Project Launch and Brainstorm - Kick off with a 'Shark Tank'-style pitch session where students brainstorm initial small business ideas, considering factors like startup costs and potential pricing. Introduce the concept of linear equations as tools for modeling business plans. (60 min)

Business Plan Drafting - Groups draft their small business plan outlines, incorporating initial linear equation models to represent costs and pricing. (30 min)

Scatter Plots and Correlation - Learn how to interpret scatter plots and identify correlations between data sets. Students will apply this knowledge to analyze potential market data related to their business ideas. (30 min)

Data Collection Simulation - Engage in a simulated data collection activity to gather information on potential customer preferences and pricing strategies. (30 min)

Analyzing Lines of Fit - Analyze lines of fit and determine how well they model the collected data. Students will begin to distinguish between correlation and causation within their data sets. (30 min)

Refining Business Model - Use analysis from lines of fit to refine the linear equations in their business plans, adjusting pricing strategies based on simulated market data. (30 min)

Arithmetic Sequences in Business - Introduce arithmetic sequences and model them as functions to solve real-life business problems. Students will extend sequences to predict future inventory needs or sales growth. (30 min)

Business Plan Presentation Prep - Begin preparing visual displays of business plans, including graphs of their linear equations and sequences. (30 min)

Exploring Linear Equations in Business Contexts - Dive deeper into linear equations by exploring examples in business scenarios. Discuss how different forms of linear equations apply to cost and revenue analysis. (30 min)

Peer Review and Feedback - Students exchange drafts of their business plans and linear equations, providing constructive feedback to each other, focusing on clarity and accuracy. (30 min)

Parallel and Perpendicular Lines in Business Layouts - Learn about equations for parallel and perpendicular lines, and apply this understanding to design efficient business layouts. (30 min)

Interactive Layout Design - Use graph paper or digital tools to create possible layouts for their small businesses, ensuring efficient use of space and resources. (30 min)

Scatter Plot Data Analysis Workshop - Engage in a workshop where students use real or simulated data to create scatter plots, identifying the correlation between variables relevant to their business. (30 min)

Data-Driven Decision Making - Analyze their scatter plot findings to make informed adjustments to their business plans, such as pricing or product offerings. (30 min)

Graphing Piecewise Functions - Introduce piecewise functions and their applications in business scenarios, such as tiered pricing strategies. (30 min)

Creating Piecewise Models - Students develop piecewise function models based on their business strategies, graphing them to visualize potential outcomes. (30 min)

Arithmetic Sequences in Inventory Management - Learn how to apply arithmetic sequences to manage inventory and predict stock needs over time. (30 min)

Inventory Planning Exercise - Students create a plan using arithmetic sequences to optimize inventory levels for their business, ensuring they meet potential demand. (30 min)

Graphing Linear Equations Review - Revisit the basics of graphing linear equations on coordinate axes. Discuss the importance of labels and scales in representing business data accurately. (30 min)

Business Plan Revision - Students apply their understanding of graphing linear equations to refine their business plans, focusing on the visual clarity of their data representation. (30 min)

Advanced Scatter Plot Analysis - Deep dive into scatter plot analysis, focusing on distinguishing between correlation and causation within business contexts. (30 min)

Refining Business Models - Use insights gained from advanced analysis to make informed adjustments to business pricing strategies and product offerings. (30 min)

Modeling with Arithmetic Sequences - Explore more complex arithmetic sequence problems and how they apply to business scenarios, such as predicting sales growth. (30 min)

Sequence Application Exercise - Students apply arithmetic sequences to a real-world scenario, forecasting their business's growth trajectory and presenting their findings. (30 min)

Piecewise Function Applications - Discuss more advanced piecewise function applications, such as multi-tier pricing models, and evaluate their impact on business plans. (30 min)

Developing Comprehensive Models - Students incorporate piecewise functions into their business models, refining their plans to reflect complex pricing strategies. (30 min)

Business Plan Finalization - Students finalize their business plans, ensuring all linear equations and models are thoroughly integrated and clearly presented. (30 min)

Presentation Preparation - Begin preparations for the final presentation, focusing on the clarity and impact of their visual displays and narratives. (30 min)

Final Review of Linear Models - Conduct a comprehensive review of the linear equations and models used in business plans, ensuring accuracy and coherence. (30 min)

Peer Presentation Practice - In pairs, students practice presenting their business plans, focusing on clear communication and visual impact. Provide constructive feedback. (30 min)

Feedback Incorporation - Allow time for students to incorporate peer feedback into their business presentations, refining their visual and narrative elements. (30 min)

Exhibition Setup - Begin setting up visual displays and presentation materials for the final exhibition, ensuring all components are ready for presentation. (30 min)

Exhibition Walkthrough - Conduct a walkthrough of the exhibition setup, allowing students to rehearse their presentations in the exhibition space. Adjust layout as needed. (30 min)

Final Presentation Rehearsal - Conduct a full rehearsal of the business plan presentations, simulating the final exhibition with peers acting as audience members. (30 min)

Exhibition Day - Students present their small business plans to an audience of peers, teachers, and community members, using their visual displays and narratives effectively. Engage in Q&A sessions to demonstrate understanding. (60 min)

Reflection and Feedback Session - Facilitate a reflection session where students discuss what they learned throughout the project, focusing on the application of linear equations in real-world scenarios. (30 min)

Project Debrief and Celebratory Wrap-Up - Summarize key takeaways, celebrate successes, and provide certificates or acknowledgments for participation and effort. (30 min)