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.


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.


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.


  1. I glanced at that article but missed the great ideas! Thanks for sharing. Now I just need to watch for the best time to use a locked box practice with my Algebra 2 students. I bet when we are solving quadratics I could make this work!

  2. What a great idea!!!!! And this is the perfect time for me to try this particular example. Now you have me searching for a locked box because I definitely could see that having it there in the room with the wonder of what's in there helping to motivate them to find the correct code. Thanks!

  3. I am a math teacher from russia, and i am reading your blog. Sorry for my english writing. I know it is not great. Thank you for this wonderful idea. I had a lessons i like very much based on this. My students are about 13 and they are rather advanced in math. I had no locked box and i hated the idea that they have to ask me if their result is correct. So i divided class

    I am a math teacher from Russia, and I am reading your blog. Sorry for my English writing. I know it is not great. Thank you for this wonderful idea. I had the lessons, I like very much based on this. My students are about 13 and they are rather advanced in math. I had no locked box and i hated the idea that they have to ask me if their result is correct. So i divided the class into two teams of 12 persons each and gave the team 12 cards with coordinates. Then i told them that they have to find correct pairs, for the y-intercepts of their lines were the same. It was very interesting for me looking their work. They were arguing for about ten minutes, then somebody began individual work, somebody just was distracted because there was not fast result. Sometimes they cooperated but then distracted again. There remained groups of about 4-5 persons in every team, who worked together, but they did not find anything in 40 minutes.

    So i have told them, that we will continue at the next lesson two days later. Nobody have done it at home. At the next lesson we have a 10-15 minute discussion about how did it feel last time. Did anybody have any plan for team work? It occurred that a few of students calculated the number of pairs they had to examine. Somebody showed the sketch of points at coordinate plane made at home. Then we discussed the team’s strategy: how the calculations could be distributed for team members and the teams began their work. Now they had found the code in 10-15 minutes. All this was very exciting now. Everybody was involved. There was some arguing about authority, though: who will be assigning the calculations to group members and collect the results.
    Then we discussed a data mining, and how the computer programs fish out useful information out of unordered data.
    I believe this was a very useful experience for my students and not in the math only. Thank you for your blog and your ideas once more.