Tag Archives: Problem Solving

Beam of Light

This month's post is based on a problem that appears in Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American. Below (and here) is a Web Sketchpad model of an orderly forest. There is a tree at every point whose x- and y-coordinates are both integers. These are the green points. You … Continue Reading ››

A Double Spiral from David Henderson

David Henderson, one of my two Cornell master's thesis advisors, died this past December. I wrote about David in a prior post, and in particular, his approach of asking us  to grapple with a small number of  rich problems, allowing us  to find our own, often non-traditional, … Continue Reading ››

Find the Secret Number

We created the Web Sketchpad game below (and here)  as part of our Dynamic Number project. It challenges elementary-age students to uncover the value of a secret number by collecting and analyzing clues that narrow its range of possible values. The game familiarizes students with inequality signs, introduces the use of x to … Continue Reading ››

The Scaled Maps Problem

Below are two maps of the United Sates, with the smaller map a 50 percent scaled copy of the original. The edges of the two maps are parallel. Imagine that the maps are printed out, with one resting on top of the other. Believe it or not, you can stick a pin straight through both maps … Continue Reading ››

Adding and Subtracting Integers

A recent post on the my NCTM discussion group asked about tools to help students visualize and understand addition and subtraction of integers. I always found this confusing for some of my Algebra 1 students, mainly because they had been told to memorize some rules about whether to add or subtract the two integers and … Continue Reading ››

Fifth Graders Investigate a Mathematical Code

How much tolerance do you have for puzzlement? When faced with a mathematical conundrum, do you embrace the challenge, or do you feel some trepidation at confronting the unknown? For many of us, an unfamiliar mathematical task is sure to raise our heart rate a beat or two. As teachers, it’s easy to translate these fears … Continue Reading ››

Deducing the “Mystery” Fraction

Estimation is an important mathematical skill, yet we rarely ask students to make estimates that relate to fractions. As part of the Dynamic Number project, we created a "mystery" fraction challenge  that presents a green point somewhere between 0 and 1 on the number line. The point's location can be represented as a fraction with … Continue Reading ››