Graphing in four quadrants-a tool search
Recently my classes completed an exercise designed to acquaint them with graphing in four quadrants. Since it is my intention to expose students to as many resources as possible, I did a search through Math Tools to see what I could find that would be appropriate for the subject and the students.
The search parameters were:
Math 7 - rectangular coordinate geometry - all quadrants
After reviewing the materials I discovered that there were additional resources which would serve as good introductory materials and relate to what we had been doing in the classroom - specifically, under 'Math 7 - rectangular coordinate geometry - first quadrant.'
Arranging these in a lesson sequential order:
1) http://mathforum.org/mathtools/support/305/ Support Material: Introduction to the Coordinate Plane and Coordinates Discussion. This support document introduce the coordinate plane as a dialogue between student and teacher. It sets up the axis' as number lines and shows the division into quadrants. This would supplement and serve as a review to an introductory lesson
1a) http://mathforum.org/mathtools/tool/support/116/ Support Material: Lines, Rays, and Planes. This support document provides a lesson on what is a coordinate plane and how you plot points and lines on a coordinate plane. It would provide a good supplement for students to check at home/in the library to review the information covered in class. While not necessary to the development of plotting in four quadrants, it is an interesting adjunct.
2) http://mathforum.org/mathtools/tool/306/ Simple Coordinates Game (1st Quadrant only). This interactive tool allows students to either determine the coordinates of the plotted object or enter coordiantes to plot a point. All coordinates are located in the first quadrant which relates to the graphing we have done so far.
3) http://mathforum.org/mathtools/tool/312/ Simple Maze Game (1st quadrant only). This is an interactive game where the student moves the robot through the minefield to reach the target. The robot moves by plotting the next goal point as an ordered pair.
4) http://mathforum.org/mathtools/tool/315/ General Coordinates Game. This game is the same game as 2) above. The difference is the plot can occur in any of the four quadrants.5) http://mathforum.org/mathtools/tool/318/ Maze Game. This game is similar to the Maze Game above,but now the robot may move through all four quadrants.
The culminating activity for the four quadrant plots is the Dot-to-Dot picture which is a 3 part activity.
Part 1.
The guidelines for the dot-to-dot picture: Set up a piece of 1/4 inch square graph paper with an x and y axis in the center.
- 1. Must have points in all 4 quadrants
- 2. Minimum of 30 points
- 3. Points must be in order and numbered. You cannot pick up the pencil and move to another place.
- 4. Lines MUST change direction at a point (i.e., a staight line only has points at the end - no intermediary points)
- 5. Retracing a line is allowed, but remember the line must change directions at a point.
The picture must be something recognizeable. Some exclusions include:
- no logos
- no letters, initials, words
- no robots or space aliens
- no Christmas trees
- no designs
Some acceptable designs might be vehicles, buildings, plants, animals, people and cartoon type characters.
Part 2.
On a separate sheet of paper, list the numbers of the dots and the ordered pair which defines the dot. Be sure to do them in order!
Part 3.
The instructor collects the picutres and the lists of coordinates. The pictures are set aside and the list of coordinates is shuffled and redistributed to the class with a blank sheet of graph paper. Students are then to recreate the picture from the coordinates.
There are tools available which can help the student to check his/her list of coordinates and/or resolve any disputes as to whether a re-creation error. is due to the author or the person recreating the drawing.
The best tool is
6) http://mathforum.org/mathtools/tool/89/ Ordered Simple Plot. The ordered simple plotter allows the student to enter the coordinate pairs in the order of the drawing and it will plot the entered points thus revealing the accuracy of the coordinates and/or the interpretation of the recreator. Students are encouraged to use this tool to check their coordinates before they hand them in.
The major advantage of this tool is that it allows the student to enter the coordinate pair in the form x,y which reinforces the notion of the coordinate pair.
In the event that internet accessing computers are not available to the students, there is an alternative procedure using Microsoft Excel. The big difference is that in Excel you need to establish x and y as two separate columns. Once the data is entered, you highlight the data in the x and y columns and click on the chart wizard.
Next, select the chart type XY Scatterplot. From the sub-types select 'Scatter with data points connected by lines' (straight with dots) and then proceed to finish.
Below is a set of data which you can cut and paste into http://mathforum.org/mathtools/tool/89/ as an example.
NOTE: http://mathforum.org/mathtools/tool/301/ Simple Plotter
http://mathforum.org/mathtools/tool/309/ Graphit and
http://mathforum.org/mathtools/tool/264/ Data Flyer, while appearing to be similar to tool 89 DO NOT connect the dots in the order plotted.
-4,-2 1,0 1,-1 3,-1 3,0 1,0 1,-2 3,-2 3,-3 2,-3 2,-2 4,-2 4,-3 3,-3 3,-2 6,-2 3,0 3,2 4,2 4,3 3,3 3,4 2,4 2,6 3,7 0,7 1,6 1,4 -1,4 -1,5 -3,5 -3,4 -5,4 -5,5 -9,5 -8,4 -5,4 -5,2 -7,2 -7,4 -6,4 -6,2 -7,2 -7,3 -5,3 -5,0 0,0 1,-1 1,-2 0,-3 -1,-3 -2,-2 -2,-1 -1,0 -3,0 -2,-1 -2,-2 -3,-3 -4,-3 -5,-2 -5,-1 -4,0 -5,0 -6,-2 -8,-2 -8,4