The Coordinate Plane: Locating Points

Lesson 1 of 1

In this lesson:

• Build the coordinate plane from two number lines
• Read and write ordered pairs
• Plot points using the two-step routine

Learning Objectives for This Lesson

1. Describe the plane as two perpendicular number lines
2. Identify the x-axis, y-axis, and origin
3. Explain what each number in a pair means
4. Plot points in the first quadrant
5. Write the ordered pair for a plotted point
6. Show that (3, 5) and (5, 3) differ

One Number Line Is Not Enough

Imagine a number line labeled 0 to 10.

• Point to 7 — easy, one number does the job
• Now point to a spot above the line — you need more info
• One number is not enough. Add a second number line!

Two Number Lines Create the Coordinate Plane

Labeling the Axes and the Origin

• x-axis: the horizontal number line (goes left-right)
• y-axis: the vertical number line (goes up-down)
• Origin: where both axes cross, at the point (0, 0)

The axes must be perpendicular — they meet at a right angle.

First Quadrant: Positive Coordinates Only

• In Grade 5, we work in the first quadrant
• Both coordinates are zero or positive
• The grid extends right and up from the origin

Other quadrants exist, but you will explore those in Grade 6.

Quick Check: Find the Origin

Where is the origin on the coordinate plane?

• What are its coordinates?
• Which two things meet there?

Think for a moment before the next slide...

Ordered Pairs Name Every Point

An ordered pair looks like this: (x, y)

• The first number is the x-coordinate (horizontal position)
• The second number is the y-coordinate (vertical position)
• Always written x first, y second

Memory trick: x comes before y in the alphabet!

Order Matters: Swapping Changes the Point

• (3, 5) means right 3, up 5
• (5, 3) means right 5, up 3
• These land in completely different spots!

Example: Decode the Pair (4, 7)

Step 1: The x-coordinate is 4 — move 4 units right

Step 2: The y-coordinate is 7 — move 7 units up

Result: The point (4, 7) is 4 right and 7 up from the origin.

Quick Check: Identify the Coordinates

In the ordered pair (6, 2):

• What is the x-coordinate?
• What is the y-coordinate?
• Which direction does each one control?

Think for a moment before the next slide...

Reading Points from the Grid

To write the ordered pair for a plotted point:

1. Look straight down to the x-axis — read the x-coordinate
2. Look straight left to the y-axis — read the y-coordinate
3. Write as (x, y)

Reading is the reverse of plotting — same skills, opposite direction.

Match Each Point to Its Ordered Pair

Write the ordered pair for each point.

Answers: Matching Points to Pairs

Did you get all four? The x-coordinate is always the horizontal value.

From Naming to Plotting: Two-Step Routine

Now that you can read and write ordered pairs, let's plot them.

The plotting routine:

1. Start at the origin
2. Move right by the x-coordinate
3. Move up by the y-coordinate
4. Mark the point and label it

Example: Plot the Point at Six, Three

Special Case: Plotting (0, 5) on the Grid

Plot (0, 5):

1. Start at the origin
2. x is 0 — do not move right at all
3. y is 5 — move up 5 units
4. The point sits on the y-axis

Zero is a real coordinate — it means "stay put" in that direction.

Special Case: Plotting (7, 0) on the Grid

Plot (7, 0):

1. Start at the origin
2. x is 7 — move right 7 units
3. y is 0 — do not move up at all
4. The point sits on the x-axis

Compare: (0, 5) is on the y-axis; (7, 0) is on the x-axis.

Common Mistake: Moving Vertically First

Wrong: Go up 3, then right 6 — lands at wrong spot!

Right: Go right 6, then up 3 — lands at (6, 3).

• Always move horizontally first, then vertically
• "Walk before you fly" — across the hall, then up the stairs

Your Turn: Plot the Point (2.5, 4)

Follow the two-step routine:

1. Start at the origin
2. Move right — how far? (Hint: halfway between 2 and 3)
3. Move up — how far?
4. Mark and label the point

Try it, then advance for the answer.

Quick Check: Where Does (0, 0) Land?

The point (0, 0):

• x is 0 — no movement right
• y is 0 — no movement up
• You stay at the origin

(0, 0), (0, 5), and (7, 0) are all different points!

Practice: Plot These Four Points

Plot each point on a coordinate grid:

1. (3, 7) — standard point
2. (8, 2) — standard point
3. (0, 4) — zero x-coordinate
4. (5, 0) — zero y-coordinate

Use the two-step routine for each one.

Answers: Where Each Plotted Point Lands

Vocabulary System: Every Term Connects to Direction

Every term ties to a direction — learn one, derive the rest.

• x always means horizontal; y always means vertical
• x-axis is the line; x-coordinate is the number

Real-World Coordinate Grids Are All Around

Coordinate systems appear in daily life:

• Maps — latitude and longitude locate any place on Earth
• Battleship — call out a letter and number to find ships
• Spreadsheets — column A, row 3 is a coordinate
• Theater seats — row and seat number describe your spot

Zoo Map: Find the Animal at (3, 7)

What is at (3, 7)? Move right to 3, then up to 7.

Zoo Map Practice: Read and Write

Use the zoo map to answer:

1. What animal is at (6, 3)?
2. What are the coordinates of the Lions?
3. You walk from Penguins (6, 3) to Gift Shop (8, 1) — how many units east?

Try all three, then check the next slide.

Answers: Zoo Map Coordinate Practice Problems

1. (6, 3) — Penguins
2. Lions are at (2, 5)
3. From (6, 3) to (8, 1): 8 − 6 = 2 units east

Coordinates make directions precise — no confusion about "near the big tree."

Key Takeaways from Today's Lesson

• Coordinate plane = two perpendicular lines at (0, 0)
• Ordered pairs (x, y) — x first, y second
• Plot: origin, right x, up y

Watch out:

• x before y — alphabetical order
• Start at the origin
• Zero means "stay"
• Count jumps, not lines

Next Up: Graphing Real-World Data

You can now plot and read points on the coordinate plane.

Coming next (5.G.A.2):

• Use the coordinate plane to display real-world data
• Graph patterns and look for relationships
• Today's plotting skill is the foundation for all of it