The Food Truck Startup: Solving Systems of Equations
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we, as food truck entrepreneurs, use systems of equations to design a business strategy that optimizes our menu, inventory, and pricing for long-term profitability?Essential Questions
Supporting questions that break down major concepts.- How can we use systems of equations to determine the exact point where our food truck shifts from losing money to making a profit? (Break-even Analysis)
- When designing a menu, how does the substitution method help us balance ingredient costs with fixed serving sizes?
- How can we use the elimination method to manage our inventory when we have limited storage space and a strict budget?
- In what scenarios is graphing a system of equations more useful for our business strategy than solving them algebraically?
- How can we mathematically justify a change in our menu pricing to ensure we stay competitive while covering our overhead costs?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Students will be able to formulate systems of linear equations that represent real-world food truck constraints, such as ingredient costs, inventory limits, and revenue projections.
- Students will be able to solve systems of linear equations using the substitution method to find unknown variables within a menu-pricing context.
- Students will be able to solve systems of linear equations using the elimination method to optimize inventory management given budget and storage constraints.
- Students will be able to identify and interpret the break-even point of a business by graphing cost and revenue functions to determine the intersection.
- Students will be able to mathematically justify business decisions—such as price increases or menu changes—by interpreting the solutions to systems of equations in the context of profitability.
Common Core State Standards (Math)
Entry Events
Events that will be used to introduce the project to studentsThe Foreclosure Rescue Mission
Students receive a 'Foreclosure Notice' for a popular local food truck along with a 'Leaked Financial Ledger' showing two conflicting lines of data: daily operating costs vs. daily sales revenue. To save the business, students must use graphing to identify the 'Breakeven Point' and determine exactly how many 'Signature Sliders' must be sold to move from debt into profit.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.The Visual Break-Even Challenge
In this introductory activity, students analyze the 'Leaked Financial Ledger' from the entry event. They will identify the fixed costs (insurance, permit fees) and variable costs (ingredients per slider) to build a cost equation, then use the selling price to build a revenue equation. By graphing these two lines, students will visually locate the 'Breakeven Point' where the food truck stops losing money and begins to profit.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA 'Financial Viability Graph' featuring labeled axes, cost and revenue functions, the intersection point clearly marked, and a written summary explaining the significance of the breakeven point in business terms.Alignment
How this activity aligns with the learning objectives & standardsThis activity aligns with CCSS.MATH.CONTENT.HSA.REI.D.11 (understanding that the intersection of two graphs is the solution) and CCSS.MATH.CONTENT.HSN.Q.A.1 (interpreting units and scale in the context of revenue and costs).The Signature Slider Secret
Students must now design their 'Signature Sauce' or meat blend. They are given specific constraints: the final product must weigh a certain amount and cost exactly a certain price per batch. Using the substitution method, students will determine the exact ratio of two different ingredients (e.g., expensive organic beef vs. affordable lean beef) to hit their target cost and quality.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA 'Recipe Precision Card' that shows the mathematical system used, the step-by-step substitution work, and the final weight/measurement of each ingredient for a perfect batch.Alignment
How this activity aligns with the learning objectives & standardsThis activity aligns with CCSS.MATH.CONTENT.HSA.REI.C.6 (solving systems exactly) and CCSS.MATH.CONTENT.HSA.CED.A.3 (representing constraints with systems and interpreting viability).The Storage Space Squeeze
The food truck has limited storage space and a strict weekly procurement budget. Students are given an invoice for two items (e.g., crates of sodas and boxes of napkins) but the individual prices are missing—only the total quantity of items and the total price are known from two different delivery days. Students will use the elimination method to uncover the unit prices and then decide if they can afford a larger order for next week.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityAn 'Inventory Procurement Order' showing the calculated unit price for each item and a justified plan for next week's order based on the remaining budget.Alignment
How this activity aligns with the learning objectives & standardsThis activity aligns with CCSS.MATH.CONTENT.HSA.REI.C.6 (focusing on the elimination method) and CCSS.MATH.CONTENT.HSA.CED.A.3 (modeling business constraints).The Food Truck Re-Launch Blueprint
In this final portfolio piece, students must react to a market change (e.g., the price of gas goes up or a competitor lowers their prices). They will use their previous data and a new system of equations to decide if they should increase their slider price or change their ingredient mix. They must mathematically justify their decision to a 'bank' (the teacher) to keep their food truck business open.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA 'Business Growth Strategy Pitch' (can be a slide deck or a formal report) that includes a summary of all systems solved, a justification for their final pricing strategy, and a 'Safety Net' calculation showing their new projected breakeven point.Alignment
How this activity aligns with the learning objectives & standardsThis activity synthesizes CCSS.MATH.CONTENT.HSA.REI.C.6, HSA.CED.A.3, and HSN.Q.A.1 by requiring students to justify mathematical solutions within a real-world business context.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioFood Truck Entrepreneurship: Systems of Equations Portfolio Rubric
Mathematical Modeling & Execution
Evaluates the student's ability to build and solve mathematical models that reflect the food truck's financial and operational reality.Algebraic System Modeling
Ability to translate complex business constraints (costs, revenue, ingredient ratios, and inventory limits) into accurate systems of linear equations.
