Students will complete several activities that involve coordinates and graph paper.
For each student:
Additional Resources
Book
Analytic geometry, the branch of geometry that deals with lines, curves, and geometric figures plotted on a set of axes using coordinates, was first developed in the 17th century by the French mathematicians Pierre de Fermat and René Descartes.
You can use a coordinate grid to locate points on the plane. The x-axis and the y-axis are number lines. They intersect at right angles at their zero points, the origin. Any point can be located using an ordered pair. The first coordinate tells you how far to move on the x-axis from the origin. Coordinates of points to the right of the origin are positive numbers. Coordinates of points to the left are negative numbers. The second coordinate tells you how far to move on the y-axis from the origin. Coordinates of points up from the origin are positive numbers. Coordinates of points down from the origin have coordinates that are negative numbers.
Students should understand the following vocabulary for this activity:
number lineA line that shows numbers in order.
positive numbersNumbers greater than zero.
negative numbersNumbers less than zero.
coordinate gridA set of lines used to locate points on a plane.
x-axisThe horizontal axis on a coordinate grid.
y-axisThe vertical axis on a coordinate grid.
originThe point (0,0) where the x- and y-axes of a coordinate grid intersect.
quadrantsThe four regions (labeled by Roman numerals) into which the two axes of a coordinate grid divide the plane (labeled in counter-clockwise order with quadrant I in upper right corner).
ordered pairA pair of numbers used to locate a point on a coordinate grid. (The x-axis coordinate is always first because x comes before y alphabetically.)
coordinateOne of the numbers in an ordered pair.
x-coordinateThe first number in an ordered pair, locating a point on the x-axis of a coordinate grid.
y-coordinateThe second number in an ordered pair, locating a point on the y-axis of a coordinate grid.
4. Communicate mathematically.
Invitation to Learn
Suppose you are having a birthday party and a friend you have
invited has asked you for directions from the school to your house. You
tell them it is five blocks away. Is this enough information for them to
find your house?
Instructional Procedures
Family Connections
Evaluate students understanding of the objective(s) using the following rubric: | |
4
Full Accomplishment |
Student accurately plots points and reads the coordinates of points on a coordinate grid. |
3
Substantial Accomplishment |
Student plots points and reads the coordinates of points on a coordinate plane, but not always accurately. |
2
Partial Accomplishment |
Student has difficulty plotting points and reading the coordinates of points on a coordinate plane. |
1 Little Accomplishment |
Student does not plot points or read coordinates of points on a coordinate grid accurately. |
Have students draw a four-quadrant grid with all quadrants labeled. Then plot two given points in each quadrant and label them with the correct ordered pairs. Example: A(3,5); B(3,-4); C(0, 4); D(-2,0); etc.
Research Basis
Johnson, D. & Johnson R. (1975). Learning together and Alone: Cooperation, Competition, and Individualization. Englewood Cliffs: Prentice Hall.
In general, organizing students in cooperative learning groups has a powerful effect on learning regardless of whether groups compete with one another.
Kagan, S. (1992). Cooperative Learning. San Juan Capistrano, CA: Kagan Cooperative Learning.
Cooperative learning increases communication, trust, leadership, decision-making, and conflict resolution.