Coordinates (age 10+)
Describe positions on the full coordinate grid (all four quadrants); use coordinates with negative values
What a learner can do afterwards
- Plot points with negative coordinates such as (−3, 4) and (2, −5) on a four-quadrant grid
- Identify the quadrant in which a given point lies
- Describe the position of a shape using coordinates in all four quadrants
1 · Read
You already know how to plot points with an x-coordinate and a y-coordinate, and how cold can fall below zero. Now the grid stretches past zero in every direction, just like the thermometer. The x-axis runs left and right of zero, and the y-axis runs above and below it. A negative x-coordinate means move left. A negative y-coordinate means move down.
The two axes split the grid into four quadrants. Quadrant I is up and to the right, where both coordinates are positive. Quadrant II is up and to the left, where x is negative and y is positive. Quadrant III is down and to the left, where both are negative. Quadrant IV is down and to the right, where x is positive and y is negative. A point with a zero in it sits on an axis, not inside any quadrant.
To plot (-5, 2), start at the origin. Move 5 left for x = -5, then 2 up for y = 2. That is quadrant II.
To plot (2, -5), start at the origin. Move 2 right, then 5 down. That is quadrant IV.
Read each pair in order, x then y. Signs give direction: left or right for x, up or down for y.
Every point has an x-coordinate for left or right and a y-coordinate for up or down, and their signs place the point in one of the four quadrants.
Quadrant practice includes an adapted OpenMiddle graphing task by Robert Kaplinsky with unverified terms. Videos by Khan Academy. Other quadrant items and coordinate readings written in repo with no upstream source.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.