Topics
3. The Coordinate Plane
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United States of America
Grade 6

Investigation: Jumping around the coordinate plane

Lesson
Practice
Overview
Activity 1
Activity 2
Reflection

Investigate the quadrants in a coordinate plane and graphing polygons.

Objectives
  • To be able to identify the four quadrants of the coordinate plane.
  • To graph polygons in the coordinate plane.
  • To calculate the side lengths of an object in the coordinate plane.
Materials
  • Painters tape
  • Deck of cards (1-10 only)
  • Colored markers
  • Pen or pencil
  • Scissors
  • Graph paper
  • Ruler

Jumping around the coordinate plane 1

The activity will start after your group of at least two people set up a life-size coordinate plane. Follow the instructions below to set up your coordinate plane.
The set up:
  • Use tape to create a set of axes on the floor. It should be fairly large, bigger than 8\text{ ft} in both directions.
  • On the horizontal axis measure, mark with tape, and label 5 tick marks on either side of the vertical axis.
  • Do the same thing for the vertical axis.
  • On each piece of tape label it appropriately with the numbers: 2, 4, 6, 8, 10 or -2, -4, -6, -8, -10.

Instructions to play:

1. Remove the Jacks, Queens, and Kings from the deck of cards so you are just left with numbers 2-10 and Aces to act as 1 for each of the suits.

2. One person will turn their back to the coordinate plane.

3. 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.

4. While the one player still has their back turned, the players who drew cards will walk to where their coordinate is located on the coordinate plane.

5. Once the players have reached their location, the person with their back turned must turn around and guess the coordinates of those on the coordinate plane.

6. The person guessing the coordinates should write down the coordinates of where the others are standing.

7. Repeat the steps until everyone has had a chance to guess and has written down all of the coordinates.

Investigate
Consider the following questions once you have completed the game using the coordinates you wrote down to answer the questions.
1.
Which quadrant was each point located in?
2.
Which person walked the farthest to the left? What coordinate were they at?
3.
Which person walked the farthest to the right? What coordinate were they at?
4.
Which person walked the farthest up? What coordinate were they at?
5.
Which person walked the farthest down? What coordinate were they at?
6.
Which person was closest to the origin? What coordinate were they at?
7.
Write each of the coordinates in terms of a ratio x:y.
8.
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))

Jumping around the coordinate plane 2

In this activity, you'll use the same setup as the previous one.

Instructions to play:

1. The first person draws two cards from the deck as before and stands at that coordinate on the coordinate plane.

2. 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.

3. 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.

4. 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.

5. 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.

Investigate
Consider the following questions once you have completed the game using the polygon you sketched to answer the following questions.
1.
What type of polygon was created? How can we tell?
2.
What quadrant is each vertex of the polygon in?
3.
Is there a relationship between the number of sides and the number of vertices in a polygon? Is this true for any polygon?
4.
Find the length of any vertical or horizontal sides.
5.
Is the length of a side ever negative? Why or why not?

Discuss your responses to the previous questions with a classmate, then answer the questions below.

Discussion
1.
After switching the x and y coordinate values, describe which quadrant the point moves to and why.
2.
Can you come up with a process other than counting that would help find the length of a very long side of a polygon in a coordinate plane?
3.
What mathematical concept could we apply to ensure that side lengths are always positive?
4.
How could you find the length of any sides of a polygon in a coordinate plane that are not vertical or horizontal?

Outcomes

6.NS.C.8

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

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