Peer Review

Average and Instantaneous Rate of Change

Material Detail page

Reviewed:: Jan 24, 2021 by Mathematics

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Ratings

Overall Rating:

Content Quality:

Effectiveness:

Ease of Use:

Overview:

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.

Type of Material:

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.

Recommended Uses:

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.

Technical Requirements:

Any browser.

Identify Major Learning Goals:

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:

Ability to visualize the average and instantaneous rate of change of ballon. It is an interactive applet.
The first graph teaches users to find the average rate of change of the balloon's height, between two different moments in time by showing the secant line and displaying the avg rate of ascent.
It interactively explains where the balloon is rising/ falling or moving quickly/ slowly. It also shows the positive/negative average rate of ascent or secant slope.
The second graph teaches users to find the instantaneous rate of change of ballon and shows the relationship between the secant line and the tangent line.
It also shows users by moving t2 closer to t1 and see the merging of the secant line and the tangent line, or to see that the secant line is a better and better approximation to the tangent line.

Target Student Population:

High School, College General Ed, College Lower Division

Targeted user groups are: High School Students and Faculty (effective teaching tool)

Prerequisite Knowledge or Skills:

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.

Content Quality

Rating:

Strengths:

Both applets are interactive and user friendly. Directions and exploratory questions are provided to support students in making connections.

Some highlights are:

Use of open-source GeoGebra Graphing Calculator
Very interactive graph, which allows users to find avg rate of ascent/descent of ballon and its relationship with the secant line.
It also allows to user to determine the instantaneous rate of ascent by approximating the slope of the tangent line (which is the instantaneous rate of change of the balloon height) to the secant line.
Excellent Assignment questions in the material for assignment/classwork/homework etc.

Concerns:

The average rate of change formula and numerical value are overlapped in both applets. Users can easily click on and move the numerical value to fix this issue.
This material is from Calculus Applets using GeoGebra project by Marc Renault, supported by Shippensburg University.
Avg rate of ascent results ft/min masked display.
Instantaneous rate of change formula not displayed i.e Limit (t-->o) delta h/delta t
Role of the observer i.e. man standing on a cliff not clear from the relativity point of view.

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

The applets provided on this site are great tools for helping students to visualize the relationship between average and instantaneous rates of change. The directions/questions are helpful for guiding students through the activity.
Calculus Applets using GeoGebra is an excellent teaching tool
Enables the student to explore the graph avg/inst rate of change with animated ballon.
Visualize the avg rate of ascent/desent vis-a-vis secant line and inst. rate of ascent at point by approximating the tangent line with secant line.
Conceptual understanding of the subject
A good number of questions in the material for students to understand the importance of calculus to find instantaneous rate of change.

Concerns:

Avg rate of ascent results ft/min masked display.
Instantaneous rate of change formula not displayed i.e Limit (t-->o) delta h/delta t
Teachers should have knowledge of GeoGebra Graphing Calculator. (Though not a pre-requisite for users).

Ease of Use for Both Students and Faculty

Rating:

Strengths:

The applets are interactive and intuitive for users. Directions and exploratory questions are provided.
Works on Desktop/notebook/tablet/smartphone chrome/Firefox/Microsoft edge
GeoGebra is an open-source software
Content & Questions in the material are pertinent and improves learning skill
Easy to navigate and use

Concerns:

Avg rate of ascent results ft/min masked display.
Role of stands on a cliff and watches a hot air balloon (the balloon is far away, it's not just very small).

Other Issues and Comments:

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.

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