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## Circle Train Problem TCM 2018_Hernandez.pdf - Google Drive

The NC School of Science and Mathematics

In this math modeling lesson, students build mathematical models for the horizontal and vertical position of a train moving along a circular track. The math topics includes transformations of sinusoidal functions connected to a contextual scenario.

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Version 1.0 - published on 12 Jun 2018 doi:10.25334/Q46X3N - cite this

Licensed under Creative Commons CC0 1.0 Universal

#### Description

I created this lesson for high school students studying trigonometric functions in Precalculus.

There are 3 files required for use with this lesson:

1. The student handout (pdf)

2. The train video

3. The Excel spreadsheet with the data

In this lesson, students are asked to make conjectures about the horizontal and vertical position of a train moving along a circular track after they watch a video of the train moving along the track.  The student handout explains how to collect data from the video using LoggerPro, but if students do not have access to LoggerPro, the lesson materials provides the data collected from marking the position of the red dot on the top of the engine.

To collect the data, a set of axes was superimposed on the video in the center of the track. The data is provided in an excel file.  Students should use their knowledge of transformations of sinusoidal functions to find models for the horizontal and vertical position of the red dot on the train as the train moves along the track. Students can then pose their own questions related to the scenario and answer those question suing their mathematical models.

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#### Notes

Version 1 - Basic Student Handout - will need to be modified if students do not have access to LoggerPro for data collection from videos

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