Created byKatherine W
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The Cookie Startup: A Bakery Production Plan
Grade 8Math1 days
★★★★★
5.0 (1 rating)Linear InequalitiesOptimizationProfit MaximizationReal-World ConstraintsCookie ProductionBakingFeasible Region
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Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we design a cookie production plan that maximizes profit for our new bakery, given limited ingredients, oven time, and the need to adapt to changing costs?Essential Questions
Supporting questions that break down major concepts.- How can we represent real-world limitations using mathematical inequalities?
- What strategies can we use to optimize our cookie production within given constraints?
- How do different cookie recipes affect our overall profit, considering ingredient costs and baking time?
- How can we visually represent and analyze our production possibilities to maximize profit?
- In what ways can we adjust our cookie prices to respond to ingredient costs and baking time constraints and maximize profit?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Students will be able to formulate linear inequalities representing real-world constraints related to ingredients and oven time.
- Students will be able to determine viable solutions within the system of inequalities.
- Students will be able to calculate profit based on cookie recipes, ingredient costs, and baking time.
- Students will be able to optimize cookie production to maximize profit within the given constraints.
- Students will be able to analyze the impact of changing costs on pricing and production strategies.
Common Core Standards
A.CED.A.3
Primary
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.Reason: Directly addresses the project's focus on modeling constraints with inequalities.
Entry Events
Events that will be used to introduce the project to studentsMystery Box Challenge: Bakery Edition
Students receive a box filled with a limited and unusual assortment of baking ingredients. Their challenge is to brainstorm cookie concepts using only these ingredients, sparking immediate problem-solving and highlighting resource constraints.📚
Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Activity 1
Ingredient Inventory Challenge
Students begin by taking stock of all available ingredients and quantifying oven time. This activity sets the stage for understanding the constraints they will be working with.Steps
Here is some basic scaffolding to help students complete the activity.1. List all available ingredients with their quantities (e.g., flour: 10 kg, sugar: 5 kg).
2. Determine the total available oven time in minutes.
3. Create a table summarizing the ingredient quantities and oven time.
Final Product
What students will submit as the final product of the activityA detailed inventory table of ingredients and available oven time.Alignment
How this activity aligns with the learning objectives & standardsPrepares students to understand and represent real-world constraints, aligning with A.CED.A.3 by setting the context for formulating inequalities.Activity 2
Cookie Recipe Breakdown: The Inequality Equation
Students select 2-3 cookie recipes and break them down to determine the quantity of each ingredient and oven time required per cookie. They then formulate linear inequalities to represent the constraints.Steps
Here is some basic scaffolding to help students complete the activity.1. Choose 2-3 different cookie recipes.
2. Calculate the amount of each ingredient (flour, sugar, etc.) required for one batch of each cookie type.
3. Determine the oven time required for one batch of each cookie type.
4. Formulate linear inequalities based on available ingredient quantities and oven time. For example, if 'x' is the number of cookies of type 1 and 'y' is the number of cookies of type 2, an inequality could be 0.1x + 0.2y <= 5 (representing sugar constraint).
5. Clearly define the variables used in each inequality.
Final Product
What students will submit as the final product of the activityA set of linear inequalities representing the constraints on cookie production, with clear definitions of variables.Alignment
How this activity aligns with the learning objectives & standardsDirectly addresses A.CED.A.3 by having students represent constraints with inequalities.Activity 3
Viable Solutions Explorer: Graphing the Production Possibilities
Students graph the system of inequalities to visually identify the region of viable solutions. They explore different points within this region to determine possible production combinations.Steps
Here is some basic scaffolding to help students complete the activity.1. Graph the system of inequalities on a coordinate plane, with each axis representing the quantity of one type of cookie.
2. Identify the feasible region (the area where all inequalities are satisfied).
3. Choose several points within the feasible region and determine the corresponding quantities of each cookie type.
4. Verify that the chosen points satisfy all the original inequalities.
Final Product
What students will submit as the final product of the activityA graph showing the feasible region and a table of viable cookie production combinations.Alignment
How this activity aligns with the learning objectives & standardsReinforces A.CED.A.3 by interpreting solutions as viable options in a modeling context.Activity 4
Profit Calculation Station
Students calculate the profit for each viable production combination, considering ingredient costs, baking time, and selling price. This involves creating a profit function and evaluating it at different points.Steps
Here is some basic scaffolding to help students complete the activity.1. Determine the cost of ingredients for each cookie type.
2. Set a selling price for each cookie type.
3. Create a profit function based on the number of cookies produced (e.g., Profit = (Selling Price - Ingredient Cost) * Number of Cookies).
