Activities, Writings, and Videos by Debra K. Borkovitz
It’s hard to make sense of multiplication and division of fractions. Before fractions, multiplication can almost always be seen as repeated addition, and the answer is never smaller than both the numbers you started with. Division is usually … Read More
This applet is a pick a number game, where the secret number is a fraction between 0 and 1. Enter a numerator and denominator and the computer will tell you if your fraction is too high or too low, until … Read More
Note: This is the second post in my series on teaching with a chronic illness. Here is the introduction to the series. When you have a chronic illness and a job, by definition you work when you are sick. Before … Read More
In my post Trigonometry Yoga, I discussed how defining sine and cosine as lengths of segments in a unit circle helps develop intuition for these functions. I learned the circle definitions of sine and cosine in my junior year of … Read More
Use the slider to change the value of k, and to see dynamically how the graph of \(h(x)=k^x-x^k\) changes. Negative values have \(x^k>k^x\). Which value of k gives a graph that is never negative? Why? Here is a very pretty … Read More
Which is bigger, the sine of 40\(^{\circ}\) or the sine of 50\(^{\circ}\)? This is a great trigonometry assessment question. Unfortunately, virtually none of my college students who haven’t used trig for a while can answer it (without a calculator). For … Read More
The handshake problem is an old chestnut — if everyone in the room shook hands with everyone else, how many handshakes would there be? Then generalize. What I have to add to teaching the problem is a handout (doc version, … Read More
Last semester, I taught my first two classes wearing sunglasses and a baseball hat tilted to cover half my face, with the lights turned off. The students thought I looked cool.
This is a great first day of class activity, which works well with math phobic students (I use it in a math for elementary teachers class). Students make a list 1:00, 2:00, etc. on a piece of paper — however … Read More
I thought it would be nice to have a place to put quotes I run across and old favorites that I need to reread now and then. If I get a lot of them, I’ll categorize, right now, it’s a … Read More