An Inspiring Quote

"To teach well is easy. To teach well enough for students to understand is not difficult. But to teach so well that the student wants to learn more is the challenge."

Are you up for the challenge?

(Courtesy of Samuel)

Geometry Java Applets

The following IES website contains very good java applets for geometry investigations:

http://www.ies.co.jp/math/products/geo1/menu.html

http://www.ies.co.jp/math/products/geo2/menu.html

There are many geometric figures that can be manipulated with questions for students to think about. There are also applets on other topics such as calculus and trigonometry. The main site can be found here:

http://www.ies.co.jp/math/products/

Introduction to Coordinate Geometry

In the learning of coordinate geometry, alot of emphasis has been placed on the more abstract concepts of the topic. For instance, students are required to formulate the equation of a line from 2 points, or the gradient of a line. However, students may not have adequate understanding about the concept of the properties of a straight line. For example, what is the significance of gradient and y-intercept? Why do we need to formulate equations of lines? But most importantly, what is the use of graphs? An a example is given below to illustrate the significance of gradient and y-intercept in everydaylife.An experiment was conducted to find the speed of tennis ball in air and a distance time graph is found using experimental tools like a data logger:

From the graph, we see that the distance travelled by the ball is linearly related to the time taken. Consider the gradient in this case. How would the graph of the slow and fast moving tennis ball differ?

The gradient of the graph represents the speed of the ball, as the gradient measures the change in distance over the change in time. In other words,

gradient = rate of change of distance= speed

Hence, there is a physical intepretation of gradient of the line in this case.
From the graph, we also see that the ball does not start from rest. What is the distance travelled by the ball when the timer was started? In this case,

y-intercept = distance travelled by ball at the 0 sec

Hence there is also a physical intepretation for the y- intercept of the line.

Flatland the movie is out!

I received the following news on 28 June 2007.

Dear Flatland Movie Enthusiast,

We are writing you because some time ago you registered to receive information about Flatland: The Movie on our website. Flatland: The Movie is an exciting animated film adapted from Edwin Abbott’s classic novel, starring the voices of Martin Sheen, Kristen Bell, Tony Hale, Michael York and Joe Estevez.

We are pleased to announce that you can now order the DVD directly on our website! You may place your order securely online at the Flatland Store

http://store.flatlandthemovie.com

Currently we are taking orders and now shipping the Special Educator Edition of Flatland: The Movie. This edition is primarily intended for educators, teachers, schools and institutions. The purchase of the DVD includes a perpetual school site license, a bonus featurette discussing the 4th dimension, and math worksheets for use in the classroom.

If you are interested in the DVD primarily for home or personal use, not to worry. We are accepting pre-orders for the Home/Personal license DVD edition of Flatland: The Movie. The private home edition of the DVD naturally costs much less than the school site license. This edition will ship in the fall and you can place your order now to be the first in line to receive the movie when it ships. Your credit card will not be charged until the DVD actually ships.

Thank you for your continued interest in Flatland: The Movie!

Warm Regards,

Seth

Algebra Scale Balance

In learning algebraic manipulation of linear equations, it is important for students to try and grasp the basic concepts of balancing the equation on both sides. For instance, in the equation 2x+1=7. Students must understand why "bringing over the 1" to the other side turns it into -1. ie 2x=7-1. Students need to understand there is balancing process here so terms like "bringing over" and "cross-multiplying" should not be used first until they get the concept right. There are 4 basic balancing methods for an algebraic equation. They are as follows:

1. Subtracting both sides by the same number, Eg: 2x+1-1=7-1
2. Adding both sides by the same number, Eg: 2x+1+(-1)=7+(-1)
3. Multiplying both sides by the same number
4. Dividing both sides by the same number

I would recommend not lumping 1 and 2 as some students may not see when and what to add or subtract on both sides. An example should be given for each case.

Ample practice should be given for students to try out manipulating algebraic equations, with a mixed variety and ultimately questions that require all 4 techniques to be used successively. For 4, it should be emphasized early that dividing both sides can only be done for non-zero numbers. This can be done by the fallacy given in previous post.

A very good manipulative for this topic is the algebraic balance. A virtual one can be found here, by Utah State University.

Index Site URL: http://nlvm.usu.edu/en/nav/vlibrary.html