Clowns and Graphing Rational Functions

I thought I had heard every silly mnemonic device for remembering mathematical formulas, but I recently heard a new one: the clowns BOBO, BOTU, and BETC for remembering how to graph rational functions.

  • BOB0: bigger (exponent) on bottom, x = 0
  • BOTU: bigger on top, undefined
  • BETC: bottom equals top eponent, coefficients (i.e., the ratio of coefficients)

Which naturally leads to this pearl of wisdom:

Impossible Cylinder

I didn’t believe this counterintuitive trick until I tried it myself… the instructions can be found at…/horizons/RichesonImpossibleCylinder.pdf

How to Draw with Math

Scientific American had a nice guest article about the intersection of math and art.


UCLA mathematicians bring ocean to life for Disney’s ‘Moana’

From the UCLA news service:

UCLA mathematicians bring ocean to life for Disney’s ‘Moana’

From the second paragraph:

“In general, the animators and artists at the studios want as little to do with mathematics and physics as possible, but the demands for realism in animated movies are so high,” [UCLA mathematician Joseph] Teran said. “Things are going to look fake if you don’t at least start with the correct physics and mathematics for many materials, such as water and snow. If the physics and mathematics are not simulated accurately, it will be very glaring that something is wrong with the animation of the material.”

I recommend the whole article.

Not Real


Five Simple Math Problems No One Can Solve

From Popular Mechanics: 5 Simple Math Problems No One Can Solve. The list:

  1. The Collatz conjecture.
  2. The moving sofa problem.
  3. The perfect cuboid problem.
  4. The inscribed square problem.
  5. The happy ending problem.

Venn diagram


A nice article on recent progress on solving the twin prime conjecture

The twin prime conjecture (see here, here and here for more information) asserts that there are infinitely many primes that have a difference of 2. For example:

3 and 5 are twin primes;

5 and 7 are twin primes;

11 and 13 are twin primes;

17 and 19 are twin primes;

29 and 31 are twin primes; etc.

While most mathematicians believe the twin prime conjecture is correct, an explicit proof has not been found. Indeed, this has been one of the most popular unsolved problems in mathematics — not necessarily because it’s important, but for the curiosity that a conjecture so simply stated has eluded conquest by the world’s best mathematicians.

Still, research continues, and some major progress has been made in the past few years. (I like sharing this story with my students to convince them that not everything that can be known about mathematics has been figure out yet — a misconception encouraged by the structure of the secondary curriculum — and that research continues to this day.) Specifically, it was recently shown that, for some integer N that is less than 70 million, there are infinitely many pairs of primes that differ by N.

For more on recent progress:







Volume of a Pyramid

Three blank sheets of paper: 5 cents.

Printer ink: more expensive per ounce than fine perfume.

15 small pieces of Scotch tape: 2 cents.

Visually demonstrating that the volume of a pyramid is one-third the product of the height and the area of the base: Priceless.

Engaging students: Defining intersection

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Tramashika DeWalt. Her topic, from Geometry: defining intersection.

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How could you as a teacher create an activity or project that involves your topic?


I would create a Kahoot to define intersection for my students. I would begin with the basic definition, which is, where lines cross over, meet, or have a common point (Unknown, Math is Fun, 2016). Thereafter, I would display pictures that visually portray intersection and that do not portray intersection. Within the same Kahoot, I would provide the students with the more advanced definition of intersection, intersection sets, “The intersection of two sets A and B is the set of elements common to both A and B” (Unknown, Math is Fun, 2016) according to Like before, I would follow the definition up with pictures for the students to determine if the set intersects or not. After the Kahoot, I would have the students to get into groups of 4, with a large piece of paper, to come up with intersections from their daily life. Finally, the groups would display their findings and we will discuss the results as a class.

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How can this topic be used in your students’ future courses in mathematics or science?


This topic can and will be used in my students’ future math courses. As I mentioned above, the basic definition of intersection will be extended to intersecting sets. In set intersection, the student will have to determine what elements each set has in common (that intersect) in order to determine where the sets intersect. The student will also have to know that the elements that are not common for both sets are not included in the intersection of the two sets. Intersection is used throughout math, so students can encounter it in high school, calculus, functions and modeling, real analysis, abstract algebra, etc. Not only will my students’ encounter intersection in future math courses, but they will also encounter intersections in life. For instance, when they are at a stop light (intersection), at a four-way stop sign (intersection), or even walking around UNT (students’ paths and sidewalks intersect all the time here).

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How can technology be used to effectively engage students with this topic? Note: It’s not enough to say “such-and-such is a great website”; you need to explain in some detail why it’s a great website.


As mentioned above, I would create a Kahoot, on, to effectively engage my students with technology to define and solidify the definition of intersection. I would layout my Kahoot by starting with the definition of intersection. Then I would have a variety of picture that would either display a form of intersection, or that would not display a form of intersection. Kahoot is awesome because it allows students to use their cell phone, iPad, or tablet to respond to questions created by the teacher. I feel the Kahoot will be very engaging because it allows the student time to play on their phone (so that the teacher doesn’t have to confiscate them for inappropriate use), listen to cool background music as they solve their problems, and learning about the particular topic at hand, all while having fun.  Now Kahoot even has a podium at the end of the Kahoot that displays the top three point earners.




Kahootit! (n.d.). Retrieved from Kahoot!:

Unknown. (2016). Math is Fun. Retrieved from Math is Fun:

Unknown. (2016). Math is Fun. Retrieved from Math is Fun: