Background Information
An initial and very powerful purpose of coordinate graphing is that it permits one to "find one's way around" in two-dimensional space. Students learning about Cartesian graphs already know how to find their way around (right
and left on a number line and up and down on a thermometer) with single-number coordinates. A way to motivate students to discover the need for paired coordinates could be to ask students who are unfamiliar with ordered pairs how to locate a point to the right and up from an origin, for example. The discussion could highlight the need for mutual agreement regarding the direction of movement indicated by the first coordinate and the direction of movement
indicated by the second coordinate.
Furthermore, finding one's way around in a playful context like dot-to-dot pictures can be explored. Why, if at all, is using coordinate pairs for vertices of a picture preferable to the dot-to-dot method employed by young
schoolchildren who connect points labeled with successive natural numbers with line segments?
Although both activities direct the student along a path in the plane, the dot-to-dot activity is essentially recursive in nature, relying only on the student's counting ability, and has a localized application -- that is, the
graph can be created only on the page where the dot-to-dot pattern is printed. The coordinate version of this activity, however, is more explicit in nature, in that each point is plotted with respect to the origin rather than to the point preceding it. Furthermore, the power of the coordinate approach is that from the list of coordinates alone, the graph can be transferred to any setting - another student, a computer program, or even the wall - where a coordinate plane is established.
Introduction
Ask students why city maps use a letter and a number for locations. Students will probably reply with something like, "To make the location more precise" or "Because location on a map is two dimensional."
Using local or famous city maps, students can work in pairs to find well-known landmarks. One student can locate the landmark and the other can give the map coordinates. Or, one student could give coordinates, and the other student can state what landmark(s) can be found within those coordinates.
Graphing Ordered Pairs on the Coordinate Plane
Students should open the Simple Plot Applet. Students will be working individually for this part of the lesson. The applet allows students to enter ordered pairs, and then the computer plots them for the student.
(It is important for students to see that the scale on the axes can change, and students need to be aware of what the hash marks on each axes really mean.)
Stating the Coordinates Given Points on the Coordinate Plane
Students should open the Coordinates Game Applet. Students will be working individually for this part of the lesson. The applet gives the student a point (by placing a picture of a house at an exact location.) The student then enters the coordinates and checks to make sure they are correct.
Alternatively, students may use the following to achieve the same goals: The Coordinate Plane Applet.
Using the Coordinate Plane to Create Geometric Figures
Each student should be given several pieces of graph paper and draw the horizontal and vertical axes using a rule. Next, draw one of each shape listed below on a separate graph:
- Square
- Rectangle
- Triangle
- One polygon of their choice
Students can work with a partner and trade pictures. The other student can first verify whether or not the four correct pictures were drawn and then state the coordinates.
