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Investigation: Find my friends

Lesson

Objectives

  • To practice identifying points on the number plane.
  • To explore the different quadrants.
  • To understand the attributes of certain points.

Materials

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

Procedure

Part 1: Set up the Number Plane

  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.

Part 2: 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 number plane.
  4. The other players will grab two cards from the deck. The first card will represent the $x$x-coordinate and the second card will represent the $y$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 number plane.
  6. Once everyone has reached their location the person with their back turned must turn around and figure out all of the coordinates of those on the number 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.

 

Discussion questions

Use the coordinates you wrote down to answer the following 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 (5, -6) would produce (-6, 5) ). If not, which quadrant is each point in after the switch? Why?

 

Optional extension

  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 be recorded on a piece of paper.
  3. Create a number plane on a piece of paper and plot each of the points.
  4. 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.
  5. Compare and contrast your story to the stories of the others in your group.

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