Investigation: Jumping around the coordinate plane

Objectives

• To practice identifying points on the coordinate plane.
• To explore the different quadrants.
• To understand the attributes of certain points.
• To practice graphing polygons on the coordinate plane.
• To find side lengths of polygons in the coordinate plane. (vertical and horizontal sides only)
• To apply the concept of absolute value to side length.

Materials

• Colored tape
• Deck of cards (1-10 only)
• Markers
• Pen
• Scissors
• Graph paper
• Ruler

The set up

1. Use the tape to create a set of axes on the floor. It should be fairly large (bigger than 2m in both directions). You may want to set this up outside.
   
2. On the horizontal axis measure mark 5 tick marks either side of the vertical axis. 
3. Do the same thing for the vertical axis.
   
4. On each piece of tape label it appropriately with the numbers: 2,4,6,8,10 or - 2 , - 4 , - 6 , - 8 , - 10 .
   

Round 1: How to play

1. Work with at least one other person.
2. Remove the Jacks, Queens, Kings and Aces from the deck of cards so you are just left with numbers 1-10 for each of the suits.
3. One person will turn their back to the coordinate plane.
4. The other players will grab two cards from the deck. The first card will represent the x-coordinate and the second card will represent the y-coordinate. Red cards (diamonds or hearts) represent negative numbers.
5. While the one player still has their back turned, everyone who drew cards will walk to where their coordinate is located on the coordinate plane.
6. Once everyone has reached their location the person with their back turned must turn around and guess all of the coordinates of those on the coordinate plane.
7. The person guessing the coordinates should write down the coordinates where they are standing.
8. Repeat the steps until everyone has had a chance to guess and has written down all of the coordinates.

Guiding questions

1. Use the coordinates you wrote down to answer the following questions.
2. Which quadrant was each point located in?
3. Which person walked the farthest to the left? What coordinate were they at?
4. Which person walked the farthest to the right? What coordinate were they at?
5. Which person walked the farthest up? What coordinate were they at?
6. Which person walked the farthest down? What coordinate were they at?
7. Which person was closest to the origin? What coordinate were they at?
8. Write each of the coordinates in terms of a ratio x:y.
9. If you switched the x and y coordinates would they still be in the same quadrant? ( Hint:  Switching \left(5, - 6 \right) would produce \left( - 6 , 5\right) )
10. If not, which quadrant is each point in after the switch? Why?

 

Round 2: How to play

1. Work with at least two other people.
2. The first person draws two cards from the deck as before and stands at that coordinate on the coordinate plane.
3. The second person draws one card. They use the same x-coordinate as person 1 but use their chosen card as the y-coordinate. The second person stands at this coordinate.
4. The third person draws one card. They use the same y-coordinate as person 1 but their chosen card as the x-coordinate. The third person stands at this coordinate.

Example: Person 1 draws a red 2 and a black 7 so they stand at \left( - 2 , 7\right), person 2 draws a black 4 (this is the new y-coordinate) so they stand at \left( - 2 , 4\right) (using the same x as person 1), finally person 3 draws a red 5 (this is the new x-coordinate) so they stand at \left( - 5 , 7\right) (using the same y as person 1).

5. If you are in a group of more than 3 people then continue this process by having person 4 draw a card for their x-coordinate and using the same y-coordinate as person 2 and so on.
6. Once everyone is in place, sketch the points on a piece of graph paper, label them with their coordinates, then connect them to create a polygon.

Guiding questions

1. Use the polygon you sketched to answer the following questions.
2. What type of polygon was created? How can we tell?
3. What quadrant is each vertex of the polygon in?
4. Is there a relationship between the number of sides and the number of vertices in a polygon? Is this true for any polygon?
5. Find the length of any vertical and horizontal sides. Can you come up with a process other than counting that would help find the length of a very long side?
6. Is the length of a side ever negative? Why or why not?
7. What mathematical concept could we apply to ensure that side lengths are always positive?
8. Challenge: Try to find the length of any sides that are not vertical or horizontal? How can you do this?

 

Optional extensions

1. All group members should walk to a point in the first quadrant.
2. Once everyone has found a coordinate, all of the coordinates should recorded on a piece of paper.

Guiding questions

1. Create a coordinate plane on a piece of paper and plot each of the points.
2. Create a story to explain the graph you have just made. You will need to come up with labels for the axes that make sense for your story. Also, be sure to title your graph.
3. Compare and contrast your story to the stories of the others in your group.