POW #12

POW #12 - Eyeballing Game Link
Complete seven estimates with an average score below 2.75.  Submit a screenshot to ejohnson@fessenden.org and also post to your mathematics folder.

Great article about nothing!

Well, about "zero".  Read it and discuss with me.  Link.

The Prisoner's Dilemma

I love teaching on the day before a break.  The boys are loud, enthusiastic and happy to be in class with the knowledge that we won't have a quiz or any graded assignment.  We are almost always missing a few boys due to travel plans but that doesn't stop us from exploring something interesting. I use these days to investigate a concept that is tangential to our curriculum and won't further our curriculum to the detriment of the boys that can't be there.

The day before Thanksgiving is the first of these opportunities during the year and last week we explored a favorite topic of mine, Game Theory.  We do this through the exploration of the Prisoner's Dilemma.  I start by telling a story of how two boys in the class were "busted" for a crime and are now awaiting sentencing in separate cells in the local jail.  However, they can reduce their sentence if they "rat" out their accomplice on a second crime.  The boys love the fiction and we discuss their options and possible consequences.  We quantify decisions by optimizing results through use of the Nash Equilibrium (made famous in the Oscar Award winning movie, A Beautiful Mind with Russell Crowe).

We then move on to a British game show based on the Prisoner's Dilemma called, Golden Balls.  We watch a few videos that have great opportunities to discuss first impressions, psychology, greed and the Nash Equilibrium.  The outcomes are often quite surprising for such a simple game.

And then we get to the best part of the day.  We play the game of Split or Steal at the front of the classroom with two boys going head to head at a time.  I place a bag of candy between the two of them and give them each two discs (one says split and the other says steal).  The goal (I think??) is for them both to put the split disc as then they split the candy evenly.  If one puts split and the other puts steal, then the one that puts steal gets all the candy.  If they both put steal, neither gets the candy.  The drama builds when the boys try to persuade each other to put the split disc and culminates with the reveal of their choices.

I preface our investigation carefully with the boys so that it is understood that we are just dealing with a bag of candy and the consequences are not so great.  That said, feelings are sometime hurt when someone chooses to steal the bag.  In my five years of playing this game though, the boys report that it was of the best days of the year.

For those that are curious, the Nash Equilibrium says to always steal!  This is because when you choose steal you will either win 100% or 0%, meaning an average of 50%.  If you always pick split, then you will win 50% or 0, meaning an average of 25%.

A video of one of our Split/Steal duels... Link.

POW #11

Submissions are due by the end of the day on Monday, December 5th.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek11.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.  LET ME KNOW IF YOU PUT IT IN YOUR FOLDER!

Algebra 1 - POW11
Geometry - POW11

POW #10

Submissions are due by the end of the day on Monday, November 21st.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek10.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.  LET ME KNOW IF YOU PUT IT IN YOUR FOLDER!

Algebra 1 - POW10
Geometry - POW10

POW #9

Submissions are due by the end of the day on Monday, November 14th.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek9.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.  LET ME KNOW IF YOU PUT IT IN YOUR FOLDER!

Algebra 1 - POW9
Geometry - POW9

POW #8

Submissions are due by the end of the day on Monday, November 7th.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek8.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.  LET ME KNOW IF YOU PUT IT IN YOUR FOLDER!

Algebra 1 - POW8
Geometry - POW8

POW #7

Submissions are due by the end of the day on Monday, October 31st.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek7.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.

Algebra 1 - POW7
Geometry - POW7

Dr. Tanton Spreading the Joy of Math

Dr. Tanton wrote our Geometry curriculum and we use many of his techniques in Algebra, too.  He was my professor at Northeastern University and also taught for many years as St. Mark's School in Southborough.  Here is a link to a current story on his work in Ireland (link).  Also check out the Maths Quiz on the same page.

POW Week #6

Submissions are due by the end of the day on Monday, October 24th.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek6.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.

Algebra 1 - POW6
Geometry - POW6

POWs Week #5

Submissions are due by the end of the day on Monday, October 17th.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek5.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.

