrying out iterative processes whose results becomes - hopefully - predictable after a few tries. When this happens, i.e., when children become able to predict the result, they can start using online simulators to verify their intuition. Until [...]

Kozma Prutkov is a collective pen name of the count Aleksey Konstantinovich Tolstoy and two of his cousins - Zhemchuzhnikov brothers, Alexei and Vladimir. Mostly in the 1850s-60s, Kozma Prutkov published aphorisms, fables, epigrams, satiric plays, humorous and nonsense verses. Many of the aphorisms became an authentic part of Russian folklore. If ever asked what [...]

The PEMDAS acronym is supposed to help students memorize the order of operations. I consider introducing and using it an education outrage. Let me explain.

The setup Draw 6 dots more or less evenly distributed over a circle: The activity Join the dots by lines of two colors, say, red and blue. Join all pairs of dots. See how many lines of the two colors emanate from each dot. What's to observe At every dot there are at least three [...]

The setup A cube whose faces have been partitioned by the midlines into four squares. The activity Color the squares in as many colors as you wish, with a single caveat: no two adjacent squares, i.e., squares that share an edge, may be of the same color. The task Determine the maximum possible number of [...]

Through a Linkedin discussion I came across an interesting blog offering an advice of how to handle the situation where "words have different meanings in academic subjects than they have in everyday language." There is a couple of nice examples: ... reducing a fraction to lowest terms has no effect on its value (e.g., 6/8 [...]