Exponent Adventure: Graphing the Future!

9th Grade Project 3 weeks

Exponent Adventure: Graphing the Future!

Evgenia K

HSA-CED.A.1

HSF-LE.A.1

HSN-RN.A.1

Self Directed Learning

Academic Mindset

+ 1 more

1-pager

Purpose

This project aims to deepen students' understanding of exponential functions by connecting mathematical concepts to real-world ecological challenges. Through hands-on activities and collaboration with environmental organizations, students will explore population growth models of endangered species, distinguishing between linear and exponential trends. The project encourages critical thinking, self-directed learning, and community engagement, fostering a sense of responsibility and belonging while enhancing academic skills.

Learning goals

Students will develop a comprehensive understanding of exponential functions and their applications in modeling real-world phenomena, distinguishing them from linear models. They will engage in critical thinking and problem-solving by analyzing population growth data of endangered species, collaborating with community partners to apply mathematical concepts to ecological issues. Through self-directed learning and reflection, students will build self-knowledge and academic mindset, enhancing their sense of identity and belonging while mastering the core content of IM Algebra 1, unit 3.

Standards

[California] HSA-CED.A.1 - Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
[California] HSF-LE.A.1 - Distinguish between situations that can be modeled with linear functions and with exponential functions.
[California] HSN-RN.A.1 - Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 531 to be the cube root of 5 because we want (531)3=5(31)3 to hold, so (531)3 must equal 5.

Competencies

Self Directed Learning - Students use teacher and peer feedback and self-reflection to monitor and direct their own learning while building self knowledge both in and out of the classroom.
Academic Mindset - Students establish a sense of place, identity, and belonging to increase self-efficacy while engaging in critical reflection and action.
Critical Thinking & Problem Solving - Students consider a variety of innovative approaches to address and understand complex questions that are authentic and important to their communities.

Products

Students will create a digital portfolio showcasing their analysis of population growth models using exponential functions, supported by graphs and data interpretation. They will also develop an interactive exhibit that allows manipulation of variables in exponential and linear functions to demonstrate real-time effects on population growth. Finally, students will prepare a project report detailing their findings and insights from collaborating with local environmental organizations, highlighting the ecological impact of exponential growth on endangered species.

Launch

Begin the project with a 'Function Adventure' scavenger hunt, where students solve clues related to exponential and linear functions to uncover hidden locations around the school. This interactive activity fosters teamwork and critical thinking, as students apply their understanding of mathematical concepts in a dynamic and engaging way. By navigating through the scavenger hunt, students will gain practical insights into the differences between linear and exponential functions, setting the stage for deeper exploration throughout the project.

Exhibition

Students will host a 'Function Fair' where they present their digital portfolios and interactive exhibits to peers, teachers, and community partners. During the fair, students will engage visitors in discussions about their findings on population growth models, highlighting the differences between linear and exponential functions. This event will provide a platform for students to demonstrate their mastery of the concepts, showcase their critical thinking skills, and connect mathematical models to real-world ecological issues.

Rubric

Competency Progression Rubric Competency-first rubric

Category	Learning Goal	Stage 1	Stage 2	Stage 3	Stage 4
Deeper Learning Competencies	Self Directed Learning	I can independently use feedback to guide my learning and create equations that model real-world scenarios, like predicting population growth using exponential functions By actively reflecting on my progress, I can distinguish between situations that require linear or exponential models and explain my reasoning using rational exponents	I can use feedback from my teacher and peers to improve my understanding of exponential functions and apply them to real-world situations, like modeling population growth I can identify when to use linear or exponential models in my projects and explain my reasoning, showing my progress in self-directed learning	I can effectively use feedback from my teacher and peers to refine my understanding of exponential functions and apply this knowledge to create accurate equations and inequalities for real-world scenarios I can use this understanding to clearly explain the differences between linear and exponential models in the context of population growth, showcasing my ability to think critically and solve problems	I can independently create and solve complex equations and inequalities using linear and exponential functions, accurately interpret the results, and apply them to real-world ecological challenges I can effectively distinguish and explain the differences between linear and exponential models, both in my digital portfolio and during interactive discussions at the Function Fair I confidently use teacher and peer feedback to refine my understanding and presentations, demonstrating a strong sense of ownership over my learning process and showcasing my ability to connect mathematical concepts to ecological issues
Deeper Learning Competencies	Academic Mindset	I confidently identify differences between linear and exponential functions and use these models to analyze real-world problems I apply mathematical concepts to ecological issues by creating equations that model population growth, and I can articulate my understanding through discussions and presentations	I can identify and explain some key differences between linear and exponential functions by using examples from my population growth model project I can create equations to represent basic scenarios and use them to solve problems, showing how exponential growth impacts endangered species I am beginning to connect my learning to real-world ecological issues, and with some guidance, I can discuss my findings with others, reflecting on how these concepts relate to the world around me	I can confidently explain how exponential functions differ from linear functions by using real-world examples, like population growth of endangered species I can create equations and interpret data to support my analysis, and I actively engage in discussions at the 'Function Fair' to share my insights on the ecological impacts of these functions, demonstrating a strong sense of belonging and purpose in my learning journey	I can confidently explain the differences between linear and exponential functions using real-world examples, like population growth models of endangered species, and apply this understanding to create accurate equations that reflect these trends I can engage in thoughtful discussions about the ecological impact of exponential growth, demonstrating my ability to connect mathematical concepts to real-world issues and effectively communicate my insights to others
Deeper Learning Competencies	Critical Thinking & Problem Solving	I can identify the differences between linear and exponential functions by solving problems and explaining my reasoning during the scavenger hunt I use critical thinking to analyze data from population growth models and distinguish situations where each type of function is applicable I collaborate with my peers to explore real-world ecological challenges, using mathematical concepts to create equations and interpret results effectively	I can identify and describe the differences between linear and exponential functions by analyzing data from population growth models, and I can use this understanding to solve real-world problems related to ecological challenges	I can analyze population growth data of endangered species, clearly distinguishing between linear and exponential trends, and use my findings to create equations that model these situations I effectively use critical thinking to explore and explain real-world ecological challenges, and I can confidently present my insights at the 'Function Fair,' engaging others in discussions about the ecological impact of exponential growth	I can effectively analyze and interpret population growth data by creating accurate equations and inequalities that model real-world ecological scenarios, distinguishing between linear and exponential functions through detailed examples I engage in innovative problem-solving by manipulating variables in interactive exhibits to show the impact of exponential growth on endangered species, clearly communicating my findings and insights during the Function Fair

