“The Purge” gets a 1047% Return on Investment

[Update: The data in the graph has been updated to fix an error.  The Purge earned “just” a 946% return on investment in week one.  Of course, that number has certainly grown well past 1000% since]

Alternate Title: Sometimes I Wish I Was an English Teacher

The talk in Hollywood this Monday is that this weekend The Purge took in $31.4M, winning the box office.  The Purge had a budget of only $3M and really only started marketing a short couple weeks prior, relying heavily on social media to create an intense buzz around the low-budget horror/thriller.  An original premise to the level rarely seen in Hollywood these days certainly helped:

There’s so much to talk about here!  Since this is a math blog, let’s start there.  The Purge had a 1047% return on investment in its first week in the box office alone.  That’s ridiculous.  It was filmed in 20 days.  There’s no investment on Earth that can rival it.  Here’s a table of the top 10 films in the box office this week that compares the films first week’s box office gross and their budgets.


10 top grossing films of the weekend of 6/7/13

Last year when we hit on stats in Algebra II, I went to box office numbers as interesting data sets.  This takes it to a whole other level.  How can we best visualize how unbelievably historic The Purge‘s opening weekend was?  Was it the best opening weekend ever, by our ROI metric?  Iron Man 3 earned $174M in its opening weekend; how does that compare to The Purge?

If you were in charge of Universal Studios, would you prefer to have invested $3M in The Purge or $200M in Iron Man?  Would knowing the latter is approaching $400M in gross box office revenue change your thoughts?

Of course, from a literary perspective, this data is also immensely interesting. The premise of The Purge is original and harkens back to the days of The Lottery.  Is it a sign that originality and a new idea still can win out over flash, CGI and star power?  As Dave Karger of Fandango says:

“Every once in a while a movie comes around that has a premise that just captures people. The Purge is one of these movies. The concept is so different. It makes people want to see the movie.”

Most reviews have lauded the concept before lamenting the execution, which is unfortunate.  I’ll probably wait for this one to hit the library shelves, but I certainly am more interested in it than I am Iron Man or Star Trek.


The Most Beautiful Math I Have Ever Seen


Click to bigify

There’s something that is just amazing about this graph.  I love it.  It’s perfectly, slightly asymmetrical.  It is deep and detailed and simply beautiful.  And my student made it which makes even more awesome.

For those of you unaware, this is a product of Sam Shah’s Families of Curves project that I shamelessly stole for my algebra II students.  This piece was created with the function:

famfun_1aThe parameter, k, varied on the interval [-7, 7] with steps of 0.25.  The window dimensions are approximately [-3.5, 3.5] in the x direction and [-120, 120] in the y direction.

I’m printing this out as a poster to hang in my room and will be giving the artist a print of their own.  I can’t wait to do this project again next year to add to what will become quite the mathematical art collection!

Tomorrow I’ll post a few of the other amazing pieces my students came up with!

Barbie Bungee and the POWER OF MATH

I’m riding my bike to school a lot in an effort to both save money on gasoline and enjoy the fact that I live just 3.5 miles from school.  The result of this, though, is that I have to be very careful about what I cram into my bag to bring to school.  Long story short: We did Barbie Bungee and not only did I leave my video camera at home, but I also happened to forget my phone.  Sigh.

However, thanks to the fact that we live in 2013 and a ridiculous number of my students have high definition cameras in their pockets, I was able to have a student email me this video, which I edited to slow down.  The video isn’t great, nor upright, but I think it hammers home a significant point:

Like, seriously, how cool is math?  A group modeled the number of rubber bands needed to maximize Barbie’s thrills (but not kills). They were given a height, used their model to predict how long their bungee cord needed to be and look at how amazingly close they got.  Go math.

Quick Note: Holy smokes this is post #99 for this blog.  I guess I need to figure out something special for the next one!

Paper Plate Unit Circles, Done Efficiently


I like the idea of doing paper plate unit circles and today was my third go at it.  However, in the past it had always been more of an exercise in using a protractor or compass than actually focusing on the unit circle and trig.  So today, I decided I would take the time and do the grunt work for the kids so they could focus on the math.

