Functioning Financials: A Virtual Business Project

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Functioning Financials: A Virtual Business Project

Grade 9Math2 days

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In "Functioning Financials: A Virtual Business Project", students in grade 9 apply mathematical functions to build and manage a virtual business, making strategic financial decisions. They model revenue, expenses, and profit using equations, tables, and graphs, and analyze the domain and range of these functions in a business context. Students will also solve for unknown variables to meet specific financial targets, enhancing their understanding of real-world business operations and the role of mathematics in strategic decision-making.

FunctionsFinancial ModelingVirtual BusinessRevenueExpensesProfitProblem-Solving

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we use mathematical functions to build and manage a successful virtual business, making strategic decisions about revenue, expenses, and profit?

Essential Questions

Supporting questions that break down major concepts.

How can mathematical functions be used to model real-world business operations?
What factors determine the domain and range of functions in a business context, such as revenue or expenses?
How can we use equations to solve for unknown variables in financial planning and decision-making?
How do different representations of functions (graphs, tables, equations) help us analyze business performance and make predictions?
How can the concept of a function help us understand the relationship between different financial variables, such as sales and profit?

Standards & Learning Goals

Learning Goals

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

Apply functions to model revenue, expenses, and profit in a virtual business.
Interpret function inputs and outputs in financial contexts.
Determine the domain and range of functions in business scenarios.
Use equations to solve for unknown variables in financial planning.
Analyze business performance using different function representations (graphs, tables, equations).

Teacher Specified

Primary

Given an input, determine the output from a graph, table, or equationReason: Directly assesses students' ability to interpret function outputs in business models.

Primary

Given an output, determine the input from a graph, table, or equationReason: Directly assesses students' ability to interpret function inputs in business models.

Primary

Determine whether the relationship between 2 variables is a function when represented in a graph or tableReason: Assesses understanding of fundamental function concepts in business contexts.

Primary

Given a function represented by a graph, table, or equation, determine the domain and range of the functionReason: Critical for understanding constraints and realistic values in business scenarios.

Primary

Given a linear equation, solve for the missing variableReason: Essential for financial calculations and projections.

Entry Events

Events that will be used to introduce the project to students

The Million Dollar Decision

Present students with a scenario: They've inherited a million dollars and must decide how to invest it. Different investment options are presented as functions (stocks, bonds, real estate), and students analyze their potential growth/loss using graphs and tables to make a pitch for where to invest their money.

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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 Builder

Students will start by defining the basics of their virtual business. They choose a business type, identify initial products/services, and forecast startup costs. This activity sets the stage for applying functions to model financial aspects.

Steps

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

1. Choose a business type (e.g., coffee shop, tech startup, clothing store).

2. Identify 2-3 initial products or services to offer.

3. Estimate startup costs (e.g., equipment, inventory, marketing).

4. Create a basic business plan outline including the business description, products/services, and startup cost estimates.

Final Product

What students will submit as the final product of the activityA business plan outline with a description of the business, products/services, and estimated startup costs.

Alignment

How this activity aligns with the learning objectives & standardsLays the groundwork for applying functions to model real-world business operations (Learning Goal 1).

Activity 2

Function Factory: Revenue Modeling

Students develop functions to model revenue based on sales volume. They create equations, tables, and graphs representing potential revenue scenarios.

Steps

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

1. Define a variable representing the number of units sold (e.g., x = number of coffees sold).

2. Determine a selling price per unit.

3. Create a linear equation to represent revenue as a function of units sold (Revenue = price per unit * x).

4. Generate a table showing revenue for different sales volumes (e.g., 10, 20, 30 units).

5. Graph the revenue function, labeling axes and key points.

Final Product

What students will submit as the final product of the activityA revenue model including a linear equation, a table of values, and a graph representing revenue as a function of sales volume.

Alignment

How this activity aligns with the learning objectives & standardsApplies functions to model revenue (Learning Goal 1); assesses ability to represent functions as equations, tables, and graphs (Standard A1).

