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GPS Alignment: Instructor Page
Week 1: Number - Intergers


McNugget Numbers? (Printable PDF)

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?
 

GPS

As seen in Problem Exploration

M6N1:  Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems.

a. Apply factors and multiples

b. Decompose numbers into their prime factorization (Fundamental Theorem of Arithmetic.)

c. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers.
 

a. You can look at multiples of each box #, ie. 6, 12, 18…, 9, 18, 27,…, 20, 40, 60,…

b. & c. 6 and 9 have a least common multiple of 18.  6 and 20 have a least common multiple of 60.  This could lead to a discussion of the common factors as well as 6 and 9 have a common factor of 3 because 6 = 3*2 and 9 = 3*3.  To find the least common multiple of 6 and 9, 18 is the third multiple of 6 and 18 is the second multiple of 9.  The 3 for the third multiple of 6 is what is left from the nine when the common factor of 3 is taken out and the two for the second multiple of 9 is left from the six when the common factor of 3 is taken out. 
 

M6A2. Students will consider relationships between varying quantities.

a. Analyze and describe patterns arising from mathematical rules, tables, and graphs.

By setting up the investigation in a spreadsheet, students can analyze the patterns that exist by adding boxes of 6, 9 or 20 McNuggets.