If you would like a copy of this project send me a message
In the Line Race project, students design, build, race, and mathematically analyze a four-track marble system built from linear sections. The goal is to create a stacked system of four different linear tracks (6–20 inches each) that allows a marble to travel unassisted from the top track to the bottom. The team whose marble takes the longest time to complete the course wins.
Students begin by sketching and writing equations in slope-intercept form (y = mx + b) for each linear section, then create a scale drawing before constructing their design using provided materials. After building and testing their system, teams record their marble’s time and submit their data.
Each student then models the system in Desmos by importing a photo, scaling it accurately, writing and restricting linear equations for each track, and identifying key features such as domain, range, continuity, asymptotes (if applicable), and overall shape.
Finally, students analyze class race times by calculating mean, median, mode, quartiles, range, and creating a box-and-whisker plot. They determine which measure of central tendency best represents the data and justify their reasoning.
The project concludes with a presentation showcasing the design process, construction, Desmos graph with equations, data analysis, and final reflections. Grading emphasizes mathematical accuracy, data analysis, modeling, documentation, and overall presentation quality.
This hands-on project integrates algebra, graphing, modeling, statistics, and mathematical communication into one engaging, competitive, and creative experience.
Common Core Standards Alignment
Integrated Math 1
Linear Functions & Modeling
- CCSS.MATH.CONTENT.HSF-IF.B.4 — Interpret key features of functions from graphs and tables.
- CCSS.MATH.CONTENT.HSF-IF.C.7a — Graph linear functions and show intercepts.
- CCSS.MATH.CONTENT.HSF-BF.A.1a — Write a function that describes a relationship between two quantities.
- CCSS.MATH.CONTENT.HSF-LE.A.1 — Distinguish between linear and exponential models.
Statistics
- CCSS.MATH.CONTENT.HSS-ID.A.1 — Represent data with dot plots, histograms, and box plots.
- CCSS.MATH.CONTENT.HSS-ID.A.2 — Use statistics appropriate to the shape of the data distribution.
Integrated Math 2
Functions & Modeling
- CCSS.MATH.CONTENT.HSF-IF.B.6 — Calculate and interpret the average rate of change of a function.
- CCSS.MATH.CONTENT.HSF-BF.B.3 — Identify the effect of transformations on functions.
Statistics
- CCSS.MATH.CONTENT.HSS-ID.B.5 — Summarize and interpret data distributions.
Integrated Math 3
Advanced Function Analysis
- CCSS.MATH.CONTENT.HSF-IF.C.9 — Compare properties of two functions represented in different ways.
- CCSS.MATH.CONTENT.HSF-IF.B.5 — Relate domain to the quantitative context of the function.
Statistical Decision Making
- CCSS.MATH.CONTENT.HSS-ID.C.7 — Interpret differences in shape, center, and spread in data distributions.
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, video analysis)
- MP6 — Attend to precision
- MP7 — Look for and make use of structure