Lesson Plan 1 McNugget's Problem

Name:
Peggy Reigle

Goals/Objectives:  To solve the McNugget's problem
McDonald's sells Chicken McNuggets in boxes of 6, 9, or 20. Obviously
one could purchase exactly 15 McNuggets by buying a box of 6 and a box
of 9. Using only combinations of boxes of 6, 9, and/or 20 McNuggets,

a. Could you purchase exactly 17 McNuggets?

b. How would you purchase exactly 53 McNuggets?

c. What is the largest number for which it is impossible to purchase
exactly that number of McNuggets?

d. Let's say you could only buy the McNuggets in boxes of 7, 11, and 17.
What is the largest number for which it is impossible to purchase exactly
that number of McNuggets?

Conjecture/Hypothesis/Prediction
Mike Callinan and I thought we could create spreadsheets and list all the possible combinations of 6, 9 and 20.  We felt this would leave us with the numbers up to the LCM of 180 which would help us answer the three questions presented in the McNuggets problem.

Procedures/Materials
1) We created an Excel spreadsheet using the constants of 6, 9 and 20
2)  first, we created a spreadsheet with two constants:  6 and 9 and found the results with rows up to 8 and
columns down to 18 (the spreadsheet used a formula of  =\$A\$2*A4
3)  we then created a second spreadsheet with adding a +20 to the columns..the formula then became:  =\$A\$2*4+20
4)  after studying the spreadsheet, we tried to find all the numbers omitted up to the LCM of 6,9,20 (180).  We did  this by     listing all the numbers up to 180 and crossing out all the possible combinations that came up.
5)  we also used these numbers to try to find a pattern. ( we thought we had found patters of +1, then +1,+2, then +1, +2, +3), finally +3.  None of these panned out.

Conclusion (analysis using technology and understanding why it works)
a. Could you purchase exactly 17 McNuggets?
Answer:  No we could not purchase exactly 17 McNuggets

b. How would you purchase exactly 53 McNuggets?
Answer:  Yes, we could purchase one box of 20, 1 box of 9 and 4 boxes of 20
or:     one box of 20, 3 boxes of 9 and 1 box of 6

c. What is the largest number for which it is impossible to purchase
exactly that number of McNuggets?
Answer:  The largest number for which it is impossible to purchase exactly that number of McNuggets is 43.

Comments and reactions (what did I learn)
I learned that with working with Mike we could explore many possibilities to solve this problem.  I learned a better understanding of Excel and the difficulty of trying three numbers in an Excel spreadsheet.  I learned that I was thankful to have Mike for a partner :).

Extensions (what other questions can I ask or explore?)

NCTM Process Standards
Standard 8:

1.  describe, extend, analyze, and create a wide variety of patterns
2.  describe and represent relationships with tables, graphs, and rules
3. analyze functional relationships to explain how a change in one quantity results in a change in another
4.  use patterns and functions to represent and solve problems

Link to my McNuggets Excel worksheet

Author and contact:

Peggy Reigle