4. Calculate the profit for several viable production combinations identified in the previous activity.
Final Product
What students will submit as the final product of the activityA table showing the profit for different cookie production combinations.Alignment
How this activity aligns with the learning objectives & standardsApplies the understanding of inequalities to a real-world scenario, further solidifying the concepts of A.CED.A.3.Activity 5
Optimization Challenge: Maximize the Bakery's Dough
Students identify the production combination that maximizes profit within the feasible region. They analyze the impact of changing costs on pricing and production strategies.Steps
Here is some basic scaffolding to help students complete the activity.1. Review the profit calculations from the previous activity.
2. Identify the production combination that yields the highest profit.
3. Analyze the impact of changing ingredient costs or selling prices on the optimal production strategy.
4. Write a brief report summarizing the optimal production strategy and the factors influencing it.
Final Product
What students will submit as the final product of the activityA report detailing the optimal cookie production strategy and an analysis of the factors affecting it.Alignment
How this activity aligns with the learning objectives & standardsCulminates the learning by optimizing production within given constraints, fully addressing A.CED.A.3 and its focus on interpreting solutions in a modeling context.🏆
Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioCookie Startup: Modeling Linear Inequalities Rubric
Category 1
I. Constraint Representation
Assesses the ability to accurately represent real-world constraints (ingredients and oven time) using mathematical inequalities.Criterion 1
A. Inequality Formulation
Accuracy and clarity in formulating linear inequalities based on the provided constraints.
Exemplary
4 PointsAll inequalities are accurately formulated and clearly reflect the constraints, with precise variable definitions.
Proficient
3 PointsMost inequalities are correctly formulated and reflect the constraints, with generally clear variable definitions.
Developing
2 PointsSome inequalities are formulated correctly, but there are errors or omissions in representing all constraints, and variable definitions may be unclear.
Beginning
1 PointsInequalities are incorrectly formulated or do not accurately represent the constraints, and variable definitions are missing or confusing.
Criterion 2
B. Variable Definition
Clarity and consistency in defining the variables used in the inequalities.
Exemplary
4 PointsVariables are clearly and consistently defined throughout the activity, demonstrating a strong understanding of their meaning in the context of the problem.
Proficient
3 PointsVariables are generally well-defined, with only minor inconsistencies or lack of clarity.
Developing
2 PointsVariable definitions are present but may be unclear, inconsistent, or missing for some inequalities.
Beginning
1 PointsVariable definitions are absent, incorrect, or completely unclear, hindering the understanding of the inequalities.
Category 2
II. Solution Viability & Graphical Representation
Evaluates the ability to graph the system of inequalities, identify the feasible region, and determine viable solutions within that region.Criterion 1
A. Feasible Region Identification
Accuracy in graphing the inequalities and identifying the feasible region.
Exemplary
4 PointsThe feasible region is accurately graphed, clearly labeled, and correctly represents the solution space for the system of inequalities.
Proficient
3 PointsThe feasible region is mostly accurately graphed, with minor errors or omissions that do not significantly impact the overall understanding.
Developing
2 PointsThe feasible region is partially graphed, but there are significant errors or omissions that affect the accuracy of the representation.
Beginning
1 PointsThe feasible region is incorrectly graphed or not identified, demonstrating a lack of understanding of the solution space.
Criterion 2
B. Solution Verification
Ability to verify that chosen points within the feasible region satisfy all the original inequalities.
Exemplary
4 PointsAll chosen points are accurately verified to satisfy all inequalities, demonstrating a comprehensive understanding of the constraints.
Proficient
3 PointsMost chosen points are verified correctly, with only minor errors in calculation or reasoning.
Developing
2 PointsSome chosen points are verified, but there are errors in calculation or reasoning, or some inequalities are not checked.
Beginning
1 PointsChosen points are not verified, or the verification process is fundamentally flawed, demonstrating a lack of understanding of the constraints.
Reflection Prompts
End-of-project reflection questions to get students to think about their learningQuestion 1
How did learning about inequalities help you figure out the real limits and decisions in our cookie business project?
Scale
Required
Question 2
Which activity (Ingredient Inventory, Inequality Equation, Production Possibilities) was most helpful in understanding how math can be applied to real-world business decisions?
Multiple choice
Required
Options
Ingredient Inventory Challenge
Cookie Recipe Breakdown: The Inequality Equation
Viable Solutions Explorer: Graphing the Production Possibilities
Question 3
What is one thing you would do differently if you were to start 'The Cookie Startup' project again?
Text
Required