Students will learn about Rene Descartes (the founder of analytic geometry) and the connection between the Cartesian coordinate system and math.
Invitation to Learn
- The Fly on the Ceiling,
a Math Reader
- Graph Paper A (pdf)
- Object that will stick on
Getting to the Point
- The Coordinate
- X/Y-axis Dry Erase Mats
- Key Graphing Cling
- Marking pens
- Paper strips
- Metal brads
- Coordinate Cards (pdf)
Points of Interest -Coordinate Activity Stations
The Fly on the Ceiling, a Math Reader, by Julie Glass; ISBN 0-679-98607-3
Math Dictionary-The Easy, Simple, Fun Guide to Help Math Phobics Become Math Lovers, by
Eula Ewing Monroe; ISBN 978-1-59078-413-6
Mathematicians are People Too, (Vol. 2), by Luretta Rimer; ISBN 0-86651-509-7
Background for Teachers
Coordinate graphs are very important since they are the place
where algebra and geometry come together.
In the 1600s, Rene Descartes, the French philosopher,
mathematician, and scientist, founded analytic geometry and originated
the Cartesian coordinates. He is given credit for coming up with the
two-axis system we use today. The story goes that he was lying in bed
and watching flies crawl over the tiles on the ceiling. He realized that
he could describe a flys position using the intersecting lines of the
tiles. The coordinate plane is often called the Cartesian plane after
The coordinate plane is divided into four quadrants, which are
labeled with Roman numerals. In the fifth-grade math curriculum,
the students need to know how to locate and write points defined
by ordered pairs of integers in all four quadrants. The center of the
coordinate plane is called the origin and has the coordinates of (0, 0).
The ordered pairs are referred to as coordinates. We write a points
coordinates inside parentheses, separated by a comma like this: (5, 6).
The first number in an ordered pair is called the x-coordinate. The
x-coordinate tells us how far from the origin the point is along the xaxis
or the horizontal number line. The second number is called the ycoordinate.
The y-coordinate tells us how far from the origin the point
is along the y-axis or the vertical number line.
Invitation to Learn
This invitation to learn, allows you to assess the level of students
mastery in locating an object on a coordinate plane using ordered
- Have a student throw an object that will stick to the board.
- Challenge the students to identify the exact location of the
object on the board. Allow time for a short discussion, but try
to do as little leading as possible.
- Project transparency of the Graph Paper A on board.
- Have a student throw object on to the projected Graph Paper A.
- Again challenge the students to identify the specific location of
- If the students suggest numbering the Graph Paper A, and
using ordered pairs, follow through on their ideas. Let them
know that they arent the first to come up with this idea; Rene
Descartes discovered this concept over three hundred years ago.
Read the book, The Fly on the Ceiling, a Math Reader.
- If they are unable to figure out what to do, proceed directly to
reading The Fly on the Ceiling, a Math Reader by introducing
Rene Descartes, a man who discovered a solution to this
problem over three hundred years ago.
- After reading the book, repeat the activity using what they
learned from the book.
Getting to the Point
- Share The Coordinate Plane PowerPoint with students
introducing them to the coordinate plane with the correct
vocabulary. Use the key points to review main ideas.
- If youre unable to access the PowerPoint, use the Key Graphing
Cling and introduce the following key points.
Plane: a flat surface that goes on forever in every direction
Coordinate plane: made up of an infinite number of points and
divided by two number lines
Point of Origin: where the two number lines meet
Axis (plural is axes):
- x-axis: the horizontal line; east of the origin is positive while
west is negative.
- y-axis: vertical line; north of the origin is positive while
south is negative.
Quadrants: the four sections divided by the x and y axes numbered
in order from I-IV starting in the upper right quadrant and
Coordinates or ordered pair:
- the two numbers used to locate points on the plane; relative to
the point of origin
- always written in parentheses with the x-value first (x,y).
- the ordered pair for the point of origin is (0,0).
- Pass out Dry Erase Mats and using the Key Graphing Cling
- Give students two different colored strips of paper.
- Have them make two individual number lines using their mats
as a guide with 0 in the center and include both positive and
- Connect the two strips at 0 using a brad.
- Rotate the second strip 90 degrees to form the y-axis .
- Overlay these on mats.
- Begin to label the mats with markers:
- x- axis
- y- axis
- point of origin
- 4 quadrants (I-IV)
- Using Coordinate Cards, have students practice locating and
plotting coordinates on their mats.
- Check for accuracy using Key Graphing Cling.
- Working in pairs, students take turns giving and plotting
ordered pairs on their Dry Erase Mats.
