"Function Frenzy: Unlock the Puzzle Path"

High School Grade

Project
4 weeks

"Function Frenzy: Unlock the Puzzle Path"

Jordan Sipes

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

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

CCSS.Math.Content.HSF-BF.B.3

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

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

+ 1 more

Purpose

The purpose of this project is to engage high school students in an immersive, hands-on learning experience that deepens their understanding of functions through creative problem-solving and real-world applications. By designing and solving puzzles based on quadratic and exponential functions, students will explore mathematical concepts in an interactive and meaningful way. The project aims to foster critical thinking, collaboration, and a deeper comprehension of how functions describe relationships between quantities, ultimately preparing students for advanced mathematical challenges.

Learning goals

Students will develop a deep understanding of quadratic and exponential functions by creating and solving puzzles that illustrate real-world applications, such as population growth and transformations of graphs. They will enhance their problem-solving skills by engaging in hands-on activities that require the use of the quadratic formula, factoring, and completing the square. Learners will explore and identify the effects of parameter changes on function graphs, fostering their ability to interpret and model relationships between quantities. Advanced students will extend their knowledge through the creation of complex puzzles involving polynomial, rational, and logarithmic functions.

Standards

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.
CCSS.Math.Content.HSF-BF.A.1 - Write a function that describes a relationship between two quantities
CCSS.Math.Content.HSF-BF.B.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
CCSS.Math.Content.HSF-IF.A.1 - Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
CCSS.Math.Content.HSF-IF.A.2 - Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
CCSS.Math.Content.HSF-IF.B.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Products

Students will create a series of engaging puzzles that can only be solved through a deep understanding of functions and their relationships. These puzzles will include scenarios modeled with exponential functions, challenges involving quadratic equations, and tasks that require identifying transformations of function graphs. Additionally, students will design more complex puzzles incorporating polynomial, rational, and logarithmic functions for advanced exploration. The final products will be showcased in a school-wide exhibition, where parents and community members can interact with and solve the puzzles, demonstrating the students' mastery of the content.

Launch

Kick off the project with a Puzzle Escape Room experience where students collaborate to solve a series of math-based puzzles involving quadratic and exponential functions. Transform the classroom into a dynamic environment with stations that provide clues and challenges, requiring students to apply their understanding of functions to unlock each stage. This immersive activity sets the tone for the project, sparking curiosity and encouraging teamwork as students begin their exploration of mathematical functions in real-world contexts.

Exhibition

Host a school-wide Function Puzzle Fair where students present their function-based puzzles and solutions to peers, teachers, and parents. Set up interactive stations where visitors can attempt to solve the puzzles, with students guiding them through the logic and math behind each challenge. Incorporate a digital component where students use graphing software to demonstrate function transformations and their impact on puzzle solutions.

Week 1	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Introduction to Functions - Begin the week by exploring the basic concepts of functions, including domain, range, and function notation. Use real-world examples to illustrate these concepts.	Activity 2: Quadratic Function Exploration - Dive into quadratic functions by examining their graphs and identifying key features such as the vertex, axis of symmetry, and roots. Use graphing technology to visualize these elements.	Activity 3: Puzzle Design Brainstorm - Facilitate a brainstorming session where students generate ideas for puzzles that can be solved using quadratic functions. Encourage creative thinking and collaboration.	Activity 4: Escape Room Planning - Introduce the Puzzle Escape Room concept, and have students work in groups to plan the puzzles they will create. Each group should outline their puzzle theme and the quadratic function application involved.	Activity 5: Quadratic Formula Workshop - Conduct a hands-on workshop where students practice solving quadratic equations using the quadratic formula, factoring, and completing the square. Provide real-world context to reinforce understanding.
Deliverables	1. Deliverable 1: Puzzle Concept Proposal - Each group submits a proposal outlining their puzzle idea, including the quadratic function involved and the problem-solving process required to solve it.
Preparation	1. Prep Task 1: Gather and prepare graphing technology and resources for students to explore quadratic functions and their graphs. 2. Prep Task 2: Develop a rubric for evaluating the Puzzle Concept Proposals to provide clear expectations for students. 3. Prep Task 3: Create a list of real-world examples and scenarios that illustrate the application of quadratic functions for classroom discussions. 4. Prep Task 4: Set up the classroom environment for the Puzzle Escape Room introduction, including any necessary materials or decorations. 5. Prep Task 5: Prepare worksheets and resources for the Quadratic Formula Workshop, ensuring a variety of problem types for practice.

