Years of mathematics education has conditioned me to always try to find the area of shaded regions.
Maybe this image belongs in a Calculus textbook.
Appreciation
Menu Consistency: An Ode to Five Guys
There are many reasons to love Five Guys: good burgers, fresh fries, and free toppings, to name a few.
But I’ve got another reason to praise this fast food establishment, one that is near and dear to my heart: menu pricing consistency.
I snapped this photo at the Five Guys in Brooklyn.
If you look closely and do the calculations, you will notice that the addition of cheese costs the same 72 cents no matter what sandwich you add it to. Not only that, but the difference in price between Burger Type X and Little Burger Type X is $1.68, regardless of which Type (“cheese”, “bacon cheese”, etc) you choose.
It should be this way. Cheese is cheese; an extra patty is an extra patty. But I’ve spent a lot of time analyzing and deconstructing menus, and rarely are they so mathematically sound. If you don’t believe me, just check out this Wendy’s menu!
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Appreciation Photography
Math Photo: Paraboloid in Nature
Resources Teaching Technology
Curvefitting With Geogebra
Inspired by some of my own forays into curvefitting with Geogebra (the squash at the right, or my Sine Waves on the Beach), I’ve created a student project built around the idea.
Finishing up a unit on trigonometry with graphs of trigonometric functions, it occurred to me that I have never really been comfortable teaching transformations. I think part of the reason is that it’s hard to get your hands dirty, play around, and develop intuition with this topic. This is where Geogebra comes in!
The project essentially works like this:
1) Students find an image, preferably one they capture themselves
2) Students paste the image into Geogebra
3) Students graph a relevant trigonometric function and play around with the various parameters (like period, amplitude, phase shift) until the curve fits the image
4) Students can use domain restrictions, and some of Geogebra’s aesthetic features, to polish everything up.
The first run of this project has produced some great results! You can see some sample student work here, and more on my Facebook page.
Related Posts
- Student Work — Curvefitting with Geogebra
- Using Mathematics to Create — Geogebra
- How Many Circles Pass Through Two Given Points?
Resources Technology
Library of Visual Manipulatives
This is another terrific resource: the Library of Visual Manipulatives from Utah State University.
There are one hundred or so simple, interactive programs available spanning Algebra, Geometry, Numbers and Operations, Measurement, and Data. And everything is sorted by appropriate age level. There are certainly a lot of interesting activities to navigate through here.
I’d say this is NSF money well-spent.