Step 0: Materials


Brads, scissors, a Paper-Mate flair fine point marker, the best Google Image search of a unit circle that is blank and has the lines drawn in, paper plates, a spare manilla folder

Step 1: Draw the Circles


Step 2: Mark off Anglesunitpaper3

This is the true genius of this method, if I may say so.  I simply cut down the unit circle I printed off so that it was slightly smaller than the circle on the paper plates and drew in the tick marks.  Perfect 30, 45, and 60 degree angles in a matter of seconds.

Step 3: Draw the Axes

The axes were drawn simply with a straight edge – I cut an easy-to-wield piece of the manilla folder to do so.  Piece of cake.

Step 4: Cut Some Terminal Rays

Just sliced some appropriate length pieces out of strips of the manilla folder. Then, I took two snipes at an end to create a point.


Step 5: Teach the Unit Circle, not Protractors/Hand-writing/Neatness

So. Much. Better. Than in the past.  We were able to construct (mathematically speaking here) the unit circle: review degrees to radians, use special right triangles to find the first quadrants, use symmetry and reason to fill in the rest.  Additionally, I still had a good 15 minutes to spare to do some exact value trig problems at the end of class (i.e. tan(30) ).  What has taken twice or three times as long in the past was done in about 25 minutes.

The process of creating 35 “ready-to-go” unit circles, took me 45 minutes. In the past, it would have taken each student about 25 minutes, on average, to do the same for their one paper plate using a protractor.  Much better use of time and we really got to get into the nuance of the unit circle and why it is so simple, elegant, and important.  Students finished it off by using the brad to connect their arrow and then filling in the angle measure (degrees and radians, of course) and the coordinates of the points on the circle.

unitpaper5Voila, here’s your unit circle.  Love it, cherish it, keep it forever and ever and post it in your dorm room freshmen year of college. You will thank me.

Exponent Properties, As Explained By Star Wars Characters

Knocks it out of the park, my student does:


Seriously, I am suspending my “over 100% is not a possible grade” rule of thumb.  This was all hand-illustrated and some of the color/sharpness did not survive the scanning/jpg-ifying process.  Plus, the cover page has been omitted to keep the student’s name off the Intertubes. I was totally blown away.

I like my timing of this project: Instead of having a test on the exponent properties, we’re doing a project since half of my class is missing this week to a yearly field trip.  However, despite how amazed I am by this student, I wonder: Can she use all these exponent rules?  On its face, this is an awesome alternative assessment, but am I really assessing my students aptitude with exponent properties?  (Clearly, there are mistakes in there, though more of the mismatching examples variety).  Right now I don’t really care – this is awesome, different, and there’s something to be said for holding students accountable to project specifications (see below) and deadlines in addition to cranking out math problems.  But I will let that thought/worry creep into our future assessments, just to make sure.

The project outline and rubric for those who are interested (note: heavily borrowed from an Internet source that I’m struggling to find at the moment. Update hopefully forthcoming):

Exponent Review Project

Integer Sequences and the Need for Proof

This post over at Mr. Honner on unstated assumptions reminded me to share a great visual that shows some sequences are not what they seem:


Of course, the pattern that jumps out is:

2, 4, 8, 16, 32, 64, …

Geometric Sequence!  Exponential function!  2^(n-1).  HOWEVA,


I have yet to bust this out in my classroom, but I envision it being my answer the question “Why do we need proofs?”  Without proof or a counterexample, it is awfully easy to assume that a pattern exists when it really doesn’t.  That’s why we need proof.  Without being able to logically show something is true or false, you can fall into the traps of assumption.

I think I like the idea of setting up students to fail here. Just give them the question and let them try to find the pattern. Of course, their assumption will be that they can find a pattern and I’m sure most would be satisfied that 2^n works with n=1, 2, 3, 4, so it must work with all n.  As Lee Corso would say, “Not so fast my friend.”


patterns5Thanks to commenter Graeme McRae for pointing out this sequence on OEIS (Online Encyclopedia of Integer Sequences).  The sequence can also be defined as the sum of the first five terms of the nth row of Pascal’s triangle:

Update #2

Andy Huynh notes that this sequence should be specified as the maximum number of regions created by putting n points on a circle and connecting them with chords.  As I mentioned in my comment, I think this observation again highlights the need to be able to prove something.  Andy notes that if you evenly space the points when n = 6 (create a regular hexagon), then you will end up with only 30 regions, not 31.  In fact, that’s what I did when I first did this problem which was shared at NCTM by Jen Szydlik.