Activity 3

Expense Tracker: Cost Function Creation

Students model expenses using functions, distinguishing between fixed and variable costs. They create equations, tables, and graphs to represent these expenses.

Steps

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

1. Identify fixed costs (e.g., rent, salaries) and variable costs (e.g., cost of goods sold per unit).

2. Define variables for fixed costs (FC) and variable costs per unit (VC).

3. Create a linear equation to represent total expenses as a function of units sold (Total Expenses = FC + VC * x).

4. Generate a table showing total expenses for different sales volumes.

5. Graph the expense function, labeling fixed costs, variable costs, and total costs.

Final Product

What students will submit as the final product of the activityAn expense model including a linear equation, a table of values, and a graph representing total expenses as a function of sales volume.

Alignment

How this activity aligns with the learning objectives & standardsApplies functions to model expenses (Learning Goal 1); assesses ability to represent functions as equations, tables, and graphs (Standard A1).

Activity 4

Profitability Predictor: Analyzing Revenue and Cost Functions

Students combine their revenue and expense functions to create a profit function. They analyze the domain and range of these functions in the context of their business.

Steps

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

1. Define the profit function as the difference between revenue and total expenses (Profit = Revenue - Total Expenses).

2. Graph the profit function, along with the revenue and expense functions, on the same coordinate plane.

3. Determine the break-even point (where Profit = 0) from the graph and/or by solving the equation.

4. Identify the domain and range of the revenue, expense, and profit functions in the context of the business (e.g., sales volume cannot be negative).

5. Write a paragraph explaining the business's profitability, break-even point, and the factors influencing profit.

Final Product

What students will submit as the final product of the activityA profit model including the profit function, a combined graph of revenue, expenses, and profit, the break-even point, and an analysis of the functions' domain and range.

Alignment

How this activity aligns with the learning objectives & standardsApplies functions to model profit (Learning Goal 1); assesses ability to determine domain and range (Standard A4) and interpret function inputs/outputs (Learning Goal 2).

Activity 5

Financial Solver: Variable Exploration

Students use their financial functions to solve for unknown variables, such as the sales volume needed to reach a specific profit target.

Steps

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

1. Choose a specific profit target (e.g., $10,000 profit).

2. Set the profit function equal to the target profit.

3. Solve the equation for the sales volume (x) needed to achieve the target profit.

4. Verify the solution by plugging the calculated sales volume back into the profit function.

5. Write a short report explaining the steps taken to solve for the sales volume and the implications of the solution for the business.

Final Product

What students will submit as the final product of the activityA report detailing the solution to finding the sales volume required to meet a profit target, including calculations and explanations.

Alignment

How this activity aligns with the learning objectives & standardsUses equations to solve for unknown variables in financial planning (Learning Goal 4); applies skills in solving linear equations (Standard A5).

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Functioning Financials Portfolio Rubric

Category 1

Business Plan Foundation

Assesses the clarity and completeness of the initial business plan outline, including the business description, products/services, and startup cost estimates.

Criterion 1

Business Description

Clarity and detail in the description of the virtual business.

Exemplary

4 Points

The business description is exceptionally clear, detailed, and engaging, providing a comprehensive understanding of the business's purpose and target market.

Proficient

3 Points

The business description is clear and provides a good understanding of the business's purpose and target market.

Developing

2 Points

The business description is somewhat vague or incomplete, lacking key details about the business's purpose or target market.

Beginning

1 Points

The business description is minimal and lacks clarity, failing to provide a basic understanding of the business.

Criterion 2

Products/Services

Relevance and feasibility of the chosen products/services.

Exemplary

4 Points

The chosen products/services are highly relevant to the business type, clearly defined, and demonstrate a strong understanding of market demand.

Proficient

3 Points

The chosen products/services are relevant to the business type and are adequately defined.

Developing

2 Points

The chosen products/services are loosely related to the business type or lack clear definition.

