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

mailto:preigle@athensacademy.org