What are Negative Co-ordinates?

Hello, Year 5! Today, we’re going to learn about something called negative co-ordinates. This might sound a bit tricky, but don’t worry! We will break it down step by step.

Understanding Co-ordinates

First, let’s talk about what co-ordinates are. Co-ordinates help us find a specific point on a grid. Imagine a big piece of graph paper. Each square on the paper can be identified by two numbers: one for how far along (left or right) and one for how far up or down.

  • The first number tells us how far along the grid we go.
  • The second number tells us how far up or down we go.

Positive and Negative Numbers

In maths, we have positive and negative numbers. Positive numbers are the ones we usually use (like 1, 2, 3…) and they are found to the right and above the zero on the number line. Negative numbers are the ones that are less than zero (like -1, -2, -3…) and they are found to the left and below zero.

Where Do Negative Co-ordinates Go?

On our grid:

  • Positive co-ordinates (like (3, 2)) go to the right and up.
  • Negative co-ordinates (like (-3, -2)) go to the left and down.

Examples

  1. Example 1: The point (-2, -3)
    • Start at the origin (0, 0).
    • Go left 2 spaces (because of -2).
    • Then go down 3 spaces (because of -3).
    • You are now at point (-2, -3)!
  2. Example 2: The point (1, -4)
    • Start at the origin (0, 0).
    • Go right 1 space (because of +1).
    • Then go down 4 spaces (because of -4).
    • You are now at point (1, -4)!

Key Rules

  1. X-axis (left/right):
    • Positive x-values go right.
    • Negative x-values go left.
  2. Y-axis (up/down):
    • Positive y-values go up.
    • Negative y-values go down.

Tips and Tricks

  • Remember the Origin: The point (0, 0) is called the origin. It’s the starting point for all co-ordinates.
  • Use a Graph: If you have graph paper, practice plotting points with both positive and negative co-ordinates.
  • Draw it Out: Visualising the points can help you understand better.

Questions on Negative Co-ordinates

Easy Level Questions

  1. What is the origin point?
  2. Plot the point (2, 3) on a grid.
  3. What does (-1, 1) mean?
  4. Is (-3, -2) to the left or right of the origin?
  5. What direction do you go to reach (0, -4)?
  6. Plot the point (-2, 0) on a grid.
  7. What is the y-value of the point (4, -3)?
  8. How many spaces do you move left to reach (-4, 0)?
  9. Is (2, 2) a positive or negative point?
  10. What point is at (0, 0) on a grid?

Medium Level Questions

  1. Plot the point (-3, 5). What direction did you go?
  2. What is the distance from the origin to the point (-2, -2)?
  3. If you move left 3 spaces and down 2 spaces, what co-ordinates are you at?
  4. What are the co-ordinates of a point that is 1 space right and 4 spaces down from the origin?
  5. How would you describe the point (-5, 3) in terms of direction?
  6. Is (-1, -2) located in the first, second, third, or fourth quadrant?
  7. What point is directly above (-2, -1)?
  8. If you are at (0, 0) and move to (-3, 2), how many spaces did you move left?
  9. Plot the point (3, -1). What direction did you move from the origin?
  10. What is the x-value of the point (-4, 3)?

Hard Level Questions

  1. Plot the point (-5, -6). What quadrant is this in?
  2. Calculate the distance from the origin to the point (-3, 4) using the grid.
  3. If you are at (1, -2) and move down 3 spaces, what are your new co-ordinates?
  4. Translate the point (2, 3) to (-2, -3). What changes did you make?
  5. Describe how to get from (-1, -1) to (0, 0) using co-ordinates.
  6. What is the difference between the x-values of (-4, 2) and (2, -4)?
  7. If you move 4 spaces left and 5 spaces up from (0, 0), where do you end up?
  8. Which point is further from the origin: (3, -4) or (-3, 4)?
  9. If you start at (-2, -3) and move right 2 spaces, what are your new co-ordinates?
  10. What do you get if you add the co-ordinates of (-1, -1) and (1, 1)?

Answers and Explanations

Easy Level Answers

  1. (0, 0)
  2. Point is plotted at 2 right and 3 up.
  3. Move left 1 space and up 1 space.
  4. Left of the origin.
  5. Down 4 spaces.
  6. Plotted at -2 left of the origin.
  7. -3
  8. 3 spaces left.
  9. Positive.
  10. (0, 0)

Medium Level Answers

  1. Left 3 spaces and up 5 spaces.
  2. 3 spaces left and 2 spaces down.
  3. (-3, -2)
  4. (-1, -4)
  5. Left 5 spaces and up 3 spaces.
  6. (-6, -1)
  7. (3, -1)
  8. (0, 0)
  9. (0, -2)
  10. -4

Hard Level Answers

  1. Third quadrant.
  2. 7 spaces.
  3. (1, -5)
  4. Change both signs.
  5. Move left 1 and up 1.
  6. -6
  7. (-4, 5)
  8. They are equally far.
  9. (0, -3)
  10. (0, 0)

Great job today, Year 5! Keep practising plotting those points, and remember to have fun with negative co-ordinates!