Beginning

1 Points

The chosen products/services are unrealistic or unrelated to the business type and are poorly defined.

Criterion 3

Startup Cost Estimates

Accuracy and justification of startup cost estimates.

Exemplary

4 Points

Startup cost estimates are highly accurate, thoroughly justified with detailed explanations, and demonstrate a strong understanding of business finances.

Proficient

3 Points

Startup cost estimates are reasonably accurate and adequately justified.

Developing

2 Points

Startup cost estimates are inaccurate or lack sufficient justification.

Beginning

1 Points

Startup cost estimates are wildly inaccurate or completely missing.

Category 2

Revenue Modeling

Evaluates the creation and representation of the revenue function, including the equation, table, and graph.

Criterion 1

Equation Accuracy

Correctness of the linear equation representing revenue.

Exemplary

4 Points

The revenue equation is perfectly accurate, clearly defined, and demonstrates a sophisticated understanding of the relationship between sales volume and revenue.

Proficient

3 Points

The revenue equation is accurate and clearly defined.

Developing

2 Points

The revenue equation contains minor errors or lacks clarity.

Beginning

1 Points

The revenue equation is fundamentally flawed or missing.

Criterion 2

Table Representation

Clarity and accuracy of the revenue table.

Exemplary

4 Points

The revenue table is exceptionally clear, accurate, and well-organized, providing a comprehensive representation of revenue at different sales volumes.

Proficient

3 Points

The revenue table is clear, accurate, and well-organized.

Developing

2 Points

The revenue table contains errors or is poorly organized.

Beginning

1 Points

The revenue table is incomplete, inaccurate, or missing.

Criterion 3

Graph Representation

Accuracy and clarity of the revenue graph.

Exemplary

4 Points

The revenue graph is perfectly accurate, clearly labeled, and effectively visualizes the relationship between sales volume and revenue.

Proficient

3 Points

The revenue graph is accurate and clearly labeled.

Developing

2 Points

The revenue graph contains errors or lacks clear labels.

Beginning

1 Points

The revenue graph is fundamentally flawed or missing.

Category 3

Expense Modeling

Evaluates the creation and representation of the expense function, including the equation, table, and graph.

Criterion 1

Equation Accuracy

Correctness of the linear equation representing total expenses.

Exemplary

4 Points

The expense equation is perfectly accurate, clearly defined, and demonstrates a sophisticated understanding of fixed and variable costs.

Proficient

3 Points

The expense equation is accurate and clearly defined.

Developing

2 Points

The expense equation contains minor errors or lacks clarity.

Beginning

1 Points

The expense equation is fundamentally flawed or missing.

Criterion 2

Table Representation

Clarity and accuracy of the expense table.

Exemplary

4 Points

The expense table is exceptionally clear, accurate, and well-organized, providing a comprehensive representation of total expenses at different sales volumes.

Proficient

3 Points

The expense table is clear, accurate, and well-organized.

Developing

2 Points

The expense table contains errors or is poorly organized.

Beginning

1 Points

The expense table is incomplete, inaccurate, or missing.

Criterion 3

Graph Representation

Accuracy and clarity of the expense graph.

Exemplary

4 Points

The expense graph is perfectly accurate, clearly labeled, and effectively visualizes the relationship between sales volume and total expenses, including fixed and variable costs.

Proficient

3 Points

The expense graph is accurate and clearly labeled.

Developing

2 Points

The expense graph contains errors or lacks clear labels.

Beginning

1 Points

The expense graph is fundamentally flawed or missing.

Category 4

Profitability Analysis

Assesses the creation and analysis of the profit function, including the combined graph, break-even point, and domain/range analysis.

Criterion 1

Profit Function

Correctness of the profit function.

Exemplary

4 Points

The profit function is perfectly accurate and clearly derived from the revenue and expense functions, demonstrating a sophisticated understanding of profitability.

