Activity 1
Depending on how long it has been since students worked with the coordinate plane, a brief review, particularly of the order in which ordered pairs are “followed” may be necessary.
Make sure each student has at least one copy of the First Quadrant worksheet (M-5-3-2_First Quadrant and KEY.docx), and each student should work with a partner.
“Take one copy of your worksheet. On the topmost coordinate plane on the worksheet, each group is going to design a map following the same instructions. During the activity, I can repeat any instructions you need, but I can’t answer any other questions. You can talk with your partner about what to do but not to any other groups.”
Read the following instructions, providing time after each instruction for students to complete the instruction.
“You are designing a map of a town you have never visited. When you get to town, your first stop is a welcome center where they provide information to tourists. This welcome center is a little unusual. They don’t have any maps of the town, but they’ll help you create your own. You’re handed a coordinate plane and a pencil and the worker at the welcome center—that’s me—starts to give you instructions so you’ll be able to find your way around town.”
“Plot a point at (4, 4) and label it Library.”
“Plot a point at (8, 4) and label it School.”
After this instruction, since it is near the beginning of the activity, it may be necessary to walk around and make sure students have correctly followed the two instructions thus far.
“Make a point halfway between the library and the school and label it Park. On the side of your worksheet, write the word Park, and then write the coordinates for the point that represents the park.” (6, 4)
“There is a farm that is 6 units above the park. Make a point to represent the location of the farm. On the side of your worksheet, write the word Farm, and then write the coordinates for the point that represents the farm.” (6, 10)
“There is a road that runs in a straight line from the Farm to the School. Draw a line to represent the road.”
“Start at the farm and travel 3 units to the left and 4 units up. There is a lake at that point. Make a point to represent the location of the lake. On the side of your worksheet, write the word Lake, and then write the coordinates for the point that represents the lake.” (3, 14)
“There is a road that runs in a straight line from the lake to the farm. The road then travels in a straight line from the farm to the school. Draw the two parts of the road using straight lines.”
“Finally, there is a road that runs in a straight line from the school to the park. Draw a line to represent the road.”
After students have finished drawing the final road, have each pair of students compare their drawing with that of another group. If their maps differ in any way, the foursome should have you repeat the necessary instructions until the larger group determines which map is correct and fixes the incorrect map.
Make sure all students have the correct map and any misunderstandings in the directions and plotting of points are corrected before continuing.
Activity 2
“In the previous activity, everyone should have ended up with the same map. The directions were specific enough that there was only one possibility for each point. In this activity, you’re going to have a little more freedom to do what you want, but you still have to follow the directions. Start on a new coordinate plane with a point at (8, 8). Label that point Library.”
“The Market is two units away from the Library in any direction you choose. Pick a point that is two units away (left, right, up, or down) from the Library and label the point Market.” Possibilities: (6, 8), (10, 8), (8, 6), (8, 10)
“The Pool is three units away from the Library and is in the opposite direction that you went to make the Market. So, if you put the Market to the left of the Library, where should the Pool go?” (To the right) “If you went up, where should the Pool go?” (Down) “Go ahead and find the location of the Pool, three units away from the Library. Plot the point and label it Pool.” Possibilities: (11, 8), (5, 8), (8, 5), (8, 11)
“The Arcade has coordinates of 10 and 2, but you can choose the order. You can choose whether the Arcade is at (10, 2) or (2, 10). Go ahead and put the Arcade on your map and label it.”
“City Hall has the same y-coordinate as the Arcade and has an x-coordinate of 7. Go ahead and put City Hall on your map and label it.” (7, 2), (7, 10)
“The last thing to put on your map is the Police Station. The coordinates of the Police Station add up to 12 and one of the coordinates is 5. Go ahead and put the Police Station on your map and label it.” (5, 7), (7, 5)
“Next to your coordinate plane, write the name of each place you graphed and write the coordinates. Remember to put the x-coordinate first and the y-coordinate second.”
Give each student the key for the activity (M-5-3-2_Activity 2 KEY.docx) which you have cut into thirds. Have students exchange and check each other’s maps and coordinates to make sure their map is correct.
Activity 3
“Now, each of you should pick a letter from your first or last name—it can be any letter you want—and we’re going to make instructions for someone to follow so s/he can graph the letter you chose. Has everyone chosen a letter?”
Once everyone has chosen a letter, continue: “Decide where you want to start drawing your letter. Remember to think ahead and make sure you have enough space on your coordinate plane to fit the entire letter. Plot the first point in your letter and, on a separate sheet of paper, write down the coordinates of the first point. Now, plot the second point and connect them with a line. Write down the coordinates of the second point underneath the first. Keep plotting points and connecting them, writing them down in order. If you get to somewhere in your letter and you don’t want the new point to be connected to the old one, write the word STOP on your paper before you write down the new point. Once you think you have all the coordinates you need so someone else can graph your letter, double-check your work.”
Once students have listed the coordinates and double-checked their work, they should give their instructions to someone else.
“Now, you have the instructions to make someone else’s letter. Go ahead and start with the first point on the list and graph the points in order. You should always connect each point to the point that came before it unless the instructions contain the word STOP. When you’re finished, compare your letter with your partner and see if your pictures match.”
If the pictures do not match, the pair should work together to either identify where the instructions do not match the original picture or where the second picture does not match the instructions (or both).
This Activity can be repeated if students struggle with writing accurate instructions.
Extension:
Use the following strategies to tailor the lesson to meet the needs of your students throughout the year.
- Routine: These concepts can be reviewed later in the year using different, more complex maps or having students explore geometric concepts by graphing them on the coordinate plane. For example, once students have learned different classifications of shapes (or parallel / perpendicular lines, etc.) they can create instructions for graphing these geometric items.
- Small Group: Students can work in a small group to create a map of a town and create “clues” to describe the map to another group. Their clues, like the ones in this lesson, can be straightforward (i.e., “The mall is located at (5, 6).”).
- Expansion: This lesson can be expanded by including points outside of Quadrant I as well as including points with decimal coordinates. The maps can always become more complicated, as can the instructions. For example, “The Junior High is located 5 units from the Police Station; plot all the possible locations of the Junior High.”
