Activity 1
Give each student a copy of the map of Australia (M-5-3-1_Map of Australia.docx).
“Does anyone know what this is a map of?” (Australia)
“I’m thinking of a place on your map, and I’m going to give you clues to figure out what the place is. My first clue is that I’m thinking of an island—NOT the biggest island on the map, though. Does everyone have a guess about which place I’m thinking of?” (Yes)
“Compare with your neighbors. Tell them what place you think it is and see if you all have picked the same place. Has everyone picked the same place?” (No)
“Why not?” (Because the first clue wasn’t very good or specific enough, because there are many islands, etc.)
“Okay, let me give you a second clue. So, don’t forget that the first clue was that I’m thinking of an island that is NOT the biggest island on the map. My second clue is that the island I’m thinking of is on the bottom half of the map. Does everyone have a guess about which place I’m thinking of?” (Yes)
Have students compare with their neighbors and go through the same line of questioning. Then, offer a third clue, reminding them not to forget about the other two clues.
“The place I’m thinking of is on the right-hand side of the map.”
Repeat the same questioning and comparing again.
“See the numbers on both sides of the map? The place I’m thinking of is between the numbers 20 and 25 on the map.” Here, students may ask, “Which 20 and 25?” even though the other clues make it so the x-coordinates of 20 and 25 are the only possible choices. If they do ask, tell them that since the numbers 20 and 25 show up in a couple different places, you’ll need to be more specific. “The place I’m thinking of is between the numbers 20 and 25 on the bottom of the map.”
Repeat the same questioning and comparing again.
“The place I’m thinking of is on the line numbered 4 on the left-hand side of the map.”
Repeat the same questioning and comparing again, as there are still two eligible islands (at 21, 4) and (24, 4).
“The place I’m thinking of is on the line numbered 21 on the bottom of the map.”
Repeat the same questioning, but note that most (if not all) of the students should have identified the island at (21, 4).
“So now we all know which place I was thinking of, but it took 5 clues to get there. That’s not that helpful, especially since we have this map with all these numbers on it. What if I had given one clue, which was that my island is on the line numbered 21 on the bottom and the line numbered 4 on the left-hand side? Is that enough information to definitely know which island I was thinking of—even if I didn’t tell you it was an island?” (Yes)
“So, we can use those numbers on the sides of the map as a set of directions to tell someone else how to find a specific place on the map.”
Activity 2
Have each student work with a partner. Each student should pick a place on the map where two of the numbered lines cross. Students should then tell their partners the numbers of the two lines on the map that determine their location. “Make sure to explain whether your partner should look at the numbers on the bottom of the map or on the side of the map.”
Have students repeat this activity a couple times until they can quickly describe and determine locations on the map.
Activity 3
Tell students that you have picked a secret place in Australia at the intersection of lines 15 and 10. “Put your finger on the map where you think my secret place is.” Students may already note that there are two intersections of lines 15 and 10.
“When you were working with your partner, you said, for example, that the 15 was on the bottom part of the map and the 10 was on the left-hand side. So it’s important that we include that information; just saying ‘15 and 10’ doesn’t uniquely identify a point on the map. When we describe locations on grids or maps like this, we typically start with the number along the bottom of the grid and then say the number on the left-hand side of the map. So, knowing that, put your finger on (15, 10).” Make sure students have correctly identified the location.
“We have names for parts of grids like this. The line that goes along the bottom is called the x-axis, and the line that goes up and down is called the y-axis.” Point these out on an overhead projection of the handout so that students can clearly identify each axis.
“Where do the x-axis and the y-axis cross one another?” Students should identify (0, 0). “We call that point the origin.” Depending on the class, discuss that the word “origin” means beginning and the origin on a coordinate plane is where the x- and y-axes each begin.
“We now know that there is an x-axis and a y-axis. If I were to give you two numbers to identify a place on the map, which number do you think I should give you first: the number on the x-axis or the number on the y-axis?” Students may have different reasons for which one to start with, but emphasize that we give the numbers in alphabetical order, so we always start with the number along the x-axis.
“I might say my secret location is at (19, 13). In this case, we call the 19 the ‘x-coordinate’ (it’s the first number) and we call the 13 the ‘y-coordinate’ (it’s the second number). Remember, the x-coordinate tells us how far to go along the x-axis, on the bottom of the map, and the y-coordinate tells us how far to go along the y-axis, up the side of the map. Go ahead and mark (19, 13) on your map.” Also, write (19, 13) on the board so students can see how to identify a point using coordinates.
“When we write (19, 13), we call it an ordered pair. Why is it called an ordered pair?” Guide students toward the realization that it is (obviously) a pair of numbers and that the order is important; changing the order results in a different location.
Write the terms discussed in the lesson on the board in no particular order: x-axis, y-axis, origin, x-coordinate, y-coordinate, ordered pair. Have students write (10, 16) on the top of their map and then label each part of their map, or the ordered pair (10, 16), using the terms on the board. They should also locate the point (10, 16).
Lastly, write the term coordinate plane on the board and explain to students that the entire grid is called a coordinate plane.
Check students’ fully labeled coordinate plane map as an exit ticket, although allow them to keep it as reference for the future.
Extension:
Use the following strategies to tailor the lesson to meet the needs of your students throughout the year.
- Routine: Later in the year, this lesson can be reviewed using different maps, particularly maps of (part of) the town in which students live. Students can pick locations on the map and describe their locations to other students as well as provide coordinates for existing places on the map. Students may also review ordered pairs using this online game:
http://www.math-play.com/Coordinate%20Plane%20Game/Coordinate%20Plane%20Game.html
- Small Group: Students can work in small groups, continuing Activity 2 but using ordered pairs and proper terminology throughout the Extension. Students can identify points on the Australian map (or other convenient map) and practice naming coordinates. They can also describe how to locate a point on a coordinate plane, i.e., “Move along the x-axis 7 units and then move up the y-axis 4 units.” Additional instruction is available using the video at the following Web site:
http://www.teachersdomain.org/resource/vtl07.math.geometry.pla.coordingrd/
Students may get additional practice using the following online game:
http://hotmath.com/hotmath_help/games/ctf/ctf_hotmath.swf
- Expansion: Students can be introduced to noninteger coordinates as well as the other three quadrants by using negative numbers, a topic students are more likely to grasp using a model like a map, which is essentially two juxtaposed number lines. Students may practice mapping ordered pairs in quadrants II through IV using the following online game: http://www.funbrain.com/cgi-bin/co.cgi