Rocket Quadratics: Launch, Transform, Graph!

Learning Goals & Products

Learning Goals

Students will be able to analyze quadratic models of rocket flight by interpreting the vertex, intercepts, axis of symmetry, domain, and range in relation to a measured launch path.

Students will be able to predict and interpret how shifts, stretches, compressions, and reflections of a quadratic equation change its graph and the modeled trajectory of a rocket.

Students will be able to evaluate multiple rocket and trajectory concepts against measurable criteria and constraints using annotated plans, mathematical predictions, and a decision matrix.

Students will be able to test and optimize a classroom-safe rocket prototype and its quadratic model by comparing predicted and actual flight data and completing at least one evidence-based revision.

Students will be able to justify and communicate shared engineering decisions using mathematical evidence, stakeholder feedback, structured reflection, and professional discussion of trade-offs and limitations.

Products

individual

Individual Rocket Trajectory Engineering Portfolio

Each student documents at least three distinct trajectory or rocket concepts with annotated plans, quadratic equations and graphs, a decision matrix, predictions, test evidence, revisions, and launch-debrief reflections. The portfolio independently explains transformations, contextual domain, design trade-offs, feedback from peers and Jim the rocket scientist, and the student's contribution to team decisions.

team

Tested Rocket Prototype and Trajectory Portfolio Board

Each team safely builds and tests an instructor-approved rocket prototype, revises it at least once using quantitative evidence, and presents its successive equations, transformed graphs, predicted and actual paths, design decisions, performance limitations, and next-step refinements on a portfolio board at the Trajectory Tech Showcase.

Rubric

Competency Progression Rubric Competency-first rubric

Category	Learning Goal	Stage 1	Stage 2	Stage 3	Stage 4
Deeper Learning Competencies	Critical Thinking & Problem Solving	I can use a quadratic model to describe a rocket’s path by identifying basic features of the graph, such as the vertex, intercepts, and whether the path rises and falls I can connect parts of the graph to the launch in a simple way and name a likely domain for the rocket’s flight with support.	I can explain how a rocket’s launch path matches a quadratic graph by identifying the vertex, intercepts, axis of symmetry, domain, and range I can predict how one change to an equation, such as a shift or stretch, will change the rocket’s trajectory and check my prediction against test data.	I can analyze multiple rocket tests to compare predicted and actual paths, identify transformation effects in the equation and graph, and revise my model based on evidence I can justify how the domain fits the rocket’s real flight path and use feedback from peers and Jim to improve my next design choice.	I can independently create and refine a quadratic model that accurately represents a rocket’s trajectory, explaining how transformations affect the graph, the flight path, and the contextual domain and range I can use test results, feedback, and patterns from prior launches to make strategic revisions and clearly defend my reasoning in the launch portfolio and showcase presentation.
Deeper Learning Competencies	Collaboration	I can participate in a team rocket-design task by sharing ideas, listening to teammates, and helping complete a shared launch plan or test record I can follow group decisions during the launch, debrief, and revision process with support from peers or the teacher.	I can work with my team to make shared decisions about a rocket design or one equation change, and I can explain my ideas using evidence from our predicted and actual launch paths I can contribute to our launch-debrief circle by naming a collaboration move I used and responding respectfully to a peer suggestion.	I can co-design our rocket tests with my team by taking on a clear role, resolving disagreements with discussion, and using peer and Jim the rocket scientist’s feedback to revise our equation or launch angle I can help my team compare predicted and actual paths and make a group decision that improves our model of the trajectory and domain of the flight.	I can lead and support my team through multiple launch cycles by helping us plan, test, critique, and revise our rocket model with shared ownership and strong communication I can use evidence from graphs, transformations, and contextual flight data to guide collaborative decisions, help others contribute, and strengthen our final trajectory portfolio board for the showcase.
Deeper Learning Competencies	Effective Communication	I can share a basic explanation of my rocket design, graph, or test results using words, labels, or a simple visual, and I can listen to a peer or Jim’s feedback and restate one idea I heard.	I can explain my rocket’s domain, key points on the graph, and one equation change using accurate math language, and I can communicate one revision I made based on feedback during our launch-debrief circle.	I can clearly present how my rocket’s equation, graph, and actual flight match or differ, using evidence from test data to explain a transformation and the domain of the flight path I can respond to peer questions and give feedback that helps my team revise our model.	I can communicate a polished, evidence-based explanation of how successive equation revisions changed our rocket’s trajectory and how the contextual domain matched the actual launch I can adapt my message for the audience at the Trajectory Tech Showcase, synthesize feedback from peers and Jim, and contribute to a clear, collaborative presentation of our final portfolio board.
Deeper Learning Competencies	Content Expertise	I can identify a rocket launch as a quadratic situation and use a given graph or equation to name basic features such as the vertex, intercepts, axis of symmetry, domain, and range I can explain, with support, how the rocket’s path on the graph matches what happens during the launch.	I can describe how one change in a quadratic equation, such as a shift, stretch, compression, or reflection, changes the shape or position of a rocket’s graph I can use test results or a launch prediction to connect the equation, graph, and real flight path with some accuracy.	I can independently analyze a rocket’s flight using a quadratic model by relating the domain to the actual launch context and interpreting the vertex, intercepts, axis of symmetry, and range in my graphs and launch data I can explain how specific transformations changed the trajectory and justify how my revised equation better fits the observed path.	I can confidently create, revise, and defend a quadratic model for rocket flight by using launch evidence to interpret the graph, domain, and transformations in context I can compare predicted and actual paths, explain discrepancies, and apply my content knowledge to make precise improvements to my model and portfolio work.
Deeper Learning Competencies	Self Directed Learning	I can use teacher prompts, peer feedback, and the launch-debrief circle to name one change I need to make to my rocket design or equation I can label basic parts of my graph and launch path, including the vertex or intercepts, and record one observation about how my predicted and actual paths are similar or different.	I can use feedback from peers and Jim the rocket scientist to revise my quadratic equation or launch angle and explain one transformation I changed, such as a shift, stretch, compression, or reflection I can connect my graph to the rocket’s flight by identifying the domain and one feature like the vertex, intercepts, or axis of symmetry in my portfolio.	I can independently use test data, reflections, and critique to monitor my progress and make purposeful revisions to my model across multiple launches I can explain how changes in my equation affect the graph and the rocket’s trajectory, and I can justify how the domain matches the actual flight path using evidence from my work.	I can consistently self-assess my launch portfolio, notice patterns across trials, and set specific next steps that improve both my quadratic model and my final trajectory board I can integrate feedback from peers, Jim, and my own reflections to make accurate, evidence-based revisions and clearly explain how transformations, domain, and flight data work together in the context of the rocket launch.