Students will complete several activities that involve coordinates and graph paper.
Main Curriculum Tie:
Mathematics Grade 6 Apply and extend previous understandings of numbers to the system of rational numbers.
For each student:
- Treasure Island, by Robert Louis Stevenson; ISBN 0-486-27559-0
Background For Teachers:
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
Students should understand the following vocabulary for this activity:
number line—A line that shows numbers in order.
positive numbers—Numbers greater than zero.
negative numbers—Numbers less than zero.
coordinate grid—A set of lines used to locate points on a plane.
x-axis—The horizontal axis on a coordinate grid.
y-axis—The vertical axis on a coordinate grid.
origin—The point (0,0) where the x- and y-axes of a coordinate grid
quadrants—The 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 pair—A 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.)
coordinate—One of the numbers in an ordered pair.
x-coordinate—The first number in an ordered pair, locating a point on
the x-axis of a coordinate grid.
y-coordinate—The second number in an ordered pair, locating a point
on the y-axis of a coordinate grid.
Intended Learning Outcomes:
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?
- Discuss the importance of giving specific directions in real-life
situations and have students give examples to illustrate.
- Hold up a piece of graph paper and explain to students that you
can also give specific directions to find an exact location on this
piece of graph paper.
- Distribute a Coordinate Grid worksheet to each student to use
as the vocabulary is discussed.
- Introduce or review the following vocabulary: number line,
positive numbers, negative numbers, coordinate grid, x-axis, y-axis,
origin, quadrants, ordered pair, coordinate, x-coordinate,
- Provide each student with 2 sheets of 1/2-inch graph paper and
1 sheet of lined paper.
- On one piece of graph paper, instruct the students to draw and
label a coordinate grid including the four quadrants and x- and
- Students draw a simple design that extends into all four quadrants
of the coordinate grid.
Note: The design should consist of a series of dots connected by
straight lines; “dot-to-dot” style with no curved lines.
- Distribute an Ice Cream Sundae worksheet to each student as an
- On the blank side of another piece of graph paper, have students
write directions for their design, consisting of sequential ordered
pairs that, when graphed and connected with straight lines, will
duplicate their design.
- After students have completed writing the series of ordered pair
directions for their design, have them bring both the designs and
their directions to the teacher for evaluation.
- Students then exchange their directions only with another
classmate who has not seen their design. (You may want to use
privacy folders so students cannot see each other’s designs.)
- On another piece of graph paper, instruct the students to draw and
label a coordinate plane including the four quadrants and x- and
- Following their classmate’s written directions, have them graph
each ordered pair on the coordinate grid.
- Sequentially connect the points with straight lines using a ruler.
- Compare the completed design with the classmate who wrote the
directions. If their designs are not congruent (same shape and
size), have the two troubleshoot and problem solve whether the
problem was in the directions, or in the way the student read and
graphed the directions. Discuss the implications these scenarios
could have in real-world situations if either the directions were
incorrect or unclear, of if they were not followed properly (e.g. an
engineer writing directions for a mechanic to build a machine the
engineer designed, an architect drawing plans for a builder to
- Students complete the Ice Cream Sundae picture on 1/4” graph
paper as they have time.
- Treasure Island is a classic story of a search for pirate treasure.
Stevenson based the story on a map drawn by his son, Lloyd.
Read this story and create connections using coordinates and
- Make an entry in your daily math journal.
- A person who makes maps professionally is known as a
cartographer. Invite students to research maps that were made at
an earlier time and compare them to maps made today.
- Students find the location of latitude and longitude coordinates on
a world map.
- Challenge advanced learners to draw and write directions for a
more complicated design on 1/4” graph paper.
- Play Battleship as a family to reinforce the idea of coordinate
grids and ordered pairs.
- Locate streets on a map of your city using coordinates.
|Evaluate students’ understanding of the objective(s) using the following
|Student accurately plots points and reads the coordinates of points on a coordinate grid.
|Student plots points and reads the coordinates of points on a coordinate plane, but not always accurately.
|Student has difficulty plotting points and reading the coordinates of points on a coordinate plane.
|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.
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
Kagan, S. (1992). Cooperative Learning. San Juan Capistrano, CA: Kagan Cooperative
Cooperative learning increases communication, trust, leadership,
decision-making, and conflict resolution.
Created Date :
Feb 27 2006 12:19 PM