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Candy Corn Colonels

Candy Corn Colonels

Author: Danny Whittaker
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Tutorial

Overview

The goal of this lesson is to introduce students to the concept of exponential and logarithmic functions.

I paused the video partway through to get them thinking a bit:

Pause 1:  "You know what we do with triangles" evil laugh

Pause 2:  After iteration 4.

Ask for questions they may have at this point.  They will likely be asking how many is she going to use?, what is the pattern?, etc.

Emphasize that she is going to ask 3 questions in the rest of the video for them to answer.  Her questions are:

1. If I used 6 bags, can you write an expression for how many I will need for the next iteration?

2. How many kernels did I use?

3. If I had $100 in pennies how big could I make this out of pennies?  (I asked for how many iterations we could do)

I added in the question (at the prompting of one of my students)

4. How many negative space triangles are there?  (The sections that don't contain candy corns.)

Candy Corn Colonels

Fun with candy corns!

Source: Created by Vi Hart http://www.youtube.com/watch?v=z8ZWlUamNPI

Conclusion

Students had about a period and a half to work.  At the end we discussed in groups and got these answers:

 

1.  18 bags (I emphasized each iteration as recreating the whole structure instead of just adding in the extra that would be needed.)

   a.    B subscript n equals 3 B subscript n minus 1 end subscript

2.   729 colonels

   a.    c subscript n equals 3 to the power of n minus 1 end exponent

3.   9 iterations  (and part of the 10th iteration)
   a.    3 to the power of 9 minus 1 end exponent less than 10000 less than 3 to the power of 10 minus 1 end exponent

4.    364 Negative Space triangles, two possibilities for equations


   a.    N subscript n equals 3 N subscript n minus 1 end subscript plus 1


   b.    N subscript n equals N subscript n minus 1 end subscript plus 3 to the power of n minus 2 end exponent