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Food Truck Formulas: Modeling a Mobile Business Plan
Grade 9Math7 days
★★★★★
5.0 (1 rating)FunctionsEntrepreneurshipMathematical ModelingDomain And RangeFinancial LiteracyAlgebraBusiness Planning
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Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we, as food truck entrepreneurs, use mathematical functions to design a sustainable business plan that predicts success and maximizes profit?Essential Questions
Supporting questions that break down major concepts.- How can we use function notation to represent the relationship between our menu prices, number of customers, and our total revenue?
- How do different representations (graphs, tables, and equations) help us communicate the financial health of our food truck to potential investors?
- How do the real-world constraints of our food truck (like storage capacity, prep time, or hours of operation) define the domain and range of our business functions?
- Why is it essential to determine if a business relationship is a function when making predictions about our food truck's future success?
- How do linear and quadratic functions model different aspects of our business, such as steady costs versus the optimization of profit?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Evaluate linear and quadratic functions using function notation to calculate projected food truck revenue and operational costs based on varying customer volume.
- Analyze multiple representations (equations, graphs, and tables) of business data to determine if financial relationships qualify as mathematical functions.
- Identify and interpret the domain and range of business-related functions, accounting for real-world constraints such as inventory limits, operating hours, and physical capacity.
- Construct linear and simple quadratic models to represent business scenarios, such as the relationship between price points and total profit.
- Communicate financial predictions and business sustainability to stakeholders by translating function-based data into verbal and visual business reports.
Common Core State Standards (Math)
HSF-IF.A.1
Primary
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).Reason: This is the foundational standard for the project, as students must determine if their business relationships (e.g., price vs. demand) represent functions to ensure predictable business outcomes.
HSF-IF.A.2
Primary
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Reason: Students will use f(x) notation to calculate revenue, costs, and profits based on specific inputs like 'number of tacos sold' or 'hours of operation.'
HSF-IF.B.5
Primary
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines, in a negative case, the domain would be the set of positive integers.Reason: Students must define the practical limits of their business, such as the maximum number of customers they can serve in a day (domain) and the resulting possible revenue (range).
HSA-CED.A.2
Secondary
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Reason: To build a business plan, students need to create the actual equations that model their food truck's financial performance and represent them visually on graphs for investors.
Common Core State Standards (Mathematical Practice)
CCSS.MATH.PRACTICE.MP4
Supporting
Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.Reason: This project-based learning experience is a direct application of mathematical modeling to a real-world entrepreneurial context.
Entry Events
Events that will be used to introduce the project to studentsThe Case of the Malfunctioning Menu
Students enter a classroom transformed into a chaotic 'Grand Opening' where a simulated Point-of-Sale (POS) system is malfunctioning. They are presented with receipts where the same input (Order #5) results in two different outputs (Tacos and Pizza), sparking a debate on why this 'glitch' makes it impossible to run a business and leading to the definition of a function.The Festival Financial Audit
A local food truck owner (via video or guest visit) presents a 'Crisis Map' showing their profit margins over a weekend festival, but the graph has gaps and impossible data points. Students must identify the 'Domain of Operation' (hours they can actually work) and the 'Range of Profit' (potential earnings) to help the owner decide if the festival is worth the registration fee.The Secret Ingredient Algorithm
Students receive a 'Secret Menu' coded in function notation, such as P(x) = 2x + 5, where x represents the number of toppings. They must use 'Input/Output' stations to build physical models of the food items, realizing that if they don't follow the notation precisely, their business costs will spiral out of control.Viral Trends & Surge Pricing Models
The class is challenged to optimize a 'Surge Pricing' model for a viral TikTok-famous food truck where the price increases quadratically as the line gets longer. Students analyze graphs of these price curves to determine the 'Sweet Spot'—the vertex where profit is maximized before the domain of customer patience is exceeded.📚
Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Activity 1
The Menu Reliability Audit
Before launching their food truck, students must ensure their 'Point of Sale' (POS) system is reliable. In this activity, students analyze different menu structures and ordering logs to determine if they qualify as mathematical functions. They will learn that for every unique input (Order Number/Item ID), there must be exactly one output (Price/Item Name). This establishes the foundational logic required to run a predictable business.Steps
Here is some basic scaffolding to help students complete the activity.1. Analyze four different sample 'Order Logs' from a malfunctioning POS system. Identify which logs show a single input resulting in multiple different outputs (e.g., Order #101 resulting in both a Taco and a Burger).
