## Friday, November 1, 2013

### Code Crackers

The latest issue of Mathematics Teacher is of great use to me.  It was a focus issue on Beginning Algebra.  One article in particular caught my attention Cracking Codes & Launching Rockets, by Teo J. Paoletti.  If you are an Algebra Teacher, you will want to get your hands on a copy of this issue.

The article that I'm referring to suggests starting class by having a discussion about national security.  In particular my students and I had a discussion about a number code that could be used to launch nuclear bombs.  You would not believe the crazy things the students came up with.  Like tattooing a random baby with the code.  Wow.  Just wow.  Anyway with a lot of directing, I finally led them to the two-person rule.  In the article, Paoletti mentions that the two-person rule can be seen in movies like The Sum of All Fears, The Hunt for Red October, and War Games.  I have seen none of these movies, but would love to get my hands on a clip that mentions the two-person rule.

Just like Paoletti suggested in the article, we discussed why everyone in the room could have different ordered pairs, use any combination of two ordered pairs, and still end up with the same line.  Note, for the activity we did in class, only pairs of students had ordered pairs that would fit a particular line.

After our little discussion I showed the students this:

Nothing piques a student's interest better than a locked box.  "Are there prizes in there?" they want to know.  "I don't know.  It's a locked box." I reply.

In this particular class we were studying writing lines given two ordered pairs.  I gave each student an index card with an ordered pair on it.  I told them that they each had a partner in the room, but they don't know who it is and neither do I so don't ask.  In order to open the box, they needed to use two of their ordered pairs together to write the equation of a line.  The y-intercept of their line will open the box if that is indeed their partner.

#### Here are the ordered pairs that I gave the students and the matches:

(-11, 90) Matches with (14, 190)
(12, 125) Matches with (-8, 140)
(-9, 152) Matches with (-7, 148)
(12, 206) Matches with (11, 200)
(-9, 170) Matches with (-7, 162)
(10, 84) Matches with (-9, 179)
(13, 173) Matches with (18, 188)
(-10, 129) Matches with (16, 142)

The code is 134.

The students kept working with a different person until the resulting y-intercept unlocked the box.  It was great to see the students working on this process over and over without getting sick of it.

You don't need to have a locked box to do this activity, but if you can get your hands on one I highly recommend it.  It was great to have something physical for the students to try to open.  Especially when they were wrong, they just walked away and tried a new partner.

I enjoyed this lesson so much I wanted more.  Then I realized that this would work for solving equations with variables on both sides.  Each student would receive and Algebraic Expression.  They work with other people, setting their expressions equal to each other.  The value of x is the code for the box.  Yay!!

Here are the Algebraic Expressions:

9(3x - 1284) + 13236 Matches with -5(4x - 1943) + 3856
7(3x - 421) - 866 Matches with -4(2x + 843) + 7896
-3(4x - 2790) + 16707 Matches with 8(3x + 946) + 8401
7x + 15661 - 11x Matches with 3x - 5(9x - 5055)
3x + 2846 + 25x + 2005 Matches with 8(2x+891) + 3x
25(2x + 384) - 6285 Matches with 14x - 3(17x - 8442)
-9x + 8492 + 20x + 6085 Matches with -8x - 382 + 14x + 16224
4x - (9x - 15072) Matches with 9(3x + 1759) - 35x

The code is 253.

#### Issues:

What if the first person a student works with is their partner and they open the box?  What do they do for the rest of the class?  I will need to develop a part-two to this activity that is just as engaging if not more.

One student allows the other person to do all the work.  I think next time, each student will have to write down the work for each partner and hand it in.  Bummer, I hate more paperwork.  Please tell me you have a better idea.

#### Tips:

Label each index card with a letter randomly and write down the matches somewhere.  This way you can easily know which cards are matches.

If there is an odd number of students, you can play along too.  My first partner is always a student who is struggling.

If you have more than 16 students, break the class into two groups make duplicates of all the index cards and let them know their partner is in that group.  If there are too many students to try to match with you may end up with no one finding their partner by the end of the class.