Two pages of visual notes for students to keep: the key words with grid pictures, how to plot any point, the four quadrants, four solved problems in the style of the Battle on the Coordinate Plane game, and where coordinates show up in real life. To make a PDF, click Print and choose "Save as PDF."

Visual Notes: The Coordinate Plane

Grades 5–6 · CCSS 5.G.A.1, 5.G.A.2, 6.NS.C.6, 6.NS.C.8 · Pairs with the Battle on the Coordinate Plane game

Name

Key vocabulary

Coordinate plane

A flat grid made by two number lines that cross.

x-axis

The number line going across (left and right).

y-axis

The number line going up and down.

Origin

Where the axes cross: the point (0, 0).

Ordered pair

Two numbers in order, (x, y), that name one point.

x-coordinate

(3, 2)

The first number: how far across from 0.

y-coordinate

(3, 2)

The second number: how far up or down.

Quadrant

One of the four parts, numbered I to IV counterclockwise.

How to plot a point (x first: walk, then climb)

Start at the origin (0, 0).
Walk across by the x-coordinate: right if positive, left if negative. For (4, 3): 4 right.
Climb by the y-coordinate: up if positive, down if negative: 3 up.
Draw the dot and label it.

Quadrant I(+, +)
right, up

Quadrant II(−, +)
left, up

Quadrant III(−, −)
left, down

Quadrant IV(+, −)
right, down

Solved Step by Step: Find the Ships

Visual Notes: The Coordinate Plane, page 2

1. Read a point

From S, look down to the x-axis: 5.
From S, look across to the y-axis: 2.
S is at (5, 2): x first, then y.

✓ Not (2, 5): that point is 2 across and 5 up

2. Plot (−2, 4)

Start at the origin.
x = −2: walk 2 left.
y = 4: climb 4 up. It's in Quadrant II.

✓ Left and up means (−, +): Quadrant II

3. Which quadrant?

A(3, −4): x positive, y negative → Quadrant IV
B(−4, −1): both negative → Quadrant III
A point with a 0, like (0, 3), is on an axis, not in a quadrant.

✓ Check the signs, then picture the grid

4. Distance on a line (grade 6)

How far is C(2, 3) from D(2, −4)?

Same x, so they're on a vertical line.
C is 3 above the x-axis; D is 4 below it.
Distance = 3 + 4 = 7 units

✓ Count the grid squares between them: 7

Watch out

x comes first. Walk across before you climb. (5, 2) is not (2, 5).
Count from the origin, not from the last point you plotted.
A negative x means left; a negative y means down.

Where you see it in real life

Maps: grid squares help you find places.

Theaters: row and seat, like (x, y).

Temperatures: numbers go below zero.

Cities: streets make a grid you can give directions on.