Learning Journey

Ask

Self Directed Learning

Critical Thinking & Problem Solving

Students will embark on a 'Function Adventure' scavenger hunt to uncover clues related to exponential functions, collaborating with peers to define the problem of modeling population growth of endangered species and identify constraints, setting the foundation for their real-world investigation.

Day 1

Milestone Activities

No activities have been added to this phase yet.

Imagine

Academic Mindset

Critical Thinking & Problem Solving

Students will collaborate in groups to brainstorm innovative solutions for applying exponential functions to model real-world population growth scenarios, utilizing insights from the 'Function Adventure' scavenger hunt to identify potential variables and data sources.

Days 2 - 3

Milestone Activities

No activities have been added to this phase yet.

Plan

Self Directed Learning

Critical Thinking & Problem Solving

Students will collaborate in small teams to select an endangered species, analyze population growth data, and devise a detailed plan to model growth using exponential functions while incorporating peer and mentor feedback to refine their approach.

Day 4

Milestone Activities

No activities have been added to this phase yet.

Create

Self Directed Learning

Academic Mindset

Critical Thinking & Problem Solving

Students will collaboratively build and test their interactive exhibit prototypes, applying their knowledge of exponential functions to real-world population growth models, while incorporating peer and mentor feedback for refinement.

Days 5 - 6

Milestone Activities

No activities have been added to this phase yet.

Test

Self Directed Learning

Critical Thinking & Problem Solving

Students will conduct tests to validate their population growth models using real-world data, examining the accuracy and effectiveness of exponential functions in predicting ecological phenomena.

Day 7

Milestone Activities

No activities have been added to this phase yet.

Improve

Self Directed Learning

Critical Thinking & Problem Solving

Students will review peer feedback and revise their digital portfolio, enhancing their population growth models with improved accuracy and clarity before presenting their findings in the final exhibition.

Day 8

Milestone Activities

No activities have been added to this phase yet.

Academic Mindset

Critical Thinking & Problem Solving

Students will present their interactive exhibits to peers and community partners at the 'Function Fair,' showcasing their population growth models and reflecting on their learning journey through constructive feedback and discussions.

Day 9

Milestone Activities

No activities have been added to this phase yet.

Ask

Define the problem and identify constraints.

Day 1

Milestone Activities

No activities have been added to this phase yet.

Plan

Week 1	Day 1	Day 2	Day 3
Phase	Ask Imagine Ask
Activities	Exponential Function Problem Statement Activity Project Launch: 'Function Adventure' Scavenger Hunt Activity (Deprecated) 80m	Introduction to Exponential Functions Activity (Deprecated) 40m Analyzing Integer Exponents Activity (Deprecated) 40m	Population Growth Concept Map Activity Exponential Function Storyboard Activity Interactive Growth Model Presentation Activity Graphing Linear and Exponential Functions Activity (Deprecated) 40m Reflection and Self-Assessment Activity (Deprecated) 40m
Preparation

Week 2	Day 4	Day 5	Day 6
Phase	Plan Create
Activities	Endangered Species Analysis Report Activity Peer Feedback Reflection Journal Activity Planning the Interactive Exhibit Activity (Deprecated) 40m Introduction to Function Notation Activity (Deprecated) 40m	Building the Interactive Exhibit Part 1 Activity (Deprecated) 80m	Interactive Exhibit Presentation Activity Peer Review and Reflection Activity Prototype Testing Documentation Activity Building the Interactive Exhibit Part 2 Activity (Deprecated) 60m Self-Assessment and Reflection Activity (Deprecated) 20m
Preparation

Week 3	Day 7	Day 8	Day 9
Phase	Test Improve Share
Activities	Interactive Growth Model Simulation Activity Peer Review and Reflection Session Activity Exhibit Testing and Peer Review Activity (Deprecated) 40m Finalizing Digital Portfolios Activity (Deprecated) 40m	Revised Digital Portfolio Activity Exhibit Improvement and Refinement Activity (Deprecated) 50m Rehearsal for Function Fair Activity (Deprecated) 30m	Interactive Exhibit Presentation Activity Function Fair Exhibition Activity (Deprecated) 60m Project Reflection Circle Activity (Deprecated) 20m
Preparation