Intermath | Workshop Support
 Write-up

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 non-routine word problems using all strategies learned in previous grades.
b. Solve single and multi-step 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 non-routine word problems using strategies learned in previous grades.
b.  Solves single and multi-step 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 non-routine word problems using strategies learned in previous grades.
b.  Solves single and multi-step 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 \$ total-4 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
mailto:prj1@aol.com

Link(s) to resources, references, lesson plans, and/or other materials