Part I: Simulations
![Picture](/uploads/2/1/5/7/21575442/4425804.png)
Plinko Simulation
Personal Reaction: As a child, I often watched The Price is Right and fondly remember Plinko. I think students often enjoy seeing 'games' in the classroom and would view this as a game, more than a lesson. Although our students might not have the same recollections, . The simulation can go slowly or quickly, as the user desires, and provides useful statistics at the bottom of the screen.
Ease of Use: I found it fairly easy to use, taking less than a minute to read through the screen and determine the options I needed to use.
Educational Value: This would be most useful in a Statistics course, for introducing randomness or distributions. Students can see the distribution being formed, and have a clear view of how each data point changes the distribution.
Grade Level: This would be appropriate for middle-school or high school math students.
Fit with Theme: This could be used in Statistics, or as part of a unit on statistics in Algebra 2. Plinko is an interesting study in randomness and the normal distribution. The simulation can extend to using the provided statistics, and be repeated to show slight variations in results.
Personal Reaction: As a child, I often watched The Price is Right and fondly remember Plinko. I think students often enjoy seeing 'games' in the classroom and would view this as a game, more than a lesson. Although our students might not have the same recollections, . The simulation can go slowly or quickly, as the user desires, and provides useful statistics at the bottom of the screen.
Ease of Use: I found it fairly easy to use, taking less than a minute to read through the screen and determine the options I needed to use.
Educational Value: This would be most useful in a Statistics course, for introducing randomness or distributions. Students can see the distribution being formed, and have a clear view of how each data point changes the distribution.
Grade Level: This would be appropriate for middle-school or high school math students.
Fit with Theme: This could be used in Statistics, or as part of a unit on statistics in Algebra 2. Plinko is an interesting study in randomness and the normal distribution. The simulation can extend to using the provided statistics, and be repeated to show slight variations in results.
![Picture](/uploads/2/1/5/7/21575442/3989693.png)
Curve Fitting
Personal Reaction: This is a fabulous simulation, and allows students to directly see how data can be used to create models. I liked the ease of the simulation, where points are dragged and dropped, and multiple types of curve fitting models are offered.
Ease of Use: Very easy to use, the line or curve automatically appears on the screen as the first two points are placed.
Educational Value: High. I will definitely use this simulation the next time I teach an Algebra 2, Precalculus or Statistics course covering regression. Students can easily see how additional data points changes the line of best fit and are given the equation as well, to perform error calculations or predict additional points.
Grade Level: High school or college students
Fit with Theme: Data and modeling are used in all 4 years of high school math courses, but especially in Algebra, Algebra 2 and Precalculus.
Personal Reaction: This is a fabulous simulation, and allows students to directly see how data can be used to create models. I liked the ease of the simulation, where points are dragged and dropped, and multiple types of curve fitting models are offered.
Ease of Use: Very easy to use, the line or curve automatically appears on the screen as the first two points are placed.
Educational Value: High. I will definitely use this simulation the next time I teach an Algebra 2, Precalculus or Statistics course covering regression. Students can easily see how additional data points changes the line of best fit and are given the equation as well, to perform error calculations or predict additional points.
Grade Level: High school or college students
Fit with Theme: Data and modeling are used in all 4 years of high school math courses, but especially in Algebra, Algebra 2 and Precalculus.
![Picture](/uploads/2/1/5/7/21575442/2570853.png)
Calculus Grapher
Personal Reaction: I've never seen an applet that graphs so quickly and on the same screen as this one for a function and its derivative. For my current calculus students, I am adding this link to their lesson immediately. It's simple and extremely useful for students trying to understand the relationship between the graph of a function and its derivative.
Ease of Use: Very easy to use, and it directs the user to begin.
Educational Value: Very useful for a Calculus class. Most students have difficulty understanding the relationship between the two functions, and being able to manipulate and see the result immediately.
Grade Level: High School and College
Fit with Theme: This would be useful for the current AP Calculus courses I teach, and for students in any level of calculus.
Personal Reaction: I've never seen an applet that graphs so quickly and on the same screen as this one for a function and its derivative. For my current calculus students, I am adding this link to their lesson immediately. It's simple and extremely useful for students trying to understand the relationship between the graph of a function and its derivative.
Ease of Use: Very easy to use, and it directs the user to begin.
Educational Value: Very useful for a Calculus class. Most students have difficulty understanding the relationship between the two functions, and being able to manipulate and see the result immediately.
Grade Level: High School and College
Fit with Theme: This would be useful for the current AP Calculus courses I teach, and for students in any level of calculus.
