How Much does it Cost Project

Michigan Grade Level Content Expectations
A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations.
A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations.
A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations and linear inequalities.

ISTE NETS Performance Indicators
Creativity and Innovation
Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
Research and Information Fluency
Students apply digital tools to gather, evaluate, and use information.
Critical Thinking, Problem Solving, and Decision Making
Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

Student Learning
Students will graph linear and nonlinear relationships based on real-world problems and will analyze double-line graphs to find specific information.
Students will represent unknown, changeable values with variables.
Students will generate algebraic equations that model a given situation.

Performance Task
Overview
Students will choose a venue that has more than one admission scheme. They will analyze the admission costs by using a table, a graph, and by creating an equation that describes the mathematical relationships accurately. Students will summarize the results of their research and give advice to consumers. Students will then present their project in a wiki format that includes all elements of their analysis and a TV commercial explaining the benefits of the pricing scheme they deem to be the best option.

Description
Students will be asked to choose a venue that is particularly relevant to them. The venue must have a variety of admission price schemes. The vast majority of venues will have an online explanation of these price schemes, so the information should be easily obtainable.
Essential Skills
Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.
Understand the use of variables in expressions such as “4x,” “x+2,” “2x-1,” and “solve for the variable,” and know how to represent expressions such as “twice the number” or “four more than the number” using variables.
Know the components and properties of the rectangular coordinate system.
Solve and graphically sketch problems involving two variables that exhibit direct and indirect variation.
Know how to find the graphic solution of systems of linear equations.



How Much Does It Cost?

Think about places that you like to go that charge an admission fee. Lots of times, the fee changes depending upon the situation!

It might cost $8.50 to go to a movie, but if you buy a block of 10 tickets ahead of time, the cost could go down to $7.00 per ticket.
It might cost $45 for a lift ticket, but if you buy a season’s pass for $400 and go skiing a lot of times, the cost per day could be a lot less.
Taking the Metro might cost $1.35 one way, but purchase a 5-trip ticket and the cost per ride could go down to $1.10.
If you go to the video store to rent a DVD, it might cost $4.00 per movie, but if you join Netflix, your monthly fee of $9.95 might make a DVD rental a lot less expensive.
Amusement parks almost always offer a number of different rates from single day tickets, to multi-day passes, to season passes with or without parking included.

For this assignment, you will use mathematics to analyze the cost of a situation of your choice.

Directions

1. You may work in a group of two to three.
2. You must choose a real-world situation where the price of admission or the price of purchasing a service is set according to a variety of price schemes (at least two).
3. You must use Microsoft Excel or another spreadsheet program to create a table that clearly compares two or more of the pricing schemes.
4. You must use Excel or another spreadsheet program to create a line graph that clearly compares two or more of the pricing schemes. Your graph must be correctly titled and labeled.
5. You must create an algebraic equation, with defined variables that accurately describes each of the pricing schemes. You must evaluate your equations for at least two values of the variables.
6. You must write a paragraph that analyzes the pricing schemes and explains the cost-effectiveness of each in a grammatically correct format that can be easily understood by anyone who reads it.
7. After your analysis is complete, use Flip video camera to record a TV commercial for the place you have investigated, highlighting the pricing schemes and advertising the scheme you and your group decides is the best deal. Your commercial must include mathematical rationale for the claims you make and be properly edited and put together. Once complete, you must embed your commercial in your wiki page.
8. You must present all elements of this project: the table, the graph, the equation, the paragraph, and your TV commercial on a wiki page created by you (and your group). After your page is created, you must invite me to be a member of your page. Make the presentation attractive and functional by including the name and perhaps a few pictures of the venue that you are analyzing or any other “extras” you feel are appropriate.


Credit:
This lesson was adapted from a project by the International Center for Leadership in Education’s Gold Seal Lessons for Algebra (Find the Cost of Admission).