2. Define the 'Domain' as the set of possible Order IDs and the 'Range' as the set of Menu Items/Prices.
3. Create a mapping diagram for your own proposed food truck menu to ensure every item has one specific price, confirming your business model is a functional relation.
4. Translate your menu mapping into a coordinate graph and apply the 'Vertical Line Test' to visually prove your menu's reliability to your business partners.
Final Product
What students will submit as the final product of the activityA 'Menu Reliability Audit' report that identifies which menu sets are functions and which are 'glitches,' including a corrected menu table and a written explanation of the 'Vertical Line Test' as applied to their business.Alignment
How this activity aligns with the learning objectives & standardsHSF-IF.A.1: Students understand that a function assigns each element of the domain exactly one element of the range. They will identify if a menu (relation) is a function.Activity 2
The Secret Ingredient Algorithm
Students will transition from simple tables to algebraic representations. They will develop a 'Secret Ingredient Algorithm' where the cost of a custom dish is determined by a function, such as C(x) = 1.50x + 5.00, where x is the number of premium toppings. Students will practice evaluating these functions to provide instant quotes to 'customers' (classmates) and interpret what notation like C(4) = 11 means in the context of a food sale.Steps
Here is some basic scaffolding to help students complete the activity.1. Develop a linear cost function C(x) for your signature dish, where x represents a variable (like extra toppings or ounces of protein).
2. Evaluate your function for various inputs: calculate C(0), C(3), and C(5) to determine the price points for different versions of your dish.
3. Interpret the meaning of 'f(x) = y' in your business context. Write a sentence explaining what the input and output represent for your specific truck.
4. Create a Revenue Function R(n) = pn, where p is your average price and n is the number of customers. Calculate your projected revenue for a 'Slow Day' (n=20) and a 'Busy Day' (n=100).
Final Product
What students will submit as the final product of the activityA 'Cost & Revenue Calculator' sheet featuring at least three different business functions (Cost, Revenue, and Profit) in function notation, with a series of solved examples for different customer order volumes.Alignment
How this activity aligns with the learning objectives & standardsHSF-IF.A.2: Students use function notation, evaluate functions for inputs in their domains, and interpret statements in context.Activity 3
Operational Boundaries: The Capacity Map
Every business has physical and temporal limits. In this activity, students define the 'Domain of Operation' (the hours they can work and the number of ingredients they can carry) and the 'Range of Success' (the possible revenue they can earn). They will analyze why the domain cannot be 'all real numbers'—for instance, you cannot have negative customers or operate for 25 hours in a day.Steps
Here is some basic scaffolding to help students complete the activity.1. Identify the physical constraints of your truck: How many meals can you physically store? How many hours can you legally park at a location?
2. Determine the 'Reasonable Domain' for your daily sales function. Should it include negative numbers? Should it be discrete (whole numbers of people) or continuous?
3. Calculate the 'Range' based on your domain. If your domain is 0 to 200 customers, what are the minimum and maximum revenue values?
4. Graph your Revenue Function on a coordinate plane, intentionally shading only the 'Operating Zone' (the valid domain and range) to show investors where the business actually functions.
Final Product
What students will submit as the final product of the activityA 'Business Constraints Map' that includes graphs of their business functions with clearly labeled 'Endpoints' and a written justification for the specific domain and range based on real-world truck constraints.Alignment
How this activity aligns with the learning objectives & standardsHSF-IF.B.5: Students relate the domain of a function to its graph and to the quantitative relationship it describes (e.g., restricted domains in real-world contexts).🏆
Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioFood Truck Entrepreneurship: Function-Based Business Assessment
Category 1
Mathematical Foundations of Business
Evaluates the student's foundational understanding of what constitutes a function within the context of a food truck's Point of Sale (POS) system.Criterion 1
Function Identification & POS Logic
Ability to distinguish between functional and non-functional business relations using multiple representations (mapping, tables, and graphs).
Exemplary
4 PointsAccurately identifies all 'glitch' scenarios; creates a flawless mapping diagram for a menu; provides a sophisticated explanation of the Vertical Line Test that connects mathematical logic to business reliability.
