Lesson 7.5Represent Rational Numbers on the Coordinate Plane
Start hereWords, worked example, and sentence starters
Learning target I can plot and identify points on the coordinate plane using ordered pairs.
Why This Matters 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).
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Coordinate planeSpanish: Plano cartesiano | A grid with a line going across and a line going up to plot points. | x-axis across, y-axis up |
| Ordered pairSpanish: Par ordenado | Two numbers (x, y) that tell where a point is on a grid. | (−3, 4) is an ordered pair |
| OriginSpanish: Origen | The point (0, 0) where the two grid lines cross. | every plot starts here |
| QuadrantSpanish: Cuadrante | One of the four parts of a coordinate grid, numbered I to IV. | Quadrant II is upper left |
| ReflectionSpanish: Reflexión | A flipped, mirror image across a line. | (3, 2) reflected over the x-axis becomes (3, -2) — same x, opposite y |
| IntegerSpanish: Número entero | Whole numbers and their opposites, like -2, -1, 0, 1, 2. | ..., -3, -2, -1, 0, 1, 2, 3, ... |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Plot (−5, −4). Name its quadrant.
- Start at the origin, (0, 0).
- Move 5 units left, because x = −5.
- Move 4 units down, because y = −4.
Answer: (−, −) is Quadrant III
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Now let's plot (2, 1). Where do we start? At the origin (0, 0).
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The ordered pair tells me to move and then .
- The point lands in Quadrant because its signs are .
- I always start at the origin because .
- A point sitting on the -axis has a coordinate of .
Word bank coordinate planeordered pairoriginquadrantx-axisy-axisx-coordinatey-coordinatehorizontalverticalleftright
Watch out!A common mistake
A common mistake in Graph on the Coordinate Plane is swapping the order of the coordinates
Lesson 7.5Represent Rational Numbers on the Coordinate Plane
Level 0Most support · every hint printed
Learning target I can plot and identify points on the coordinate plane using ordered pairs.
Why This Matters 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).
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Plot (−5, −4). Name its quadrant.
- Start at the origin, (0, 0).
- Move 5 units left, because x = −5.
- Move 4 units down, because y = −4.
Answer: (−, −) is Quadrant III
-
1Circle the letter of the best answer. Show how you know.
A point is at (6, 2). What does the 6 tell you?
- AMove 6 units to the right
- BMove 6 units up
- CMove 6 units to the left
- DThe point is in Quadrant 6
Steps to try- In (6, 2), the 6 is the FIRST number. First and second positions have different jobs.
- First number = x = horizontal (right/left). Second number = y = vertical (up/down). Positive means right or up.
- The 6 sits in the x spot and it's positive, so it describes a horizontal move. Which direction is positive x?
Show your work -
2Write the name of the correct group on each line.
Put these steps in order for plotting the point (4, 5).
- Start at the origin (0, 0)
- Move 4 units to the right along the x-axis
- Move 5 units up from that spot
- Place a dot at the point (4, 5)
Steps to try- Every plotting routine begins at the same home spot before any moving happens.
- Think: start point, then horizontal move, then vertical move, then mark the dot. Order the cards to tell that story.
- Place 'Start at the origin (0, 0)' first. Then ask: does the 4 (x) move or the 5 (y) move come next?
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3Circle the letter of the best answer. Show how you know.
Which ordered pair names a point 3 units right and 7 units up from the origin?
- A(0, 7)
- B(3, 7)
- C(3, 3)
- D(7, 3)
Steps to try- Re-read the moves: 3 units right, then 7 units up. Which move comes first in an ordered pair?
- An ordered pair is (x, y): x is the right/left distance, y is the up/down distance. Match each move to its slot.
- Start at the origin and go right 3 — that 3 is the x, the first number. Now decide where the 'up 7' goes.
Show your work -
4Circle the letter of the best answer. Show how you know.
What are the coordinates of the origin?
- A(0, 0)
- B(0, 1)
- C(1, 1)
- D(1, 0)
Steps to try- The origin is the exact spot where the x-axis and y-axis cross. Picture that crossing point.
- Ask: how far right have you moved at the origin? How far up? Those two distances are the coordinates.
- At the crossing point you haven't moved right at all, so x = 0. Now figure out the y-value the same way.
Show your work
Explain your thinkingYou plotted a triangle. How did the ordered pairs tell you exactly where to place each point?
Sentence starter The first number in the ordered pair tells me ___ and the second number tells me ___. The point (5, 4) means ___.