Points of Interest -Coordinate Activity Stations
These activities are designed for two players each. Pass out Points
of Interest Guidelines for each team. Have enough materials at each
point for at least three to four groups depending on the size of your
class. Groups may rotate through each point independently or as
directed by teacher. After visiting all Points of Interest, have students
reflect in journals what they have learned about the coordinate plane
and locating points in all four quadrants
Point 1: Tic Tac Toe
- Tic Tac Toe game board.
- Scratch paper and pencil for each player to record their
- Play rock, paper, and scissors to determine who starts. The
winner begins the games, while the other picks X or O symbol.
- The object of the game is to get four Xs or four Os in a row
vertically, horizontally, or diagonally.
- Player one writes down the ordered pairs on scratch paper,
then points to that location. It is up to the other player to check
for accuracy before a symbol can be placed. If the point is
mislabeled, no symbol is made on the game board.
- Players take turns writing and locating the ordered pairs until
one player has four in a row.
- Students continue playing until they have played a game in all
Point 2: In Search of Buried Treasure
- The object of this game is to practice naming coordinates on a
- Each player gets one game board, In Search of Buried Treasure.
- Play rock, paper, and scissors to determine who buries the
- Player one: Hides the treasure in one quadrant by marking it
on their coordinate plane (keeps it hidden-a book works well
for hiding it).
- Player two: Guesses the location by writing an ordered pair in
the guess box on their page while telling Player 1. They then
mark it on their coordinate plane.
- Player one: Marks the same coordinates and then uses the
compass to tell Player two in which direction they must go to
find the treasure. Caution the students that if Player 1 does
not mark their partners point, they may give out the wrong
- Player two: Writes the direction in theirclue box.
- The game continues until the treasure is found.
- Players switch roles and play again using the second coordinate
Point 3: Space Wars
Point 4: Internet Games (optional)
- Object of the game is to find and destroy each others hidden
- Players each mark (vertically or horizontally only) their Fleet
of five ships on their Air Space on the coordinate plane.
There must be at least one ship in each quadrant.
- The ships should remain hidden from the opponents view. A
book works well.
- Taking turns, players call out their shots attempting to get
hits on the opponents spaceships and destroy them.
- Hits or misses should be marked on the other coordinate
- Use an X for a hit and an O for a miss.
- A spaceship is destroyed when all points on the craft are hit.
- A player wins when all five opponents ships are destroyed.
There are many sites on the internet that have interactive games to
reinforce the coordinate plane. Here are just a couple.
- Mole Game - http://funbasedlearning.com/algebra/graphing/
The students try to catch a mole located within the four
quadrants. There are three levels in this game.
Easy version of Graph Mole - If you are learning how to plot
points for the first time, try this fun and easy tutorial and game.
Medium version of Graph Mole - If you are reviewing how to
plot points, play this game.
Hard version of Graph Mole - Once you have mastered plotting
points, try this random question arcade style game.
- Maze game http://www.shodor.org/interactivate/activities/
This game lets students practice using coordinates by having
them move a robot through a mine field to a given target. The
students must specify the coordinates of the new location. In
order to win, the path must not cross a mine. Challenge the
students to place more than five mines. Use the Help tab on
this site for instructions.
- Art: Have students create simple drawings using coordinates for
other students to recreate.
- Place Points of Interest -Coordinate Activities in centers for
students to continue working with coordinates.
- If students have access to the internet have them play the games
found on the internet.
- Play any of the activities from Points of Interest with family.
- In their math journals, have students write what they have
learned about the coordinate plane and locating points in all
- The Coordinate Plane Assessment worksheet
Irwin, K.C., (2001). Using everyday knowledge of decimals to enhance understanding.
Journal for research and mathematics education. 32(4). 399-420.
This study investigated the role of students everyday knowledge
of decimals in supporting the development of their knowledge of
decimals. One group worked with problems presented in familiar
context, the others were given no contextual connections. The
students ability to make connections between the known and
unknown greatly enhanced their understanding of mathematical
concepts. Presenting students with real life applications is important
when being challenged with new concepts.
Furner, J. M., Yahya, N., and Duffy, M. L., (2005). Teach mathematics: Strategies to reach all
students. Interventions in school and clinic. 41(1),16-23.
In this article, the authors list 20 different strategies that can help
teachers reach all students. These strategies are based on the belief
that all students have the right to learn math and feel confident in
their ability to do math. It is the responsibility of all teachers to see
that mathematics can be learned by every student. The strategies
introduced in this article can enable teachers to accomplish this goal.