Neft Teacher · Learn It

Unit 7 · Standard 6.NOS.6

Represent Rational Numbers on the Coordinate Plane

Lesson 7-5 · Learn It — how the math works

Why we're learning this

Captain Vega left a treasure map, but instead of an 'X marks the spot,' she hid the directions as ordered pairs! To find the treasure, you need to plot each point on the coordinate plane and connect them in order. The first clue says: Start at (2, 1), then go to (5, 4), then (8, 1).

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Learn It

How do you plot a point on the coordinate plane?

An ordered pair (x, y) is two numbers that tell you exactly where a point goes. The first number moves you right or left. The second number moves you up or down.

Picture itSee what the math looks like before you read about it

Three points are plotted on this coordinate grid. Only one of them sits to the right of and above the origin O, where the two number lines cross — the other two are on the far side of one of those lines.
Where you see this in real lifeThree points are plotted on this coordinate grid. Only one of them sits to the right of and above the origin O, where the two number lines cross — the other two are on the far side of one of those lines.

Watch me solve itI do — read one step at a time

The problem looks like this
A coordinate grid with (5, 4) plotted.−6−6−5−5−4−4−3−3−2−2−1−1112233445566 x y 0 (5, 4)
  1. I will plot the point (5, 4). The 5 is the , and the 4 is the y-coordinate.
  2. I start at the , which is (0, 0).
  3. First I move 5 units to the right along the .
  4. Then I move 4 units up. I place my dot. That is the point (5, 4).

Watch out — mistakes students make here

  • The point moved up 3 too — the y-coordinate isn't zero.
  • The first number is the horizontal (right/left) distance.
  • The 3 for the move right is correct, but the second number is the move up, which is 7.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Now let's plot (2, 1). Where do we start?
    Check this step
    At the (0, 0).
  2. How far do we move right?
    Check this step
    The first number is 2, so we move 2 right.
  3. How far do we move up?
    Check this step
    The second number is 1, so we move 1 up and place the dot.

On your ownYou do — solve this one by yourself

Before you start, remember:

  • In the explore, plot Captain Vega's waypoints (2, 1), (5, 4), and (8, 1) to trace the treasure route.

Solve: Which names a point 3 units right and 7 units up from the ?

My answer

Stuck? Open one hint at a time.

Hint 1

Re-read the moves: 3 units right, then 7 units up. Which move comes first in an ordered pair?

Hint 2

An ordered pair is (x, y): x is the right/left distance, y is the up/down distance. Match each move to its slot.

Hint 3

Start at the origin and go right 3 — that 3 is the x, the first number. Now decide where the 'up 7' goes.

Check my answer
✅ Answer: (3, 7)
The first coordinate is horizontal (right 3), the second is vertical (up 7). So (3, 7).

Turn & TalkSay it out loud with a partner

On the , why do we always start at the (0, 0) and move sideways before we move up or down to plot a point?

Try starting with:

  • The first number in (x, y) tells me to move ___.El primer numero en (x, y) me dice que me mueva ___.
  • The second number tells me to move ___.El segundo numero me dice que me mueva ___.
Use these wordscoordinate planeoriginordered pairx-axisy-axis