In the Triangular Pyramid Catapult Project, students design and build a working triangular pyramid catapult and use mathematics to model projectile motion and analyze performance data. The project integrates quadratic functions, geometric structure, and statistical reasoning into a competitive, hands-on challenge.

Students construct a triangular pyramid catapult using craft sticks, skewers, straws, tape, and a rubber band. They modify the build to include straw spacers and record the construction process. Once built, teams attempt to launch a marshmallow or ball to knock down a six-cup pyramid. The first team to successfully complete the build and hit the cup tower wins.

Using slow-motion video, students capture the projectile’s motion with a visible x–y axis marked in one-inch increments. Each student then imports a screenshot into Desmos, scales the image to match the coordinate grid, and writes a quadratic equation in vertex form:$$y = a(x – h)^2 + k$$

with domain restrictions to model the flight path of the projectile from launch to impact. Students identify and interpret the vertex, direction of opening, and key features of the parabola in context.

For the statistical component, each team member attempts to knock down all cups while teammates record the number of shots required to touch a cup. Students combine class data to calculate mean, median, mode, range, first quartile, third quartile, and interquartile range, then create a box-and-whisker plot. Finally, they use the data to make and justify a probability-based prediction about the likelihood of the next shot touching a cup.

The project culminates with submission of build documentation, a Desmos graph with quadratic modeling, and a complete statistical analysis.

This project blends quadratic modeling, geometric reasoning, statistics, and mathematical communication into a dynamic applied learning experience.

Common Core Standards Alignment

Integrated Math 1

Quadratic Functions & Modeling

• CCSS.MATH.CONTENT.HSF-IF.B.4 — Interpret key features of functions in context.
• CCSS.MATH.CONTENT.HSF-IF.C.7a — Graph quadratic functions and show intercepts and vertices.
• CCSS.MATH.CONTENT.HSF-BF.A.1a — Write a function that describes a relationship between two quantities.

Statistics

• CCSS.MATH.CONTENT.HSS-ID.A.1 — Represent data with plots on the real number line (dot plots, histograms, box plots).
• CCSS.MATH.CONTENT.HSS-ID.A.2 — Use statistics appropriate to the shape of the data distribution.

Integrated Math 2

Quadratic Functions & Structure

• CCSS.MATH.CONTENT.HSF-IF.C.8a — Use completing the square to identify maximum or minimum values (vertex interpretation).
• CCSS.MATH.CONTENT.HSF-BF.B.3 — Identify the effect of transformations on graphs of functions.

Geometry

• CCSS.MATH.CONTENT.HSG-MG.A.1 — Use geometric shapes and their measures to model real-world situations.

Statistics

• CCSS.MATH.CONTENT.HSS-ID.B.5 — Summarize, represent, and interpret data on a single count or measurement variable.

Integrated Math 3

Advanced Function Analysis

• CCSS.MATH.CONTENT.HSF-IF.B.6 — Calculate and interpret the average rate of change of a function.
• CCSS.MATH.CONTENT.HSF-IF.C.9 — Compare properties of two functions represented in different representations.
• CCSS.MATH.CONTENT.HSF-IF.B.5 — Relate the domain of a function to its graph and context.

Statistical Inference

• CCSS.MATH.CONTENT.HSS-ID.C.7 — Interpret differences in shape, center, and spread in data distributions.
• CCSS.MATH.CONTENT.HSS-IC.B.3 — Evaluate reports based on data (probability prediction).

Mathematical Practice Standards (All Courses)

• MP1 — Make sense of problems and persevere in solving them
• MP2 — Reason abstractly and quantitatively
• MP4 — Model with mathematics
• MP5 — Use appropriate tools strategically (Desmos, slow-motion video, measurement tools)
• MP6 — Attend to precision
• MP7 — Look for and make use of structure
• MP8 — Look for and express regularity in repeated reasoning