Week 2	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Exponential Functions Introduction - Introduce students to exponential functions through interactive demonstrations such as growth and decay simulations. Students will explore real-world applications like population growth and radioactive decay, using technology to visualize these functions.	Activity 2: Puzzle Design Development - Groups refine their puzzle concepts from Week 1 to incorporate exponential functions. Facilitate discussions on how exponential growth or decay can be integrated into their puzzles to create a challenge.	Activity 3: Exponential Graph Exploration - Use graphing technology to experiment with exponential function graphs. Students will investigate the effects of varying parameters on the shape and direction of the graph, analyzing transformations and their real-world implications.	Activity 4: Peer Review and Feedback - Conduct a peer review session where groups present their evolving puzzle designs to classmates. Encourage constructive feedback focused on the integration of exponential functions and the clarity of the puzzle-solving process.	Activity 5: Puzzle Prototype Creation - Guide students in creating a prototype of their puzzle, incorporating feedback from peers. Each group will construct a physical or digital model of their puzzle, ensuring it aligns with their mathematical concept and narrative.
Deliverables	1. Deliverable 1: Revised Puzzle Design Document - Each group submits a detailed document outlining their revised puzzle concept, including the use of exponential functions and the expected solution process. 2. Deliverable 2: Puzzle Prototype - A physical or digital model of the puzzle developed by each group, showcasing the integration of quadratic and exponential functions.
Preparation	1. Prep Task 1: Collect and prepare materials for hands-on demonstrations of exponential functions, including technology tools for graphing and simulations. 2. Prep Task 2: Develop guidelines and a rubric for the Peer Review and Feedback activity to ensure focused and productive sessions. 3. Prep Task 3: Prepare resources such as graphing calculators or software for students to explore exponential functions and transformations. 4. Prep Task 4: Set up a schedule and structure for the Peer Review session, ensuring each group has time to present and receive feedback. 5. Prep Task 5: Gather materials and tools necessary for students to create their puzzle prototypes, such as craft supplies, digital design software, or 3D printing resources.

Week 3	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Polynomial and Rational Function Exploration - Introduce students to polynomial and rational functions. Use graphing technology to explore these functions and discuss their characteristics, such as end behavior, asymptotes, and intercepts.	Activity 2: Puzzle Integration Workshop - Facilitate a workshop where students incorporate polynomial and rational functions into their puzzle designs. Encourage creative ways to challenge solvers using these functions.	Activity 3: Logarithmic Function Challenge - Provide an overview of logarithmic functions and their properties. Engage students in solving real-world problems involving logarithms, highlighting their relationship with exponential functions.	Activity 4: Advanced Puzzle Design Session - Guide students in integrating logarithmic functions into their puzzles, offering extensions for those ready for more complex challenges. Foster collaboration and peer support.	Activity 5: Function Transformation Exploration - Conduct an interactive session where students experiment with function transformations using graphing calculators or software. Have them apply these transformations to their puzzles, enhancing their complexity.
Deliverables	1. Deliverable 1: Advanced Puzzle Design Document - Each group submits a comprehensive document detailing their puzzle, including polynomial, rational, and logarithmic functions, and explaining the problem-solving process. 2. Deliverable 2: Function Transformation Presentation - Groups prepare a short presentation demonstrating the transformations applied to their puzzles, using visual aids and technology to illustrate their impact.
Preparation	1. Prep Task 1: Prepare graphing technology and resources for polynomial and rational function exploration, ensuring access for all students. 2. Prep Task 2: Develop instructional materials and examples for logarithmic function applications in real-world contexts. 3. Prep Task 3: Create guidelines and support materials for the Advanced Puzzle Design Session, including extension challenges for advanced learners. 4. Prep Task 4: Organize materials and resources for the Function Transformation Exploration session, ensuring availability of graphing calculators or software. 5. Prep Task 5: Coordinate with technology staff to ensure all digital tools and platforms are functional and accessible for presentations and explorations.

Week 4	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Activity 1: Final Puzzle Refinement - Students finalize their puzzles by integrating all feedback received from peers and teachers in previous weeks. Ensure all mathematical concepts are accurately represented and that the puzzles offer a challenging yet solvable experience.	Activity 2: Puzzle Testing and Iteration - Facilitate a session where students test each other’s puzzles in a mock exhibition setup. Gather data on problem areas and iterate based on peer feedback to improve puzzle design and clarity.	Activity 3: Exhibition Preparation - Organize and decorate the exhibition space. Students design informational placards and interactive elements that explain the mathematical concepts and solutions behind their puzzles.	Activity 4: Exhibition Run-through - Conduct a rehearsal of the exhibition where students practice presenting their puzzles and guiding participants through the solution process. Provide feedback on presentation skills and clarity.	Activity 5: Function Puzzle Exhibition - Host the school-wide Function Puzzle Exhibition. Each group presents their puzzles to parents, teachers, and classmates, facilitating interactive problem-solving sessions and demonstrating their understanding of functions.
Deliverables	1. Deliverable 1: Final Puzzle - Each group submits their fully completed and tested puzzle, incorporating quadratic, exponential, polynomial, rational, and logarithmic functions as appropriate. 2. Deliverable 2: Exhibition Presentation - Groups prepare and submit a presentation outline that includes the key mathematical concepts, puzzle solution process, and any visual aids or technology used.
Preparation	1. Prep Task 1: Coordinate with school administration for space and materials needed for the exhibition, ensuring it is accessible and engaging. 2. Prep Task 2: Prepare evaluation rubrics for the final puzzles and presentations, focusing on clarity, mathematical accuracy, and creativity. 3. Prep Task 3: Set up exhibition space with necessary technology and ensure all materials and tools are ready for student use during the exhibition. 4. Prep Task 4: Organize logistics for the exhibition day, including schedules, rotations, and any necessary permissions or communication with parents. 5. Prep Task 5: Provide feedback and support during the exhibition run-through, ensuring students are ready to present their puzzles effectively.