Exemplary
4 PointsIndependently translates complex business scenarios into accurate systems of equations. Equations perfectly reflect all constraints, including nuanced units (price per ounce vs. total pounds) without error. Equations are elegantly structured for the most efficient solving method.
Proficient
3 PointsCorrectly translates business scenarios into systems of equations. Most constraints are represented accurately with appropriate variables and constants. Equations are functional and aligned with the problem context.
Developing
2 PointsTranslates some constraints into equations but struggles with complex relationships (e.g., mixing up slope and y-intercept). Systems may be incomplete or contain errors in variable definition.
Beginning
1 PointsStruggles to identify variables or represent relationships mathematically. Equations do not reflect the business constraints provided in the ledger or recipe cards.
Procedural Precision in Solving
Accuracy and fluency in solving systems of equations using graphing, substitution, and elimination methods.
Exemplary
4 PointsDemonstrates flawless execution of all three methods (graphing, substitution, elimination). Algebraic work is organized, showing all steps clearly. Solutions are checked for accuracy and 'viability' (no impossible negative quantities).
Proficient
3 PointsSolves systems accurately using the required methods with only minor computational errors. Shows most steps of the algebraic process and identifies the correct solution $(x, y)$.
Developing
2 PointsShows basic understanding of the methods but makes frequent signs or arithmetic errors. May struggle to isolate variables or eliminate terms correctly without significant prompting.
Beginning
1 PointsUnable to complete the solving process. Work is disorganized or stops after the first step. Cannot find a numerical solution for the system.
Graphical Interpretation
Focuses on the visual representation of data and the ability to find meaning in graphical intersections.Visual Break-Even Analysis
Accuracy in creating and interpreting the Break-Even Graph, including axis scaling, labeling, and identifying the intersection point.
Exemplary
4 PointsCreates a professional-grade graph with perfect scaling, clear labels, and precise line placement. Correctly identifies the intersection as the break-even point and provides a sophisticated explanation of what the regions above and below the point represent for profit/loss.
Proficient
3 PointsCreates an accurate graph with labeled axes and identifies the intersection point correctly. Provides a clear written explanation of the break-even point's significance in business terms.
Developing
2 PointsGraph is mostly accurate but may have inconsistent scaling or minor plotting errors. The explanation of the intersection point is present but lacks depth or clarity.
Beginning
1 PointsGraph is messy, inaccurately plotted, or missing labels. Unable to identify the intersection point or explain its meaning for the food truck.
Synthesis & Business Strategy
Assesses the student's ability to bridge the gap between abstract algebra and real-world entrepreneurial strategy.Data-Driven Decision Making
The ability to use mathematical solutions to justify business decisions (pricing, inventory, menu changes) and evaluate the 'viability' of those decisions.
Exemplary
4 PointsProvides a highly persuasive, data-backed justification for business decisions. Uses mathematical solutions to anticipate future market shifts and proposes innovative strategies. Demonstrates a deep understanding of how variables impact long-term profitability.
Proficient
3 PointsUses mathematical solutions to justify pricing and inventory decisions. Justification is logical and clearly links the algebra back to the business goal (e.g., 'we must sell 50 sliders to cover our fixed costs').
Developing
2 PointsMakes business decisions but the mathematical justification is weak or disconnected from the solutions found. Shows limited understanding of how the 'answer' affects the food truck's success.
Beginning
1 PointsDecisions are made without mathematical evidence. Fails to explain how the system solutions relate to the viability of the business or the 'Market Shift' scenario.