Math is composed of building blocks. Students learn to manoeuvre the coordinate plane, and then advance to transformations and beyond. Prior to middle school, students typically have experience working solely in the first quadrant of a Cartesian grid. In middle school, they use positive and negative numbers to plot points in all four quadrants. Students learn best when they are actively involved. Teach the basics of the coordinate plane, and then introduce students to engaging activities.
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Middle-school students want to know how math is used in real life. Show them the "Introduction to Coordinates" (mathcrush.com/graph_worksheets.html) video by Math Crush. They will see several links to real-life applications. Accompanying worksheets are available.
You will need a large area for this activity. Using the floor as a canvas, make a four-quadrant grid with duct tape. Place the students in two teams. Call out an ordered pair for a team member to locate. If he is correct, the team receives two points. If he has to solicit help, he gets one point. Alternate play until one team reaches twenty points. This is especially effective for slow learners, who typically need kinetic involvement.
Print the directions for coordinate grid pictures from Super Teachers Worksheets (www.superteacherworksheets.com/ordered-pairs.html). The easy and intermediate selections involve only the first quadrant. The advanced option uses all quadrants. As students plot the ordered pairs in sequence, a picture unfolds.
Billy Bug 2
Students move around the four quadrants of the coordinate plane with this online activity from Oswego (www.oswego.org/ocsd-web/games/BillyBug2/bug2.html). Users are given ordered pairs, using numbers from -5 to 5. They press the arrows to move to the requested positions on the grid. This activity helps students feel comfortable with four quadrants.
This online practice from Beacon Learning Center (www.beaconlearningcenter.com/weblessons/gridgraph/default.htm) provides questions similar to those on standardised tests. Students are given letters on a coordinate plane and must name the corresponding ordered pairs.
In this online game from FunBased Learning (funbasedlearning.com/algebra/graphing/points/), the user receives a list of ordered pairs. He must choose the pair that corresponds to the mole's position on the grid. The easy level has an introduction and a tutorial; it is a good choice for remedial classes. The medium level might be the best starting point for average students. The hard level is fast-paced and should be used as a challenge for accelerated students.
Geoboard and Rubber Bands
Students work with pairs. Each pair needs a large geoboard or four small geoboards to represent the four quadrants of a coordinate plane. Students are given rubber bands and asked to create several shapes on the geoboards. Shapes could include polygons, such as a triangle, rectangle or hexagon. They form the polygons and list their coordinates on paper.
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