**Goals/Objectives: **We want to solve the following 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**

Peggy Reigle and I decided to calculate all combinations
of 6, 9, and 20 up to the LCM of 180 and see answer the questions posed
above.

**Procedures/Methods:**

1. Peggy Reigle and I created an Excel spreadsheet.

2. We set up the first worksheet to show combinations
of 6 and 9.

3. We then created another worksheet to add
the third combination as if there were 0 boxes of 20.

4. We created a third, fourth, and fifth worksheet
with 1 box of 20, 2 boxes of 20 and 3 boxes of 20.

5. Finally, we created a worksheet with all
possible numbers, leaving a blank when we could not get a combination of
the 3 variables.

**Conclusion (analysis using technology and understanding why it works)**

a. Could you purchase exactly 17 McNuggets? no

b. How would you purchase exactly 53 McNuggets? yes (1-20, 1-9, 4-6 or 1-20, 3-9, 1-6)

c. What is the largest number for which it is impossible to purchase

exactly that number of McNuggets? 43 (by process
of elimination up to 180)

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? to be continued
**Comments and reactions, what did I learn**

Working with 3-dimensional combinations is difficult
with a 2-D spreadsheet.

**Extensions (what other questions can I ask)**
** **To be continued

**Here's my link to the **McNuggets Excel
worksheet