This lesson teaches students about the coordinate plane and its components. The students will: 
- learn the vocabulary for the coordinate plane (x-axis, y-axis, origin, x- and y-coordinates, ordered pair). 
- learn the fundamentals of using the coordinate plane to locate points. 

- How do spatial relationships, such as shape and dimension, help to create, construct, model, and portray real-world situations or solve problems? 
- How may geometric properties and theorems be utilized to describe, model, and analyze problems? 
- How may using geometric shape features help with mathematical reasoning and problem solving? 

- Coordinate Plane: Formed by the intersection of two number lines (called axes) that meet at right angles at their zero points. Used to locate points in the plane or in space by means of two numbers that represent the distance the point is from the horizontal axis and the vertical axis. 
- Origin: The point at which the number lines of a coordinate plane intersect. As an ordered pair, the point (0, 0). 
- x-Axis: The horizontal number line of a coordinate plane. Used to show horizontal distance. 
- x-Coordinate: The first number in an ordered pair, it designates the distance a point is along the horizontal axis. 
- y-Axis: The vertical number line of a coordinate plane. Used to show vertical distance. 
- y-Coordinate: The second number in an ordered pair, it designates the distance a point is along the vertical axis.

- copies of Map of Australia (M-5-3-1_Map of Australia) for each student
- a large version of the map of Australia or one that may be projected onto a screen or smart board

- Students are evaluated based on their completed map of Australia, which serves as an exit ticket.

Scaffolding, Active Engagement, Metacognition, and Modeling 
W: The lesson teaches students to locate points on a map or coordinate grid. Students will become acquainted with the basic vocabulary for a coordinate plane and ordered pairs. 
H: The lecture engages students by describing a secret location using clues. Students predict the location and can revise their guesses as the number of possible locations shrinks. The guessing game continues until students can uniquely identify the secrete place chosen. 
E: Students have hands-on experience with the coordinate plane, studying gridlines and intersections. They learn that lines and coordinates do not always determine a point (unless coordinates are correctly ordered). Students reach these realizations on their own, and at the end of the lesson, they are given definitions for the topics they have learned. 
R: Students will review what they have learned about ordered pairs and coordinate plane concepts by exploring the map of Australia. They will evaluate and transform clues such as "bottom half" into math-specific descriptions based on ordered pairs, etc. 
E: In Activity 2, students will self-evaluate by describing points on their maps with a partner. Students' comprehension can be measured by observation as they label the various parts of their map in Activity 3 and the use of an exit ticket. 
T: The Extension section provides options for modifying the session to match students' requirements. The Routine part allows for the incorporation of lesson themes into other classes throughout the year, keeping students engaged with the coordinate plane topic. The Small Group section provides students with additional possibilities for practice or instruction. The Expansion section includes ideas for students who have mastered the course concepts and want to go above and beyond the standard requirements. 
O: The lesson opens with the popular interactive game, "What am I thinking of?" This engages and draws students into the lesson. Subsequent exercises transition from working with the full class to working in pairs, allowing students to complete their exploration of how to express the map mathematically. The class concludes with students working independently, consolidating their findings by connecting them to mathematical concepts and definitions. 

Activity 1

Give each student a copy of the map of Australia (M-5-3-1_Map of Australia).

"Does anyone know what this is a map of?" (Australia) 

"I'm thinking of a location on your map and will provide you with clues to help you find it. My first hint is that I am thinking of an island—but not the largest island on the map. Does anyone have any ideas regarding where I'm thinking of?" (Yes) 

"Compare with your partners. Tell them where you think it is, and see whether you all picked the same location. Has everyone chosen the same location?" (No) 

"Why not?" (Because the initial clue was not very good or detailed enough, and there are several islands, etc.)

"Okay, here's a second hint. Don't forget that the first clue was that I'm thinking of an island that isn't the largest on the map. My second hint is that the island in question is located on the map's bottom half. Does anyone have any ideas regarding where I'm thinking of?" (Yes) 

Have students compare themselves to their partners and ask the same questions. Then, add a third clue, telling them not to forget about the previous two. 

"The place I'm thinking of is on the right-hand side of the map."

Repeat the same questions and comparisons.

"Notice the numbers on both sides of the map? The location I am thinking of is between the numbers 20 and 25 on the map." Here, students may question, "Which 20 and 25?" Even if the other hints indicate that the x-coordinates 20 and 25 are the only possible options. If they do ask, explain that because the numbers 20 and 25 appear in several locations, you will need to be specific. "The place I'm thinking of is between the numbers 20 and 25 on the bottom of the map." 

