Title
Ski Resort
Problem Statement
A ski resort offers 2 package plans. Plan A gives one person 4 nights lodging
and 3 dinners for $326.00. Plan B gives one person five nights lodging and 4
dinners for $413.00. Assuming that the costs per night for lodging and dinner
are the same for both plans, how much does one dinner cost?
GPS Alignment
M6P. Process Skills
Students will apply mathematical concepts and skills in
the context of authentic problems and will understand concepts rather
than merely following the sequence of procedures. They will also use the
process standards as a way acquiring and using content knowledge.
M6P1. Using
appropriate technology, students will solve problems that arise in
mathematics and in other context.
a. Solve nonroutine word problems using all strategies learned in
previous grades.
b. Solve single and multistep routine word problems related to all
appropriate sixth grade math standards.
c. Determine the operation(s) needed to solve a problem.
d. Determine the most efficient way to solve a problem (mentally,
paper/pencil, or calculator).
M7P. Process Skills
Students will
apply mathematical concepts and skills in the context of authentic
problems and will understand concepts rather than merely following the
sequence of procedures. The student will use the process standards as a
way acquiring and using content knowledge.
M7P1. Using appropriate technology the student will solve problems
that arise in mathematics and in other context.
a. Solve nonroutine word problems using strategies learned in previous
grades.
b. Solves single and multistep routine word problems related to all
appropriate seventh grade math standards.
c. Determine the operation(s) needed to solve a problem.
d. Determine the most efficient way to solve a problem (mentally,
paper/pencil, or calculator).
M8P. Process Skills
Students will
apply mathematical concepts and skills in the context of authentic
problems and will understand concepts rather than merely following the
sequence of procedures. They will also use the process standards as a
way acquiring and using content knowledge.
M8P1. Using
appropriate technology the student will solve problems that arise in
mathematics and in other context.
a. Solve nonroutine word problems using strategies learned in previous
grades.
b. Solves single and multistep routine word problems related to all
appropriate eighth grade math standards.
c. Determine the operation(s) needed to solve a problem.
d. Determine the most efficient way to solve a problem (mentally,
paper/pencil, or calculator).
Problem setup
A ski resort has two deals. One deal
is 4 nights lodging and 3 dinners for $326.00. The other deal is 5 nights
lodging and 4 dinners for $413.00. Meals cost the same in both deals. How much
is a meal?
Plans to Solve/Investigate the
Problem
We used Excel to solve this problem.
One student realized that if we subtract 326 from 413, we get 87. This is the
most crucial fact in the problem because there is no specification as to how
much lodging or dinner costs. So the values could be endless. Since we know that
87 is the difference between the two deals, we know that one nights lodging and
one meal costs $87.00. Therefore, the values we put in Excel must equal 87. .
Investigation/Exploration of the
Problem
The columns we labeled in Excel were
lodging $, dinner $, total 4 nights and 3 dinners, total 5 nights lodging and 4
dinners. The equations that were put into Excel were the following = 4*A2+3*B2
for 4 nights lodging and =5*A2+B2 for 5 nights lodging. This is the Excel
spreadsheet that resulted:
lodging $ 
dinner $ 
total4 nights + 3 dinners 
total 5 nights + 4 dinners 
50 
37 
311 
398 
55 
32 
316 
403 
60 
27 
321 
408 
65 
22 
326 
413 
70 
17 
331 
418 
75 
12 
336 
423 
The only solution that worked was
that lodging is $65.00 and dinner is $22.00.
Extensions of the Problem
There were no extensions to this
problem.
Author & Contact
Pam Joseph
eaglepjo@aol.com
Link(s) to resources, references, lesson plans, and/or other
materials
Link 1
Link 2
