Year 1 Lesson Plan 28 - Cartesian Coordinates

To coaches:
This lesson introduces cartesian coordinates, but also uses a lot of what the students have been studying: the number line, areas of polygons and working with negative numbers. In this regard, it reinforces other concepts previously mastered in a slightly different context.

Note: There are 2 parts of this lesson:
  1. An introduction to Cartesian coordinates
  2. Completing a square: Given 3 points on a grid, find a 4th that makes a square.
If you think the completing a square part makes the lesson too long you may delete it. The reason I included it in this lesson is because the WSMC Math Olympiad has numerous problems of this type.

There are no units used in this lesson. The kids don't have to supply units. The addition of units does not add anything to the lesson.

No mental math for this lesson.
  1. (20 min) Introduce cartesian coordinates
    • Before class, draw a big cartesian grid on the board, at least 8 units positive and negative in x and y. Use a big ruler (or a yard stick) if you have one to make the lines as straight as possible. Or, your school may have gridded easel pads like this.
    • Pass out the Cartesian Coordinates handout (page 1) and use it to guide the discussion:
      1. You can make a grid by using two number lines crossed at 90o. Both number lines cross at zero, the origin. This lets you give a location to any point on a plane.
      2. Discuss the examples in the handout.
      3. Ask for volunteers to come to the board and plot points. You can take about 3 kids at a time. Here are some points to plot (make sure the left-most kid does the negative x points and the right-most the positive x points):
          (-3,-5) (kid #1)
          (+1,+4) (kid #2)
          (+4,-5) (kid #3)
          (-7,-7) (kid #1)
          (-1,+8) (kid #2)
          (+7,-7) (kid #3)
      4. Have the kids discuss quadrants. Follow the handout. Point to several points on the board and ask the kids which quadrant they are in.
      5. Ask the kids to plot two points of their own and then, one by one, turn and tell you (and the class) their coordinates.
      6. If you have more than 3 kids who want to plot points, repeat the above process with these points:
          (-8,+6)
          (-1,-8)
          (+7,+2)
          (-5,-8)
          (+1,-7)
          (+6,-5)
      7. If you have more kids, make up some points on your own and have them plot them on the board.
      8. Areas of triangles and rectangles on a cartesian grid:
        • Draw the triangle between these points that are already on the board: (-3,-5),(+4,-5), and (+1,+4). Have the kids determine the base and height of this triangle and then compute it's area.
          They talk, you write the base and heights and then the area on the board.
        • Draw the trapezoid between these points that are already on the board: (-7,-7), (+7,-7),(+4,-5), and (-3,-5). Have one of the kids come up and cut up the trapezoid into two triangles and a rectangle. Solve the problem together: find the areas of each of the triangles and the rectangle and then add them all.
      9. Pass out the in-class exercise, page 1, and have the kids work on it.
  2. (15 min) Complete a square
    As the kids finish up the in class page 1, discuss finding a 4th point on a grid that completes a square given its other 3 points:
    • Put these points on the board: A: (3,2) B: (6,-2) C: (2,-5)
    • Show how the offset of A from B is the same as the new point D from point C.
      Subtract B from A
    • Find those offsets:
      X: 3 - 6 = -3
      Y: 2 - ( -2) = 2 + 2 = +4.
      The total offset of A from B is (-3,+4)
    • Apply those offsets from C to find point D: (2,-5) + (-3,+4) = (-1,-1)
    • Hand out the In-class, page 2 for 2 of these problems.
  3. Hand out homework as students successfully complete the in-class exercise(s).