Repeat the same questions and comparisons. 

"The place I'm thinking of is on the line numbered 4 on the left-hand side of the map."

Repeat the same questions, but keep in mind that the majority (if not all) of the students should have recognized the island at (21, 4). 

"So now we know where I was thinking, but it took 5 hints to get there. That isn't really useful, especially when we have this map with all these numbers on it. What if I had only given one hint: my island is on line 21 at the bottom and line 4 on the left-hand side? Is it enough information to identify the 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 collaborate with a partner. Each student should choose a location on the map where two numbered lines cross. Students should next tell their partners the numbers of the two lines on the map that show 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." 

Students should complete this activity several times until they can quickly describe and identify locations on a map.

Activity 3

Tell students that you've chosen a secret location 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 have already seen that lines 15 and 10 meet at two intersections.

"When you were working with your partner, you mentioned that the 15 was at the bottom of the map and the 10 was on the left-hand side. So it's critical that we add that information; simply stating '15 and 10' does not uniquely identify a spot on the map. When describing locations on grids or maps like this, we usually begin with the number at the bottom of the grid and then move to the number on the left side of the map. So, knowing that, place your finger on (15, 10)." Ensure that students have accurately recognized the location.

"We have names for grid parts like this. The x-axis runs along the bottom, whereas the y-axis runs up and down." Point these out on an overhead projection of the handout so that students can easily 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, explain that the word "origin" means beginning, and that the origin of a coordinate plane is where the x- and y-axes begin.

"We now know that there are two axes: x-axis and y-axis. If I were to offer you two numbers to identify a location on a map, which number do you think I should give you first: the x-axis or the y-axis?" Students may have varied reasons for choosing which one to begin with, but highlight that we provide the numbers in alphabetical order, therefore we always begin with the number along the x-axis.

"I might claim my secret location is at (19,13). In this situation, we refer to the 19 as the 'x-coordinate' (the first number), and the 13 as the 'y-coordinate' (the second number). Remember that the x-coordinate tells us how far to go along the x-axis at the bottom of the map, while the y-coordinate tells us how far to go up the map's side. Go ahead and mark (19, 13) on the map." Also, write (19, 13) on the board to demonstrate how to identify a point using coordinates.

"When we write (19, 13), we refer to it as an ordered pair. Why is it called an ordered pair?" Encourage students to see that it is (clearly) a pair of numbers and that the order is significant; changing the order results in a different place. 

Write the terms covered in the lesson on the board in no particular order: x-axis, y-axis, origin, x-coordinate, y-coordinate, ordered pair. Students should put (10, 16) at the top of their map and then identify each section of their map, or the ordered pair (10, 16), using the terms on the board. They should also find the coordinates (10, 16).

Finally, write the term coordinate plane on the board and explain to students that it refers to the entire grid. 

Check students' properly labeled coordinate plane maps as a exit ticket, but allow them to keep it as a reference in the future.

Extension:

Use the strategies listed below to adjust the lesson to your students' needs throughout the year.

Routine: Later in the year, this lesson can be repeated with different maps, particularly maps of (part of) the town where students live. Students can select sites on the map, describe them to other students, and offer coordinates for existing locations. Students can practice ordered pairs with this online game: http://www.math-play.com/Coordinate%20Plane%20Game/Coordinate%20Plane%20Game.html. 

Small Group: Students can work in small groups to complete Activity 2 while using ordered pairs and suitable vocabulary throughout the extension. Students can find places on an Australian map (or another useful map) and practice naming coordinates. They can also describe how to find a point on a coordinate plane, such as "move along the x-axis 7 units and then up the y-axis 4 units." The video at http://www.teachersdomain.org/resource/vtl07.math.geometry.pla.coordingrd/ provides additional teaching.

Students can receive more practice with the following online game: 

http://hotmath.com/hotmath_help/games/ctf/ctf_hotmath.swf 

Expansion: Students can be exposed to noninteger coordinates as well as the other three quadrants by using negative numbers, a concept that students are more likely to understand when represented by a map, which is effectively two juxtaposed number lines. Students can practice mapping ordered pairs in quadrants II-IV using the following online game: http://www.funbrain.com/cgi-bin/co.cgi