Numbers on a number line
Understand a coordinate system defined by two perpendicular number lines (axes) with an origin at (0,0); know that an ordered pair (x, y) specifies a unique point where the first number gives horizontal distance and the second gives vertical distance from the origin
What a learner can do afterwards
- Identify the x-axis, y-axis, and origin on a coordinate grid
- Explain that (3, 5) means go 3 along the x-axis and 5 up the y-axis
- Distinguish (2, 4) from (4, 2) by explaining each coordinate's meaning
The lesson
A coordinate grid is made from two number lines that cross each other. The line going side to side is the x-axis. The line going up and down is the y-axis. The point where they cross is the origin, and its coordinates are (0, 0).
Every point on the grid has an address made of two numbers, called an ordered pair, written as (x, y). The first number tells you how far to move right along the x-axis. The second number tells you how far to move up along the y-axis. You always start counting from the origin.
To find the point (3, 5), start at the origin. Move 3 steps right along the x-axis. Then move 5 steps up, straight above where you stopped. That spot is the point (3, 5).
Order matters. (2, 4) means 2 right and 4 up, but (4, 2) means 4 right and 2 up. Swap the numbers, and you land on a different point.
An ordered pair (x, y) always means x steps right from the origin, then y steps up.
Watch it
Where it sits
Learn first
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Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.