So for next year, I have some recommendations for my teaching of this concept:
- Really dig in deep to make sure students have a strong background in graphing coordinates, beginning with the x- and y-axes. Last year (when I taught fifth grade), I copied two number lines onto two different transparencies. In the middle of each number line, I placed a zero. On the left side of the zero went the negatives and on the right, the positives. I introduced each one by itself. One I kept horizontal (x-axis), the other I turned so that it was in vertical direction (y-axis). After a brief explanation of each one, I combined them so that my students could see why the numbers going right (x-axis) and up (y-axis) are positive and negative when going left (x-axis) and down (y-axis).
- After teaching the axes, really drill the actual graphing of coordinates. My students are having a difficult time reading the grid (for example, counting over 3 and up 1 for (3,1)). I guess the best way to do this is by relating it something they know, like a street map or Battleship (but most tell me they played that in 6th grade!) But the biggest problems lie with graphing a shape!
- Connect the translating of a point to adding and subtracting integers; perhaps even teach the two together. My students had a TERRIBLE time with integers. So maybe when they translate point A (3, 1) four units to the left, they can see that they are going in negative direction. Therefore, to get the new coordinates, they need to subtract 4 from 3 (3-4 = -1).