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Created byWilliam Baker

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Amusement Park Designer: Linear Equations

Grade 8Math1 days

In this project, 8th-grade students design an amusement park, applying linear equations to model the cost and revenue of rides. They determine optimal ticket prices and operating costs to maximize profit, representing financial relationships through graphs and equations. The project culminates in a financial report detailing the park's profitability and strategies for improvement, blending mathematical modeling with creative design.

Linear EquationsFinancial ModelingProfit MaximizationAmusement Park DesignCost AnalysisRevenue ProjectionBreak-Even Point

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we design an amusement park that maximizes profit, using linear equations to model the relationship between ticket prices, operating costs, and revenue for each ride?

Essential Questions

Supporting questions that break down major concepts.

How can linear equations model real-world financial situations?
How do different ticket prices and operating costs affect the profitability of a ride?
What strategies can be used to maximize profit in an amusement park?
How can we represent the relationship between cost, revenue, and profit using graphs and equations?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:

Apply linear equations to model the cost and revenue of rides.
Design an amusement park layout incorporating mathematical models.
Maximize profit by adjusting ticket prices and operating costs using linear equations.
Represent financial relationships using graphs and equations.

Entry Events

Events that will be used to introduce the project to students

The 'Too-Safe' Amusement Park

Students watch a tongue-in-cheek news report about an amusement park shut down for being too boring and safe. They are then challenged to redesign the park, making it thrilling while staying within a budget modeled by linear equations.

Amusement Park Pitch Tank

Students watch short video pitches of outlandish, failed amusement park ideas. They then brainstorm their own ride ideas and must 'pitch' them, using linear equations to demonstrate the ride's financial viability to a panel of judges.

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Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.

Activity 1

Blueprint Bonanza: Mapping Your Park

Students will begin by designing the layout of their amusement park. This involves sketching a map and planning the placement of different rides.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Sketch a preliminary layout of the amusement park, including different zones (e.g., thrill rides, family zone, food court).

2. Decide on the number and types of rides in each zone.

3. Label each ride with a placeholder name and its anticipated category (high, medium, or low cost).

Final Product

What students will submit as the final product of the activityA detailed map of the amusement park layout with labeled zones and ride placeholders.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Design an amusement park layout incorporating mathematical models.

Activity 2

Equation Expedition: Ride Cost Modeling

Students will create linear equations to model the cost of operating each ride. This includes fixed costs (maintenance, insurance) and variable costs (electricity, staffing).

Steps

Here is some basic scaffolding to help students complete the activity.

1. Research typical operating costs for different types of amusement park rides (e.g., roller coaster, Ferris wheel).

2. Identify the fixed and variable costs associated with each ride.

3. Write a linear equation in the form y = mx + b to represent the total cost of operating each ride, where x is the number of riders, m is the variable cost per rider, and b is the fixed cost.

Final Product

What students will submit as the final product of the activityA set of linear equations modeling the cost of operating each ride in the amusement park.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Apply linear equations to model the cost and revenue of rides.

Activity 3

Revenue River: Ticket Price Strategies

Students will develop strategies for setting ticket prices to maximize revenue for each ride. This involves considering the cost of the ride, the target audience, and the competition.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Determine the target audience for each ride (e.g., families, thrill-seekers).

2. Research ticket prices for similar rides at other amusement parks.

3. Write a linear equation in the form y = px, where y is the total revenue, p is the ticket price per rider, and x is the number of riders.

Final Product

What students will submit as the final product of the activityA detailed pricing strategy for each ride, including the rationale behind the chosen price.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Maximize profit by adjusting ticket prices and operating costs using linear equations.

Activity 4

Profit Peak: Graphing for Success

Students will graph the cost and revenue equations for each ride to visually represent the profit potential. They will analyze the graphs to identify the break-even point and the optimal number of riders to maximize profit.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Graph the cost and revenue equations for each ride on the same coordinate plane.

2. Identify the break-even point (where cost equals revenue) for each ride.

3. Analyze the graphs to determine the number of riders needed to achieve a desired profit level.

Final Product

What students will submit as the final product of the activityA set of graphs showing the cost and revenue curves for each ride, with annotations indicating the break-even point and optimal rider volume.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Represent financial relationships using graphs and equations.

Activity 5

Amusement Park Financial Report

Students compile all their data and analysis into a comprehensive financial report for their amusement park.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Compile all cost and revenue equations, ticket prices, and profit analysis for each ride.

