Interactive applet exploring average and instantaneous rates of change using GeoGebra Graphing Calculator with animation.
In the first applet, it shows an observer standing on the cliff watching a hot air ballon moving rise and fall. The applet displaces the average rate of accent, i.e. average rate of change of the balloon's height, between two different moments in time
The Graph provides information on the average rate of change and instantaneous rate of change and their relation using secant and the tangent line in the second applet.
Simulation, Visualizing average rate of change and instantaneous rate of change.
It is an interactive Graphing Calculator created using open-source software GeoGebra.
GeoGebra is a dynamic mathematics software that joins geometry, algebra and calculus.
This material can be used in-class to graphically show avg/instantaneous rate of change of ballon with the help of the secant line and the tangent line.
It can also be used as homework for students to answer some of the questions asked in the material.
The material is well suited for in-class demonstrations and individual study. The included exploratory questions could be incorporated in a group activity or class discussion.
Any browser.
The main goal of this site is to illustrate and aid users in visualizing the concepts of average and instantaneous rates of change.
In particular the goals are:
High School, College General Ed, College Lower Division
Targeted user groups are: High School Students and Faculty (effective teaching tool)
College Algebra
Basic knowledge of Algebra, Calculus and Graphing.
Ability to learn and use GeoGebra Graphing Calculator (Not a pre-requisite for users), however for faculty learning GeoGebra might help them to improve their teaching methodology and ability to present a complex topic in a simple way, in this case to see that the secant line is a better and better approximation to the tangent line.
Both applets are interactive and user friendly. Directions and exploratory questions are provided to support students in making connections.
Some highlights are:
The website is not completely secure: This is the message I receive when I click 'Go to Material
The information you’re about to submit is not secure because the site is using a connection that’s not completely secure, your information will be visible to others.
It looks like you have entered an ISBN number. Would you like to search using what you have entered as an ISBN number?
You entered an email address. Would you like to search for members? Click Yes to continue. If no, materials will be displayed first. You can refine your search with the options on the left of the results page.
You entered an email address. Would you like to search for members? Click Yes to continue. If no, materials will be displayed first. You can refine your search with the options on the left of the results page.