# CARTESIAN COORDINATE SYTEM!!!

Introduction

CARTESIAN COORDINATE SYTEM

In math, there is often a need to plot points on a chart or grid.  Think about points on a map.  To find a particular point, it would be helpful to start in a corner, and then know how far to the right to move, and how far up.  In math, we have a system that works like this.  It's called the Cartesian Coordinate System, in which we use what are called X and Y coordinates to help identify a point.

Look at the diagram at right.  The horizontal line along the bottom is called the X-axis, and the numbers on that line are called X-coordinates.  The vertical line at left is called the Y-axis, and the numbers on that line are called Y-coordinates. All of this should bememorized.  To identify a point on the grid, we always list the X-coordinate first, followed by the Y-coordinate.  We put these coordinates in parentheses, like this:  (x, y).

Let's find the coordinates of the points on the grid at right.  The square is at (1, 3).  We move 1 unit to the right, and then 3 units up.  The circle is at (2, 4).  The star is at (3, 1), and the triangle is at (5, 2).  Note that had there been a point in the very lower left hand corner, its coordinates would have been (0, 0).  This is only a very basic introduction to the Cartesian coordinate system.  You'll learn much more about it later.

Rene Descartes indeed is correct when he said, "I think, therefore I am."

Students will be working in a group of 4 and will be conducting an investigation about cartesian coordinate sytem. Each member of the group has a role on their given task as follow:

1. Researcher- responsible for identifying the task and determines the steps necessary to solve the problem, sort out all information from the given link to address the given problem and relay the same information to the note taker.
2. Note Taker- highlights the information relayed and identify which of these informations are necessary to address the problem.
3. Time Keeper/Organizer-tracks record of the time by checking the number of minutes left and identify the duration and length of time to work on the problem and organize the different steps in solving the problem
4. Presenter-presents the group's work and discuss the different steps taken to solve the problem.
Process

Step 1 The teacher will write the aim and the objective on the board and give the students a bird's eye view of the activity related to the lesson and will write the terminologies on the board (quadrants, abscissa, ordinate, origin, x-axis, and y-axis). Teacher will then divide the class into several groups with atleast 4 members for each group. Each member of the group will have a role of the activity as follow: researcher, note taker, time keeper/organizer, and planner. Every roles will be defined by the teacher and the expectations for each group will be discussed. The following questions will be used to guide students in their investigation

What is a cartesian plane?

What are the sections formed by the intersection of the two major vertical and horizontal lines?

http://www.mathopenref.com/coordintersection.html

What are the coordinates of a point?

http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/geometry/basic.html

Graphing points and line in two dimension

Step 2 Group Work- students will use the link below to aid them in their investigationhttp://www.purplemath.com/modules/plane.htm and http://www.mathsisfun.com The teacher will be supervising the students' work and evaluate the work of every group. Teacher will make sure that each member of the group will do their assigned roles.

Step 3 Presentation- Each group will have a presenter and present the result of their investigation. The presenter will first discuss the problem, then explain the steps and the procedures taken to address the problem and present their recommendations to the class. Questions will only be entertained only when the presenter is through with his or her presentation.

Step 4  Wrap Up- Teacher will summarize the activity through question and answer and make an overall evaluation of the activity.

Conclusion

Cartesian plane has so many practical uses in the 21st century. We use grids to locate a certain country either in a regular map or a three-dimensional globe. Our GPS which is vital for navigating the streets and mapping traffic and rerouting are few of the highly sophisticated applications of the cartesian plane.

Rene Descartes' infusion of geometry and algebra contributed to the exponential growth of human development. It seemed more than a century discovery but proved to be a lifetime advantage to our fast growing wolrd.

Indeed true that "I think, therefore I am."

Teacher Page

Webquest is a very powerful tool to differentiate instruction. It increases students' engagement of the lesson, which is actually one of our primary goal. Through discovery approach, students will find learning as fun and not just as a prerequisite to diploma but to success.

21st century learners are fun to deal with. And to better equip them with the challenges of this world is to feed their minds using whatever available resources we have in the class, and much better if we fully maximize the use of technology in the class.  And for a sample lesson and sample activities, are they not available online?