Objectives:
1) To learn all the components of the coordinate plane
2) To be able plot a point on the coordinate plane
3) To construct a scatter plot and use the data in an application problem
1) To help the students learn the various components of the coordinate plane, I would give each student a handout containing a large coordinate plane. As we discussed each component, they could label these on their handouts. There are several things to discuss here. First, talk to the students about the origin, the point (0,0). Now, discuss with them the x and the y-axis. Don't forget to talk to them about the quadrants and the value that x and y take in each quadrant. For example, in quadrant I, the x and the y value will be positive; in quadrant II, the x value will be negative and the y value will be positive. The students will be able to discover this on their own if you allow them. (If you have a pull down coordinate plane, as I do, you can use this as your teaching tool or you can use an overhead transparency of a coordinate plane.)
2) To teach the students how to plot points on the coordinate plane, the first thing is to teach them what an ordered pair is. The most important thing for them to learn here is that in an ordered pair, the x value comes first and the y value comes second. Using the same coordinate plane from above, or possibly a second one that is one the back of the first, have them plot a few points. I would give them 9 points: two points from each quadrant and the origin. Once they have completed this, you could some students come to the front and using the grid in GSP, have those students plot the 9 points. Each student can use this as a self check of their own work.
3) The rest of the instruction time would be devoted to applications. Take applications from your text or make up your own. Have the problems be so that the students have to take some data, make a grid, plot the points, and then use the data to answer some questions. A problem that I came up with follows. Feel free to use it in your classroom.
A football coach is looking at the plays the team ran the previous night in their win over their in-town rivalry. There are two plays that he called a good bit and he wants to know how many yards the team got each time they ran each play. The first play that he looks at is called 44 Fullback Lead. The second play is called 88 Bootleg Keep. Here is the number of times each play was ran with the amount of yards that each play made.
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1) Make a scatter plot for each play.
2) In general, how did each play do as the game went on?
3) If the coach had called each play again, how many yards do you think each play would have gained?
4) Were there any plays that did not follow the general trend? If so, what are some explanations for these particular plays?
5) Which play should the coach have called more at the beginning and which one should he have called more towards the end of the game?
If the students have access to graphing calculators, the scatter plots could be constructed using those.