Introduce Coordinates

Est. Class Sessions: 2–3

Developing the Lesson

Introduce Coordinates. Introduce the lesson by reading the vignette in the Great Barrier Reef section in the Student Guide which sets up the context for work with the coordinate system. You can use a map or globe to remind students of Australia's location.

The Great Barrier Reef. The Great Barrier Reef, off the coast of Australia, was discovered in 1770 by Captain James Cook. It is made of coral and is surrounded by tropical fish and other marine life. While the coral can appear rock-like, the reef is a living thing. Coral are rock-like structures formed by small marine animals that live in colonies. The structures provide habitat for a diverse population of fish, crustaceans, microorganisms, and other wildlife. The reef is considered an Australian National Park.

Maps and Coordinates on a Globe. Since the earth is not flat, it is not possible to map large portions of the planet using Cartesian coordinates. For example, longitude lines are not really parallel—they meet at the north and south poles. However, as long as we look at a sufficiently small region, the earth appears to be flat and Cartesian coordinates can be reasonably accurate.

Explore the Great Barrier Reef. Direct students' attention to Exploring the Great Barrier Reef using Cartesian coordinates section in the Student Guide. This map shows one section of the Great Barrier Reef covered by a grid system known as Cartesian coordinates. Use a world map or globe to show the relative location of Australia and the Great Barrier Reef.

When looking at the coordinate axes, it is important for students to view the axes as number lines on which they can move back and forth. They should also note that the axes are identified as the x-axis and y-axis.

If your classroom has a tiled ceiling, place stickers on your ceiling at or near the tile intersections. Then have students look at the ceiling. Use a flashlight or laser pointer as you tell the story of how some people believe René Descartes developed the Cartesian Coordinate System while lying in bed one day watching a fly move about his ceiling. Have your students describe the location of your “fly” on the ceiling using the ceiling tiles as a guide. You can then use the flashlight to move the “fly” to another location for students to describe.

After reading about the Great Barrier Reef, Questions 1–4 in the Student Guide help students understand the process of locating places on the coordinate plane using ordered pairs. In an ordered pair, the “x” coordinate is shown first, followed by the “y” coordinate. For example: (3, 2) means a location 3 spaces to the right of the origin (0, 0), and 2 spaces above the x-axis. In earlier grades, students referred to directions as right/left and front/back of the origin. Since the example involves a map, it is also appropriate to talk about 3 units east and 2 units north.

Ask:

How is the x-axis on the grid like the number lines we used in Lesson 1? (Possible responses: the x-axis is just like a number line with positive numbers to the right of 0 and negative numbers to the left of 0.
If you move 3 units to the right of 0 (the origin) on the x-axis and 1 unit north, what would be the ordered pair coordinates? (3, 1)
What island is located at these coordinates? (South Molle Island)

In Questions 5–10, students find locations based on given coordinates and locate points on the Great Barrier Reef in the first quadrant, with positive xand y-coordinates. Use a display of the Great Barrier Reef Map Master to help facilitate discussion of these questions.

Expand Grid to Four Quadrants. In Questions 11–12, students are challenged to describe the location of a town that is not within the first quadrant. Ask a few students to share their ideas before you use a display of the Quadrant Overlay Master or the Great Barrier Reef Map with Overlay Master to extend the coordinate grid.

Ask:

How will this expanded grid give us a more accurate location for Rockhampton? (Possible response: I can now locate Rockhampton exactly on the map and tell its distance from the origin.)
What do you notice about the x- and y- axis when we expand the grid to 4 quadrants? (The x-axis is a number line with both positive and negative numbers: positive numbers are to the right of the origin, and negative numbers are to the left of the origin. The y-axis is a vertical number line, with positive numbers above the x-axis and negative numbers below the x-axis).
Describe the location of Rockhampton. (It is 3 units east and 5 units south of Mckay, or the origin.)
What are the coordinates for Rockhampton? (3, −5).
What are the coordinates for Jericho? (Jericho is 7 units west and 6 units south of Mackay, or the origin. Its coordinates are (−7, −6)).
What are the coordinates for Townsville? (−5, 5)
Where is Townsville from Mackay? (Townsville is 5 units west and 5 units north of Mackay).

Introduce the Barrier Reef Game. Direct students' attention to the Barrier Reef Game section in the Student Guide. This game provides additional experience with the use of coordinates. Display the Four-Quadrant Grid Paper Master and tell students you are going to draw the location of objects in a Barrier Reef. Following the directions in Step 1, demonstrate how to add objects to the grid. Be sure the objects cover a few coordinate points. Give each student a Four-Quadrant Grid Paper Master and ask them to place the same objects on the grid. Students need to do this in private, as classmates will name coordinates to locate each object. Tell students to fold their Barrier Reef map in half to hide it until they are ready to play the game.

Remove your map of the Barrier Reef from the display. Ask a student to name a coordinate pair and record it in a three-column data table. See Figure 1.

Demonstrate Step 3 of the directions using the coordinates that students provided.

Ask:

Do you know where the [whales] are located?
What coordinate should you check next?

Tell students that the game would continue in this way until all the objects are located.

Play Barrier Reef Game. Arrange students in groups of three to play the game: two opponents and one moderator. Ask students to reread through the directions of the game making sure all students understand what to do. Students switch roles in the group as the games are completed.

Encourage students to place their objects in locations that have negative coordinates. Remind students that the first number in an ordered pair is always the x-coordinate.

Discuss Results of Barrier Reef Game.

Ask students to share their strategies for finding “sightings” in the game.

Did you find any strategies that would help you be successful in the game?
Once you found an object, what did you do next?
Did you have any suggestions about how you found the objects? (Possible response: test large areas at the start of the game; once an object is located, stay with the object until all of it is found.)