Marc Johns: Thinking About Parallelograms

While this print is no longer available in Marc John‘s shop, many other amazing pieces are. Like this one:


Khan Academy

If you haven’t heard about Khan Academy, then you probably aren’t in the field of education. There has been tremendous criticism of Khan Academy by educators because it ultimately just lectures to students and many educators – at least the ones I keep up with – prefer having students approach math in a different way. Math is often seen as something that you learn and then practice. With more practice, you’re supposed to – with the traditional thought behind mathematics education – get better at math but I don’t think the point of math is to be able to memorize and practice problems over and over until you’ve mastered the skill. Although this can be one way people learn math, I don’t think they’ll truly understand it this way. Many other teachers really like Khan Academy because it does the lecturing for them. The program does have its benefits as it does allow students to work and learn at their own pace. Unfortunately, I’ve witnessed teachers just have their entire class watch a lesson in lieu of them teaching it, then pass out a worksheet for them to practice this new concept that they have just “learned.” While I may not be its biggest fan, I know Khan Academy does help some students. So for those of you that may get some benefit from it, check it out. Here’s a sample of what the videos are like:

Minimalist Geometry/Art

Meet Tilman, an interactive and graphic designer in Germany, who has taken some time off from his usual work to create digital representations of geometrical shapes and properties. His tumblr presents a new piece each day and is worth checking out.

NASA Has Space Math

Here’s just a quick heads up on the awesomeness that is NASA. They have a page dedicated to math! My favorite are the “Problem Archives” where teachers can present real data, pictures, graphs, etc. from NASA to their students in an already lesson-friendly PDF. There’s nothing better than supplementing a textbook with this kind of stuff!

Space Math @ NASA

Just Cut, Fold, and Paste

So there are these things called “nets” in math. I actually didn’t even know what the term “net” was referring to until I started student teaching and the Geometry students starting asking me what it was. Their textbook was asking them to draw a net for a given 3D shape.

A net is a two-dimensional figure that can be folded into a three-dimensional object.


If you were to unfold a certain three-dimensional polyhedron, you could cut the shape at its edges and get pieces in which you could then lay flat. For example, take this pyramid:

Imagine it has a square bottom, it is made of paper, and you can hold it in your hand. Think about what it would look like if you unfolded it, if you could take the faces and lay them all flat.

This is probably the most common way to think about the above pyramid unfolded but there are more. Consider it a challenge to discover another.

Here are some additional shapes to think about:

You can also work the other way. Given a net, you could build the 3D shape. There are many print outs available online which include tabs on the nets to make it easier to glue or tape these shapes together. Here’s an example.

The cube has many different nets that all represent the cube. I’ve seen questions on standardized tests that tests an individual’s spacial skills by giving them different options and asking which is or isn’t a valid net.

For example: Which of the below nets will build a cube?

One group of professors and students took this idea a little further. They started building nets out of fabric and zippers, trying to see which nets they could construct that would use only one zipper to build the corresponding 3D object.

Check it out!

You can check out other math related art at the Bridges Math Art Galleries webpage.

Mathy FoxTrot

Since Borders is going out of business, I had to use a gift card I had so I purchased Bill Amend’s themed FoxTrot collection:

In general, this is a pretty amazing little collection. I highly recommend it to those that are especially fond of math, science, and/or computer programming. As you can see in the above photo, I took my new gift to myself outside and decided to share some particularly mathy gems in one of the least-tech ways possible, by taking pictures of them. Please excuse the quality, I just don’t have a scanner. Enjoy.

When Will I Ever Use This?

It’s the question that makes math teachers cringe: When will I ever use this?

It’s true that many of the exercises that teachers make students go through may never be used outside of math class. What I hope is that students see math as a different way of thinking about problems and how to solve those problems.

“There are people who say, ‘I’ll never need this math. These trig identities from 10th grade, or 11th grade.’ Or maybe you never learned them. Here’s the catch: Whether or not you ever again use the math that you learned in school, the act of having learned the math established a wiring in your brain that didn’t exist before, and it’s the wiring in your brain that makes you the problem solver.”

-Neil deGrasse Tyson

The Eyeballing Game

I came across this site a while ago and only now remembered it. It can be pretty addicting, both for mathy and non-mathy people alike. Enjoy!

Test your geometry skills by trying to eyeball a parallelogram,


angle bisector,

the center of a triangle,

the center of a circle,

a right angle,

and where three lines converge.

The Eyeballing Game