Woman: Final Project
- Author:
- Jake Feldt
The problem is the instantaneous rate of change of the tip of a woman's shadow who is moving away from the light pole. The woman is 5.5 feet tall, and the light post is 12 feet tall.
The geogebra animation illustrates the woman shuffling at a rate of 1 foot per second. The slider value times 1.25 determines the woman's speed in feet per second. Click walk to make the woman walk, and stop to make the woman stop. Distance over feet per second, and instantaneous rate of change are calculated in real time on the right pane. Point R on the right pane represents the distance from the pole as the x coordinate, and the y coordinate as feet per second [1.25 x Speed]. Additionally, the green tangent line represents a light ray to also show the tip of her shadow.
Distance over feet per second is calculated by: x(R) / 1.25 Speed.
Rate of Change is calculated by 12 times the change in distance/time [as represented by the slider speed times 1.25] divided by 6.5.
IMG_0518
Presentation Script Key Points
1) My name is Jake and the purpose of my project was to explore rate of change.
2) I wanted to look at rate of change as the woman's position changes.
3) The basic sketch description is included above. [Illustration Explanation]
4) The main way Geogebra provides an advantage over pen and paper is it can show the woman moving, as well as instantaneous rate of change calculations.
5) Tools I used are: animation[the woman's movement], buttons [go and stop], trace [point R in graphics 2], spreadsheet [hidden for more space, but formulas from spreadsheet appear in the table in graphics 2], table [in graphics 2], and a slider [for the woman's speed].
6) The two standards for mathematical practice I used are #1: Make Sense of Problems and Persevere in Solving Them, and #5: Use Appropriate Tools Strategically. #1 applies because it allows students to analyze information, be actively engaged in the problem, and be able to check their answers by pausing the woman and checking the table. #5 applies because students can use these tools strategically, and use these technological tools to better understand the concept.
7) The thing I like best about my project is how it can calculate rate of change in real time.