# TechMAP - On the Botpath - Teacher Edition

### Author: Gary Froelich

The primary contextual setting of this module is robot paths (botpaths). Through the modeling criterion of maximizing distance from obstacles, the concepts of midpoint and perpendicular bisector are developed. Coordinate systems are introduced as a way to precisely describe locations of obstacles and robot paths, leading to discussions of slope, distance, and solving systems of linear equations. A supplemental section features 30 related problems from various state high school mathematics exams.

**TechMAP**

Covering topics from Algebra I to Precalculus, TechMAP modules show high school students real, immediate uses for mathematics.

**All students MUST PASS the same standardized tests in order to graduate and succeed. All 22 TechMAP modules show tangible, real-world applications of the material on these exams, driving home required math skills.**

**The mathematics required by state tests is taught in algebra and geometry courses, but for many students this is not enough. TechMAP modules demonstrate these skills in vocational fields; they help reinforce existing mathematics courses through actual career activities. These modules are self-contained with exercises, teacher notes, handouts, etc., and can be used individually or together. Each module takes one to three weeks of classroom time.**

**A builder finds the slope of a roof the same way an**

algebra student finds the slope of a line.**A farmer selling her wheat must decide between several**

grain elevators in different locations. She uses conic

sections and parameters on elementary models to make

her decision.**An exploration into the packaging industry reveals area**

formulas.**GPS devices are everywhere today, and our module**

explains how they actually work; students become well-versed

in spherical geometry, time differences, and codes.**Carpenters work with shapes and relationships every**

day, and in our modules we explore circle relationships,

differential equations, linear regression, and more.

#### Mathematics Topics:

#### Application Areas:

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