Algebra 1 - POW5
Geometry - POW5

The New Scanstand

Math work requires time, patience and typically paper and pencil.  It is a challenge to complete homework well on a computer as there are too many symbols, lines, fractions, radicals and too much formatting to be efficient.  However, computers do bring much to the table when it comes to archiving and sharing.  For this reason, I have my students scan their best work (projects, tests/quizzes and larger assignments) into their Google Drive / Mathematics folder.  This allows for easy access for me, the boys and their parents from anywhere and anytime.  The major issue with this idea was that scanning was difficult for students as there wasn't a public scanner and not all students have Scan Apps or a cellphone.  To solve this problem,  I built a "scanstand" so that they can upload their work easily.  This final version was developed after five iterations (prototypes).  The benefits of this model is that the iPod is on the Fessenden network, is secured with tamper proof screws and is simple to use.  The stand also works as a wireless document camera and as a music source.  The boys are opening my eyes to more contemporary music!

POWs Week 4

Submissions are due by the end of the day on Friday, October 7th.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek4.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.

Algebra 1 - POW4
Geometry - POW4

POWs Week 3

Submissions are due by the end of the day on Friday, September 30th.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek2.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.

Algebra 1 - POW3
Geometry - POW3

Science Friday Math Stories

Check 'em out. Link.

Mr. J, can I make one of your puzzles?

Why, yes you can!  You just need a piece of plywood (1/8"x12"x12"), 15 minutes and access to the Ciongoli Center for Innovation.  I have saved my files in a folder in "documents" named "Johnson".

To make a puzzle, you need to print two different files.  A greenblue file and a red file.

The greenblue file is to raster (engrave) the wood with words and designs.  It also includes a vector pass which outlines letters for emphasis and draws simple lines quickly on the surface of the wood.   Note: rastering takes a long time and is impractical for drawing thin lines - much better to go with fast speed vectoring!

The red file does the real cutting (through the wood) and is typically done after the greenblue print.

The settings I use for the two prints:

greenblue:  Raster 100% speed / 100% power    
                    Vector  100% speed / 100% power

red: Raster Off  
        Vector 10% speed / 100% power

After printing, my puzzles usually require gluing.  Make sure you take your time and are as precise as possible with alignment as a small mistake will send your puzzle to the trash heap.

Hope you give it a try!  Let me know how it goes.
Ed

Stewart Coffin, the geometry genius behind the puzzles

He designed most of the puzzles I find the most clever and counterintuitive.  See this article about the life and work of Stewart Coffin Link.  Also, Indiana University has an extensive puzzle collection (I must go!) and a database of 496 Stewart Coffin puzzles can be found here.

POW - Week 2

Submissions are due by the end of the day on Friday, September 23rd.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek2.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.

Algebra Week 2 - Link

Geometry Week 2 - Link

Fluency leads to Understanding

Great piece on how mathematical fluency relates to skills, procedures and conceptual understanding.  It's no surprise that it requires practice and chunking to develop proficiency.  Link.

A fun little puzzle from youcubed.

What is the fewest number of squares that you can draw within an 11x13 rectangle.  I found fewer than 8...

The first Problems of the Week!  Submissions are due by the morning of Friday, September 16th.  Make sure to scan your work and put it in your Mathematics/POW folder with a name of LASTNAMEWeek1.  See me with questions.  You may work with a partner but make sure you note that on your submission and you both must submit a copy for credit.

Algebra - Week 1
Geometry - Week 1

As you finish up your summer vacation, take some time to read the two articles below.  The first is a bit scary (or maybe disturbing is the right word).  The second discusses a major motion picture released in April called, The Man Who Knew Infinity.  I have not seen the film yet but the article reminded me of the interesting biography of this math prodigy.  The link is from a blogger who writes a review of the film but also makes many astute conclusions about what makes mathematics important.

Why No One Wanted A&W's Third-Pound Burger

The Man Who Knew Infinity (also read this link if you want additional details).