Pythagorean Proof

Here is a simple proof of that right angle formula we all memorize in geometry and algebra!  Best of all, I was able to make this video using my new tablet toy and a free program called TuxPaint.

The Pythagorean Theorem

limit of (1-cosx)/x as x approaches 0 =0

A new video with another limit proof!

We can use the last proof of 

limit of sinx/x as x approaches 0 =1

 to help prove another "famous" proof

 limit of (1-cosx)/x as x approaches 0 = 0

I used my new tablet and an easy to use program called Skitch to create this.

Proof of limit of sinx/x as x approaches 0

Just bought a tablet to try making videos as part of my flipped classroom experiment.  Since I am working on studying for the math CSET III, I though I would try my hand at a well known calculus proof. 

Limit of sinx/x as x approaches zero

Learning about solids of revolution in Calculus can be confusing, especially if you have learned two different methods (often called the disk and shell methods).  Below is a concept map created in Bubbl.us to help students understand which would be easiest to use. You will have to zoom in to see all of the writing. You can use your mouse to move around the content.

Pythagorean Theorem

Go on a quest to explore the Pythagorean Theorem 
and learn that Pythagorus isn't the only one who discovered the beautiful connection between the sides of a right triangle.

Watch on Khan Academy

Read on Wikipedia

Explore on pbs

Read about different cultures and the theorem

Chinese Proof

Hint

visualizing 1

visualizing 2

visualizing 3

pbs ladder and baseball problem

braining camp

History of Math
Timeline of a section of history using Time Toast http://www.timetoast.com/

Slope Intercept form of a Line

Web 2.0 Evaluation of GeoGebra

GeoGebra is a free program that integrates geometry, algebra, and calculus.  It runs on any platform that supports java.  GeoGebra can be used for teacher presentations, simulations, and both student and teacher authoring.  GeoGebra allows for students to explore a concept in depth and with a visual approach.  Time is reduced in modeling and exploring, and students are allowed to discover patterns and connections.  Students and teachers are able to use this a collaboration tool and can share what they have learned, although embedding a project onto websites or in blogs requires more technology knowledge.  GeoGebra is a powerful program and moderately easy to use.

For teachers, GeoGebra can be used to decrease modeling time, increase motivation, and engage them in critical thinking.  Teachers can show geometric constructions, calculating the area under a curve, and manipulation of parent graphs with ease rather than relying on tedious pencil and paper methods.  Students are able to receive immediate feedback as the equation changes (by changing the slope of a line or the vertex of a parabola.) Using visual representations gives teachers another method to reach students who are visual learners, and for others, it encourages full understanding of a concept.  Not only are students able to see the visual representation, but also they are able to discover patterns by manipulating variables and receiving immediate visual conformation.   

GeoGebra can also be used a student authoring tool.  GeoGebra allows students to explore real life applications and discover patterns in self-directed projects.  Since it easily models equations, calculations involving long decimals and complex calculations are not a deterrent.  The interactive and student led nature of the program increases the control the student has over their own learning as well as the motivation.

Since GeoGebra runs on a Java application it has a tendency to lag.  However, it can be downloaded to your computer and use it without connecting to the Internet.  GeoGebra is moderately easy to use and is fairly intuitive using buttons to represent actions (the text buttons have ABC written over them and the move button is represented as an arrow.)  Any questions on how the program works can be answered in the clear tutorials on the website as well as on YouTube.

Teachers and students can use created applications to share their knowledge.  GeoGebra has a site where projects can be downloaded and used by the online community.  The site is easy to use with a vast source of material available for a variety of math concepts.  If teachers or students want to embed a project into their websites or blogs, the process is more complicated, but achievable.

Overall, GeoGebra is a helpful tool when teaching mathematics.  It gives teachers a way to easily model concepts.  Students are able to be part of discovering patterns in mathematics, as well as receiving immediate visual feedback.  This tool will be especially useful with the problem solving emphasis of the Common Core Standards.  Both students and teachers can use the program to create their own projects with relative ease.  They are also able to access a variety of resources on the website using this program. 

I have created a new applet using Geogebra so that students can use sliders to change the slope and intercept of a line and receive immediate feedback. This applet requires that java is enabled. Use the sliders to change the slope and/or intercept of the line to see how it changes.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com