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Locating Points with Two Coordinates · Measurement and Reasoning · CCSS.MATH.CONTENT.5.G.A.1 · coordinate plane

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Locating Points with Two Coordinates

with Lumi

Lumi stands on a giant floor grid in a sunlit map room, holding a glowing marker and pointing toward a spot marked with an X shape on the grid, with one foot planted firmly on the horizontal line.

Explain what an ordered pair is and what each number tells you.
Identify the x-axis and y-axis on a coordinate grid.
Locate and plot a point on a coordinate plane using an ordered pair.
Describe the order of steps: move along the x-axis first, then up the y-axis.
Compare two ordered pairs and explain why switching the numbers gives a different location.

Key terms

Ordered pair: Two numbers that name one spot.
x-axis: The flat line going left and right.
y-axis: The line going straight up and down.
Origin: The spot where the two lines cross.

The Map Grid

A coordinate grid is like a map made of lines. The flat line going side to side is the x-axis. The straight up-and-down line is the y-axis. They cross at a special spot in the corner called the origin, written as (0, 0). We use this grid to find exact spots, just like finding a treasure on a map. Every spot has its own pair of numbers to name it.

Across Then Up

To find a spot, we use an ordered pair like (3, 4). The first number tells how many steps to go across to the right. The second number tells how many steps to go up. So go across first, then up! Say it like this: across the hall, then up the stairs. The order matters a lot. If you switch the numbers, you land at a totally different spot on the grid.

Worked examples

Plot the point (2, 3) on the grid.

Start at the origin, which is (0, 0).
Go across to the right 2 steps along the x-axis.
Then go up 3 steps and mark your point.

Answer: The point is 2 right and 3 up.

Hey explorer! I'm Lumi, and today we're going to learn how to find any spot on a map using just two numbers. Imagine a grid on the floor — like graph paper or a city with streets and avenues. The flat line going left and right is called the x-axis. The line going straight up and down is called the y-axis. They cross at a special spot called the origin, which we label (0, 0). Now, when we want to name a location, we write two numbers inside parentheses with a comma between them — like (3, 4). This is called an ordered pair. The ORDER matters, so we always say the numbers in the same sequence. Here is the trick I use: go across first, then go up. The FIRST number tells you how many steps to take along the x-axis. The SECOND number tells you how many steps to take up the y-axis. So for (3, 4): take 3 steps to the right, then 4 steps up — and mark your spot! If the first number is 0, stay right where you are at the origin and just go up — no steps across needed. Watch out for a sneaky mix-up: (3, 4) and (4, 3) land in totally different places, even though they use the same numbers. Order always matters in an ordered pair! Try saying this aloud: 'Across the hall, then up the stairs.' That helps me remember which number comes first every single time.

Activity

Drag each treasure chest to the correct point on the coordinate grid using the ordered pair shown on its label.

Practice

Describe how to plot the point (4, 1) step by step.

Are (2, 5) and (5, 2) the same spot? Tell why.

Common mistakes to avoid

Go up first then across.No. Always go across first along the x-axis, then go up.
(3, 4) and (4, 3) are the same.No. The order matters, so they land on different spots.

Check your understanding

You want to plot the point (5, 2) on a coordinate grid. What do you do first?

A student plots (3, 6) and another plots (6, 3). Are these the same location on the grid?

Which ordered pair names the origin — the point where the x-axis and y-axis cross?

Recap

A coordinate grid uses an x-axis and a y-axis that cross at the origin. An ordered pair names a spot by telling you to go across first, then up. The order of the two numbers always matters.

Reflect

How could a grid help you find a hidden treasure on a map?