2. Write a summary of the overall financial performance of the amusement park.

3. Suggest strategies for improving profitability based on the mathematical models.

Final Product

What students will submit as the final product of the activityA detailed financial report outlining the profitability of the amusement park and strategies for improvement.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goals: Apply linear equations to model the cost and revenue of rides; Maximize profit by adjusting ticket prices and operating costs using linear equations; Represent financial relationships using graphs and equations.

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Amusement Park Financial Report Rubric

Category 1

Mathematical Modeling

Accuracy and appropriateness of linear equations used to model cost and revenue.

Criterion 1

Cost Equations

Correctness of linear equations representing the cost of operating each ride, including fixed and variable costs.

Exemplary

4 Points

All cost equations are accurate and thoroughly represent fixed and variable costs with clear justification.

Proficient

3 Points

Most cost equations are accurate and represent fixed and variable costs effectively.

Developing

2 Points

Some cost equations are inaccurate or incomplete in representing fixed and variable costs.

Beginning

1 Points

Cost equations are largely inaccurate or missing, with minimal representation of fixed and variable costs.

Criterion 2

Revenue Equations

Correctness of linear equations representing the revenue generated by each ride, based on ticket prices.

Exemplary

4 Points

All revenue equations are accurate and clearly linked to ticket prices and rider volume.

Proficient

3 Points

Most revenue equations are accurate and linked to ticket prices and rider volume effectively.

Developing

2 Points

Some revenue equations are inaccurate or incomplete in representing ticket prices and rider volume.

Beginning

1 Points

Revenue equations are largely inaccurate or missing, with minimal representation of ticket prices and rider volume.

Category 2

Financial Analysis

Analysis of cost, revenue, and profit, including break-even points and optimal rider volume.

Criterion 1

Break-Even Analysis

Accuracy in determining the break-even point for each ride.

Exemplary

4 Points

Break-even points are accurately calculated and clearly explained, with a detailed interpretation of their significance.

Proficient

3 Points

Break-even points are mostly accurately calculated and explained.

Developing

2 Points

Break-even points are calculated with some inaccuracies or lack clear explanation.

Beginning

1 Points

Break-even points are largely inaccurate or missing.

Criterion 2

Profit Optimization

Strategies for maximizing profit based on the mathematical models.

Exemplary

4 Points

Strategies for profit maximization are well-reasoned, innovative, and clearly supported by the mathematical models.

Proficient

3 Points

Strategies for profit maximization are reasonable and supported by the mathematical models.

Developing

2 Points

Strategies for profit maximization are basic or not well-supported by the mathematical models.

Beginning

1 Points

Strategies for profit maximization are missing or unrealistic.

Category 3

Presentation and Communication

Clarity and organization of the financial report, including graphs and explanations.

Criterion 1

Data Presentation

Effectiveness of graphs and tables in presenting cost, revenue, and profit data.

Exemplary

4 Points

Graphs and tables are clear, accurate, and effectively communicate key financial information.

Proficient

3 Points

Graphs and tables are mostly clear and accurately present financial information.

Developing

2 Points

Graphs and tables are somewhat unclear or contain minor inaccuracies.

Beginning

1 Points

Graphs and tables are unclear, inaccurate, or missing.

Criterion 2

Report Clarity

Overall clarity and organization of the financial report.

Exemplary

4 Points

The financial report is well-organized, clearly written, and easy to understand, with a logical flow of information.

Proficient

3 Points

The financial report is organized and clearly written.

Developing

2 Points

The financial report is somewhat disorganized or unclear in places.

Beginning

1 Points

The financial report is disorganized, unclear, and difficult to understand.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning

Question 1

Looking back at your initial amusement park design, what is the biggest change you made to maximize profit and why?

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Question 2

Which learning goal do you feel you mastered the most during this project: Applying linear equations to model cost and revenue, designing the park layout, maximizing profit, or representing financial relationships using graphs and equations?

Multiple choice

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Options

Applying linear equations to model the cost and revenue of rides.

Designing an amusement park layout incorporating mathematical models.

Maximizing profit by adjusting ticket prices and operating costs using linear equations.

Representing financial relationships using graphs and equations.

Question 3

On a scale of 1 to 5, how well do you think linear equations can model real-world financial situations, with 1 being 'not at all' and 5 being 'very well'?

Scale

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Question 4

What was the most challenging aspect of using linear equations to model the financial aspects of your amusement park, and how did you overcome it?

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Question 5

If you could give one piece of advice to students starting this project next year, what would it be?

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