Proficient
3 PointsCorrectly identifies most POS glitches; develops a mapping diagram where each input has one output; applies the Vertical Line Test correctly to verify the menu's reliability.
Developing
2 PointsIdentifies some POS glitches but may confuse inputs and outputs; mapping diagram contains minor errors; shows emerging understanding of the Vertical Line Test.
Beginning
1 PointsStruggles to identify non-functions in the order logs; mapping diagram is incomplete or allows multiple outputs for one input; unable to apply the Vertical Line Test.
Category 2
Operational Modeling & Evaluation
Assesses the ability to translate business operations into mathematical language and perform calculations to predict financial outcomes.Criterion 1
Function Notation & Algebraic Modeling
Competency in building and evaluating algebraic models using proper function notation (f(x)) to represent costs, revenue, and profit.
Exemplary
4 PointsDevelops complex, accurate functions (Cost, Revenue, and Profit); evaluates multiple inputs without error; provides nuanced interpretations of notation (e.g., explaining exactly what C(x) = y represents for the business).
Proficient
3 PointsCreates accurate Cost and Revenue functions; correctly evaluates functions for specific inputs (like customer volume); provides clear, context-based explanations for function notation.
Developing
2 PointsBuilds basic functions but may have errors in algebraic setup; evaluates inputs with some calculation errors; interpretation of notation is surface-level or partially incorrect.
Beginning
1 PointsAttempts to create functions but lacks proper notation; significant errors in evaluating inputs; cannot explain the meaning of f(x) in a business context.
Category 3
Constraint Analysis & Real-World Limits
Focuses on the application of domain and range to the physical and logical limitations of running a food truck business.Criterion 1
Contextual Constraints (Domain & Range)
Ability to define and justify the reasonable limits of business variables based on physical and temporal constraints.
Exemplary
4 PointsDefines precise domain and range endpoints; provides a sophisticated justification for why the domain is discrete or continuous; accurately identifies constraints like storage and 'The Operating Zone.'
Proficient
3 PointsCorrectly identifies domain and range based on truck constraints (e.g., hours and inventory); differentiates correctly between discrete and continuous variables in context.
Developing
2 PointsIdentifies general domain and range but may include unrealistic values (e.g., negative numbers); justification for constraints is vague or missing key physical limits.
Beginning
1 PointsShows significant confusion regarding domain and range; fails to relate mathematical boundaries to real-world food truck constraints.
Category 4
Communication & Representation
Evaluates how well students can present their mathematical business plan to others through visual and written means.Criterion 1
Visual Representation & Stakeholder Communication
Effectiveness in using graphs and written reports to communicate mathematical findings to potential business stakeholders.
Exemplary
4 PointsProduces professional-grade graphs with precise scales, labels, and 'Operating Zones'; written report is persuasive and seamlessly integrates mathematical data to justify business sustainability.
Proficient
3 PointsCreates clear, accurate graphs with appropriate labels and scales; written report clearly explains how the functions model the business's success and sustainability.
Developing
2 PointsGraphs are mostly accurate but may lack specific labels or use inappropriate scales; written report is present but lacks a strong connection between the math and the business plan.
Beginning
1 PointsGraphs are messy, inaccurate, or missing; written communication fails to explain the mathematical business model or its predictions.
Reflection Prompts
End-of-project reflection questions to get students to think about their learningQuestion 1
Looking back at your 'Menu Reliability Audit,' why is the mathematical definition of a function (one input leads to exactly one output) so critical for the trust between a business and its customers? What would happen to your food truck's reputation if your pricing or ordering system wasn't a function?
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Question 2
How confident do you feel in using mathematical functions (like cost, revenue, and profit functions) to predict the future financial success or failure of a business venture?
Scale
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Question 3
Which aspect of the 'Operational Boundaries' (Domain and Range) was the most eye-opening or surprising when you were planning the physical limits of your food truck?
Multiple choice
Required
Options
Realizing that negative numbers (customers/time) don't make sense in business (Domain)
Discovering the physical limits of storage and prep capacity (Domain)
Calculating the maximum possible revenue we could make in a single shift (Range)
Understanding how hours of operation directly limit our total profit potential (Domain/Range)
Question 4
Our driving question asked how functions can help design a sustainable business. Based on your work, what is the single most important 'mathematical insight' you would give to a real-world food truck owner to help them stay profitable and avoid business failure?
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