CTK Insights

This Is Just Plain Counting I and many others think it's a good idea to start a math class with a simple non-traditional problem to get the students into the right mood for the class. My main source for the problems below is a Russian booklet by E. G. Kozlova intended for early and middle [...]

Nowadays, finding the area of curvilinear shapes falls in the purview of calculus. But the problem of finding areas draw much interest in antiquity and preoccupied mathematicians ever since. One of the acknowledged results by Hippocrates of Chios (470-410 B.C.) is the Squaring of a Lune. The problem of squaring a shape refers to a [...]

At the beginning of his career, Doug Rohrer - presently Professor of Psychology at the University of South Florida - was a math teacher. As such, he was used to begin his mathematics classes with thought provokers, the kind of puzzles that are intrinsically provocative and whose solution - often surprising - does not require [...]

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? The setup for this activity is the graph with 8 nodes joined as shown: What is the task? The task is to place the integers 1 through 8 onto the nodes of the graph so that no two successive integers are "graph neighbors", i.e., joined by an edge. What to observe? [...]

The setup Students are seated in a circle. The number of students may be arbitrary, but in a small group it is much easier to discern the idea behind this activity. With a large number of students, it is preferable to form several groups of about 4-5 kids than to have a single big one. [...]

Much of problem solving in mathematics is about finding a representation in a way that simplifies if not trivializes a given problem. Come to think of it, putting a word problem into algebraic terms - as an equation or a system of equations - is ultimately finding another representation of the problem, a representation more [...]

Breaking chocolate bars is one of my most favorite activities. Assume you have a chocolate bar consisting, as usual, of a number of squares arranged in a rectangular pattern. Your task is to split the bar into small squares (always breaking along the lines between the squares) with a minimum number of breaks. How many [...]

For Day 4 of the break, I shall present 4 games that may at first appear rather unrelated; this is the purpose of the activity to discover the commonality between the four. All four are two-players games, with the players moving in turns. The Fish Soup game For the game you should prepare 9 cards [...]

To an average student (and, perhaps, an average teacher used to teaching from a textbook) it may come as a surprise that there are numerous problems with multiple known solutions. "How come?" - may wonder the average student, "Who would want the drudge of solving a problem whose solution is already known?" Why, it's a [...]