CTK Insights

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 Write a sequence of integers from 1 through some number n, say, 20-30. Do that with ink. Draw a square around each number. (Draw squares with a pencil; they need to be erasable.) The activity The activity proceeds in a sequence of steps. On step #i consider all multiples of i. If a [...]

The setup A student is presented with a small pile of objects. The task To split a pile into two; count the number of objects in each, and compute the product of the two numbers. This step is repeated with any of the present piles until the only remaining piles each contain a single object. [...]

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 [...]