![Picture](/uploads/2/1/5/7/21575442/660558.png)
Equation Grapher
Personal Reaction: This is a basic grapher that shows quadratic equations, and how the graph changes based on which constants are input. My only complaint with the app is that the form of the equation is not as useful as it could be; typically, another method is used to teach students graphing by hand, and I would have liked to see this presented in the same way.
Ease of Use: Easy to input values and see that they change the graph.
Educational Value: Useful for an Algebra 2 course, but not as good as others with an equation in the proper form. Students can see that certain values change the equation.
Grade Level: High School
Fit with Theme: This simulation could be used when studying quadratic equations in Algebra 2, or reviewing quadratics and curve sketching in Precalculus.
Personal Reaction: This is a basic grapher that shows quadratic equations, and how the graph changes based on which constants are input. My only complaint with the app is that the form of the equation is not as useful as it could be; typically, another method is used to teach students graphing by hand, and I would have liked to see this presented in the same way.
Ease of Use: Easy to input values and see that they change the graph.
Educational Value: Useful for an Algebra 2 course, but not as good as others with an equation in the proper form. Students can see that certain values change the equation.
Grade Level: High School
Fit with Theme: This simulation could be used when studying quadratic equations in Algebra 2, or reviewing quadratics and curve sketching in Precalculus.
Part II: Math Internet Resources
Precalculus & Calculus Resources:
Visual Calculus: A site with tutorials and applets to view calculus concepts. This site could be used in a calculus course to reinforce lessons, or offer another way to visualize processes and problem solving.
This meets the first goal from the AP course description:
TI-83/84 Basic Programs for Calculus: A large number of free downloadable programs for the TI-83+ or TI-84+ operating systems that use the graphing calculator to explore ideas and theorems in calculus. In class, students could use the graphing calculator to better explore functions and see connections between the graph and calculus concepts. It meets the 7th goal:
This meets the first goal from the AP course description:
- Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal . They should understand the connections among these representations .
- Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation, and should be able to use derivatives to solve a variety of problems .
- Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and should be able to use integrals to solve a variety of problems .
- Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal . They should understand the connections among these representations .
TI-83/84 Basic Programs for Calculus: A large number of free downloadable programs for the TI-83+ or TI-84+ operating systems that use the graphing calculator to explore ideas and theorems in calculus. In class, students could use the graphing calculator to better explore functions and see connections between the graph and calculus concepts. It meets the 7th goal:
- Students should be able to use technology to help solve problems, experiment, interpret results, and support conclusions .
- Students should be able to use technology to help solve problems, experiment, interpret results, and support conclusions .
Algebra/Geometry/Algebra 2 Resources:
BrightStorm: An online site with videos and practice problems for all levels of algebra, geometry and beyond. This could be used in a classroom to reinforce concepts or for students that need to work ahead independently.
Illuminations: A collection of online videos, games, worksheets and activities for all levels of math, provided by NCTM. Students can use these activities to enrich their learning and make new connections as well as gain practice in a less-tedious manner.
Math Forum @ Drexel: A wealth of resources for teachers and students, including math homework help, forums, puzzles, activities and teacher exchanges. Teachers can use the forums to discuss teaching ideas and exchange lesson plans, while students can ask homework questions or participate in challenges with other students around the country.
Analyze Math: Tutorials and applets for calculus, precalculus, geometry, statistics and college level math. These tutorials are all HTML based, so students with any computer can access them, and can be used with or without the applets. Topics do not cover the full range of the course, but rather have the more challenging or interesting concepts from each of these areas.
Illuminations: A collection of online videos, games, worksheets and activities for all levels of math, provided by NCTM. Students can use these activities to enrich their learning and make new connections as well as gain practice in a less-tedious manner.
Math Forum @ Drexel: A wealth of resources for teachers and students, including math homework help, forums, puzzles, activities and teacher exchanges. Teachers can use the forums to discuss teaching ideas and exchange lesson plans, while students can ask homework questions or participate in challenges with other students around the country.
Analyze Math: Tutorials and applets for calculus, precalculus, geometry, statistics and college level math. These tutorials are all HTML based, so students with any computer can access them, and can be used with or without the applets. Topics do not cover the full range of the course, but rather have the more challenging or interesting concepts from each of these areas.
Statistics Resources
BBN School AP Statistics: Large list with links to applets, worksheets, practice tests, data sets, projects, etc. for AP Statistics teachers and students. Teachers could use these activities and data sets to supplement their classroom, while students could use the worksheets and applets to further their understanding in an introductory or AP level statistics course.