"Linear Legends: Crack the Code!"

Plan

8th, 9th Grades Project 4 weeks

"Linear Legends: Crack the Code!"

Emily P

CCSS.Math.Content.HSA-CED.A.2

CCSS.Math.Content.HSA-REI.D.10

CCSS.Math.Content.HSF-BF.A.1

CCSS.Math.Content.HSF-LE.A.2

CCSS.Math.Content.HSF-BF.A.1

+ 3 more

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Purpose

Students will engage in a hands-on project where they design a small business plan, such as a food truck or pop-up shop, using linear equations to analyze costs, pricing, and profits. This real-world application allows students to connect mathematical concepts to everyday decision-making, fostering deeper understanding and critical thinking. Through collaborative work and iterative problem-solving, students will create equations, interpret data, and construct functions that model business scenarios, culminating in a presentation of their optimized business strategy.

Learning goals

Students will develop the ability to create and analyze linear equations to represent real-world business scenarios. They will explore the relationship between costs, pricing, and profits by designing a business plan for a food truck or pop-up shop. Through hands-on activities, students will interpret scatter plots, analyze lines of fit, and construct arithmetic sequences to model business operations. By the end of the project, students will confidently write and graph linear functions to optimize business decisions, meeting the specified Common Core standards.

Standards

[Common Core] CCSS.Math.Content.HSA-CED.A.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
[Common Core] CCSS.Math.Content.HSA-REI.D.10 - Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
[Common Core] CCSS.Math.Content.HSF-BF.A.1 - Write a function that describes a relationship between two quantities
[Common Core] CCSS.Math.Content.HSF-LE.A.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
[Common Core] CCSS.Math.Content.HSF-BF.A.1 - Write a function that describes a relationship between two quantities
[Common Core] CCSS.Math.Content.HSF-BF.A.2 - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
[Common Core] CCSS.Math.Content.HSF-IF.C.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
[Common Core] CCSS.Math.Content.HSF-LE.A.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Products

Students will develop a comprehensive business plan for a hypothetical small business, such as a food truck or pop-up shop. They will create and graph linear equations to represent cost structures, pricing strategies, and profit margins. By analyzing scatter plots and lines of fit, students will determine optimal pricing and inventory levels. The final product will include a presentation of their business plan, complete with visual graphs and a written report that outlines their findings and recommendations.

Launch

Kick off the project with a "Shark Tank"-style pitch session where students brainstorm and present initial ideas for a small business, such as a food truck or pop-up shop. Have them consider factors like startup costs, potential pricing strategies, and target profits. Use this session to introduce the concept of linear equations as tools for modeling and optimizing their business plans. Encourage students to ask questions and provide feedback to their peers, setting the stage for collaborative learning and problem-solving throughout the project.

Exhibition

Students will present their small business plans, showcasing how linear equations were used to determine costs, pricing, and profits. Each group will create a visual display, including graphs and functions, to illustrate their data analysis and decision-making process. The exhibition will be open to peers, teachers, and community members, who can engage with students through questions and feedback, simulating a real-world pitch scenario.