Proficient

3 Points

The profit function is accurate and clearly derived from the revenue and expense functions.

Developing

2 Points

The profit function contains minor errors or lacks clarity in its derivation.

Beginning

1 Points

The profit function is fundamentally flawed or missing.

Criterion 2

Combined Graph

Clarity and accuracy of the combined graph of revenue, expenses, and profit.

Exemplary

4 Points

The combined graph is exceptionally clear, accurate, and well-labeled, effectively visualizing the relationships between revenue, expenses, and profit, and highlighting the break-even point.

Proficient

3 Points

The combined graph is clear, accurate, and well-labeled.

Developing

2 Points

The combined graph contains errors or lacks clear labels, making it difficult to interpret.

Beginning

1 Points

The combined graph is fundamentally flawed or missing.

Criterion 3

Break-Even Point

Accuracy in determining the break-even point.

Exemplary

4 Points

The break-even point is accurately determined and clearly explained, demonstrating a thorough understanding of its significance for the business.

Proficient

3 Points

The break-even point is accurately determined and adequately explained.

Developing

2 Points

The break-even point is inaccurately determined or lacks clear explanation.

Beginning

1 Points

The break-even point is not determined or is fundamentally flawed.

Criterion 4

Domain and Range Analysis

Correctness and relevance of the domain and range analysis.

Exemplary

4 Points

The domain and range analysis is exceptionally thorough and relevant, demonstrating a sophisticated understanding of the constraints and realistic values for revenue, expenses, and profit in the context of the business.

Proficient

3 Points

The domain and range analysis is accurate and relevant.

Developing

2 Points

The domain and range analysis contains inaccuracies or lacks relevance to the business context.

Beginning

1 Points

The domain and range analysis is incomplete, inaccurate, or missing.

Category 5

Financial Problem Solving

Evaluates the student's ability to solve for unknown variables to meet specific financial targets.

Criterion 1

Solution Accuracy

Correctness of the calculated sales volume needed to achieve the target profit.

Exemplary

4 Points

The calculated sales volume is perfectly accurate, and the solution process is clearly and logically explained, demonstrating a deep understanding of financial problem-solving.

Proficient

3 Points

The calculated sales volume is accurate, and the solution process is adequately explained.

Developing

2 Points

The calculated sales volume contains minor errors, or the solution process lacks clarity.

Beginning

1 Points

The calculated sales volume is fundamentally flawed or missing.

Criterion 2

Verification

Verification of the solution by plugging the calculated sales volume back into the profit function.

Exemplary

4 Points

The solution is thoroughly verified, and the verification process is clearly explained, demonstrating a commitment to accuracy and a deep understanding of the relationships between variables.

Proficient

3 Points

The solution is verified, and the verification process is adequately explained.

Developing

2 Points

The solution is verified, but the verification process lacks clarity.

Beginning

1 Points

The solution is not verified or the verification process is flawed.

Criterion 3

Report Clarity

Clarity and completeness of the report explaining the solution and its implications.

Exemplary

4 Points

The report is exceptionally clear, concise, and insightful, providing a comprehensive explanation of the solution and its implications for the business.

Proficient

3 Points

The report is clear, concise, and provides a good explanation of the solution and its implications.

Developing

2 Points

The report lacks clarity or completeness, making it difficult to understand the solution or its implications.

Beginning

1 Points

The report is minimal, confusing, or missing.

Reflection Prompts

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

Question 1

How did creating and managing a virtual business using mathematical functions enhance your understanding of real-world business operations?

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Question 2

What were the biggest challenges you faced when modeling revenue, expenses, and profit using functions, and how did you overcome them?

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Question 3

How did different representations of functions (graphs, tables, equations) help you analyze your business's performance and make predictions? Provide specific examples.

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Question 4

In what ways did determining the domain and range of functions in your business models help you understand the limitations and realistic values of your financial variables?

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Question 5

How has this project changed your perspective on the role of mathematics in making strategic business decisions?

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