Lesson Plan 1: Mathematical Modeling, Circular Movement and Transmission Ratios
In this lesson, students will learn to use mathematical models to represent real life situations. In particular, they will use tables and equations to represent the relationship between the number of revolutions made by a "driver" and a "follower" (two connected gears in a system), and they will explain the significance of the radii of the gears in regard to this relationship.
Two 50-minute class periods
Transmission factors, explicit and recursive equations, and mathematical modeling
Students will be able to:
Understand the significance of the transmission factor in the design of rotating objects (gears) that are connected.
Determine the transmission factor using the radii of connected pulleys.
Describe the differences between negative and positive transmission factors.
Determine the distance a point on the circumference of a pulley travels, given the speed at which the pulley is turning.
Standards: Principles and Standards for School Mathematics, National Council of Teachers of Mathematics (NCTM), 2000: