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Understand Axes and the Coordinate Plane

Students learn that two perpendicular number lines (the x-axis and y-axis) form a coordinate plane. They identify the origin, x-axis, y-axis, and the first quadrant, understanding how the axes create a grid for locating points.

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Understand Axes and the Coordinate Plane

Grade 5 · Coordinate Plane · question 1 of 3

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20 rungs. A star at the top.

A map is drawn on two number lines that cross. A pin sits where they meet. What pair names that pin?

How it is taught

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Two number lines cross at the origin.

The horizontal line names how far across.

The vertical line names how far up.

Read it: Points on the coordinate plane

The point (4, 5): start at (0, 0), where the axes cross. Walk 4 across, along the x-axis, then 5 up. The first number is always across, the second always up.

  1. Start at (0, 0), where the x-axis and the y-axis cross.
  2. Walk the first number across, to the right.
  3. Walk the second number up, and mark the point.

Across first, then up, so every pair names exactly one point.

(4, 5) and (5, 4) are different points: the order is part of the pair.

A point on an axis has a 0 in its pair: (4, 0) is on the x-axis.

The first number goes across and the second goes up, always from (0, 0).

Walking 5 across and 4 up, which lands on (5, 4).

The first number goes across: (4, 5) is 4 across, then 5 up.

A point is 9 across and 2 up from (0, 0). Its pair is (9, ___) — 2. Across comes first and up comes second: (9, 2).

Build the plane and plot (3, 2)

Today we'll build a coordinate plane — a grid that can pinpoint any spot using just two numbers.

Start with a horizontal number line going left and right. We call this the x-axis.

Now draw a second number line going up and down, crossing the first at a right angle. This is the y-axis.

The point where the two axes cross is called the origin. Here, both x and y are zero.

Mark equal steps along the x-axis going right: one, two, three, four, five.

Do the same on the y-axis going up: one, two, three, four.

The corner where both x and y are positive is called the first quadrant — that's where we'll work today.

Let's locate the point three, two. The first number is the x — how far right. The second is the y — how far up.

Start at the origin and step three units to the right along the x-axis.

Build a grid to find any pointxyorigin (0, 0)123451234Quadrant IFind the point (3, 2)(3, 2)POINT(3, 2)3 right, 2 up
Grade 5 · Two axes, one grid

From there, step two units straight up, parallel to the y-axis.

Drop a point right there. That's the location three, two!

Two axes, one origin, and a grid that can find any point. That's the coordinate plane!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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