Here is another installment in my series reviewing the NY State Regents exams in mathematics.
There is something of a history with Regents exams and the force of gravity.
An infamous problem years ago modeled a falling object with the quadratic function
This would imply that the acceleration due to gravity, or g, would be equal to 4 f/s², not the -32 f/s² we are accustomed to. This amusing error inspired my talk “g = 4, and Other Lies the Test Told Me“.
So, it was interesting to see projectile motion appear twice in the most recent round of math Regents exams. This is from the Integrated Algebra exam.
I was pleasantly surprised to see the proper coefficient!
And then I noticed a second appearance of gravity. This is from the Common Core Algebra exam.
Of course, I had to check. Kudos to the exam writers for looking up the actual force of gravity on the moon. If we’re going to go to the trouble of trying to establish “real world” contexts for these problems, we should make sure physical forces are accurately represented.
There is a lot of math to see when you look up, especially if you’re standing inside the skeleton of a hexagonal pyramid.
Desmos, the free, browser-based graphing utility, has quickly become an indispensable tool in the mathematics classroom. It provides easy, intuitive access to graphs of functions and relations, and creates unique opportunities to understand mathematical relationships dynamically.
But to me, its greatest virtue may be that Desmos provides opportunities to use mathematics to create. I like to think of Desmos as a mathematical makerspace, where the tools at our disposal are exactly the tools of mathematics.
To that end, when I introduce students to Desmos, we always work toward the creation of something mathematical. Below are some beautiful examples of student work from our latest round of Desmos projects.
You can find more of my work with Desmos here.
When I describe the role mathematics plays in my life, I often say that it gives me a set of tools to process and understand the world. One way that manifests itself is that I see graphs everywhere.
For example, when I look at a pole on the subway, I see the distribution of hands that have been on the pole.
I think about things like this because they are interesting, but also because they are practical. Where is the pole the dirtiest, and cleanest? Where are germs most likely to reside? New Yorkers know instinctively to touch as little as possible, but sometimes you have no choice. Best to know your probabilities ahead of time.
This colorful Venn diagram was a lucky find in the dollar bin. Maybe it was so cheap because it only has 12 regions, instead of the 63 that six sets should generate.
I suppose it would be more realistic if everything outside the colored region was black, and the point at the very center was white.