PBL Paradise: Project-Based Learning Adventures!

Products & Rubric

9th Grade Project 4 weeks

PBL Paradise: Project-Based Learning Adventures!

Melissa R

Jan 20, 2026

Updated Apr 9, 2026

NC.M2.A-APR.1

NC.M1.A-APR.3

NC.M1.A-SSE.3

NC.M2.A-REI.4

NC.M1.F-IF.9

+ 7 more

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Purpose

The purpose of this project is to guide 9th-grade students in using polynomial functions to invent practical solutions to real-world challenges faced by teenagers. By engaging collaboratively in a design-thinking process, students build mathematical proficiency while honing communication, problem-solving, and self-directed learning skills. This experiential approach empowers students to create innovative products that are meaningful to their lives, fostering a deeper connection to the content and their community.

Learning goals

Students will deepen their understanding of polynomial functions by modeling real-world data relevant to teenage challenges, predicting patterns, and proposing innovative solutions. They will hone critical-thinking and problem-solving skills by designing products that creatively apply mathematical principles to everyday issues. Collaboration will be key as students work together, sharing responsibilities and decision-making throughout the project, while also enhancing communication skills by presenting solutions in user-friendly, interactive formats. Through guided self-reflection, they will evaluate their learning process and its impact both personally and within their community.

Standards

[North Carolina] NC.M2.A-APR.1 - Extend the understanding that operations with polynomials are comparable to operations with integers by adding, subtracting, and multiplying polynomials.
[North Carolina] NC.M1.A-APR.3 - Understand the relationships among the factors of a quadratic expression, the solutions of a quadratic equation, and the zeros of a quadratic function.
[North Carolina] NC.M1.A-SSE.3 - Write an equivalent form of a quadratic expression ax² + bx + c, where a is an integer, by factoring to reveal the solutions of the equation or the zeros of the function the expression defines.
[North Carolina] NC.M2.A-REI.4 - Solve for all solutions of quadratic equations in one variable.
[North Carolina] NC.M1.F-IF.9 - Compare key features of two functions (linear, quadratic, or exponential) each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions).
[North Carolina] NC.M3.F-LE.3 - Compare the end behavior of functions using their rates of change over intervals of the same length to show that a quantity increasing exponentially eventually exceeds a quantity increasing as a polynomial function.
[North Carolina] NC.M1.F-BF.1 - Write a function that describes a relationship between two quantities.

Competencies

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.
Collaboration - Students co-design projects with peers, exercise shared-decision making, strengthen relational agency, resolve conflict, and assume leadership roles.
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.
Effective Communication - Students practice listening to understand, communicating with empathy, and share their learning through exhibiting, presenting and reflecting on their work.
Content Expertise - Students develop key competencies, skills, and dispositions with ample opportunities to apply knowledge and engage in work that matters to them.

Products

Students will collaborate to design and develop a mobile app that predicts and manages teenage screen time using polynomial functions, incorporating algorithmic insights to optimize break periods. During the project's Inventor's Workshop, teams will brainstorm and sketch prototypes for additional polynomial-powered products addressing common teenage issues such as sleep patterns or study efficiency. At the culmination of the project, these products will be showcased at the Innovation Expo, where students will present their designs and mathematical reasoning through interactive stations, effectively demonstrating their understanding and application of core algebraic concepts.

Launch

Begin the experience with an engaging 'Inventor's Workshop' where students interactively brainstorm innovations using polynomial functions to tackle common challenges faced by teenagers. They will actively collaborate in design-thinking groups to sketch preliminary ideas and provide constructive feedback, fostering an environment rich in creativity and shared learning. This hands-on session sets the stage for students to further explore mathematical concepts in a practical, meaningful context.

Exhibition

During the 'Innovation Expo', students showcase their polynomial-powered mobile apps at interactive stations, engaging visitors with demonstrations of their solutions to common teenage problems. Attendees learn through visual and digital storytelling techniques that illuminate the mathematical concepts woven into each design. The event fosters dialogues between students and visitors, including a Q&A session that delves into the mathematical models and innovation processes employed throughout the project.

Plan

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Ask

Students will kick off the project by engaging in the 'Inventor's Workshop', where they'll collaboratively brainstorm and define common teenage problems that can be addressed using polynomial functions, while identifying constraints for their product design.

Days 1 - 3