Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.5Represent Rational Numbers on the Coordinate Plane

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can plot and identify points on the coordinate plane using ordered pairs.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
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 exampleplotting a point with rational coordinates

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Plot the point (−3.5, 2.5) on a coordinate plane and name the quadrant it lands in.

  1. Start at the origin, the point where the two axes cross.
  2. The x-coordinate is −3.5, so move left three and a half units along the x-axis.
  3. The y-coordinate is 2.5, so move up two and a half units from there.
  4. Left and up together land the point in the upper left section. Label it.

Answer: The point (−3.5, 2.5) sits in Quadrant II — left of the y-axis and above the x-axis.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Plot the point (1.5, −4.5) on a coordinate plane and name the quadrant it lands in.

  1. Start at the , the point where the two axes cross.
  2. The x-coordinate is , so move that many units.
  3. The y-coordinate is , so move from there.
  4. Those two moves land the point in Quadrant . Label it.
Answer:the plotted point and its quadrant

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 outA common mistake

A common mistake in Graph on the Coordinate Plane is swapping the order of the coordinates — moving up/down first instead of right/left first. For example, when plotting (5, 2), students often move up 5 and right 2, landing on the wrong point (2, 5) instead of (5, 2). Remember: the x-coordinate (first number) always tells you how far to move right or left along the x-axis; the y-coordinate (second number) tells you how far up or down along the y-axis.

Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.5Represent Rational Numbers on the Coordinate Plane

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can plot and identify points on the coordinate plane using ordered pairs.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    A point is at (6, 2). What does the 6 tell you?

    1. AMove 6 units to the right
    2. BMove 6 units up
    3. CMove 6 units to the left
    4. DThe point is in Quadrant 6

    Hint In (6, 2), the 6 is the FIRST number. First and second positions have different jobs.

    Show your work
  2. 2Write the name of the correct group on each line.

    Put these steps in order for plotting the point (4, 5).

    Groups:
    • 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)

    Hint Every plotting routine begins at the same home spot before any moving happens.

  3. 3Write the letter of the matching item on each line.

    Match each ordered pair to its description.

    1. (0, 0)
    2. (4, 2)
    3. (1, 6)
    4. (5, 5)
    5. (3, 0)
    6. (0, 4)
    • AOrigin
    • BRight 4, Up 2
    • CRight 1, Up 6
    • DRight 5, Up 5
    • EOn the x-axis
    • FOn the y-axis

    Hint Each pair is (x, y): first number = right, second = up. A 0 means you don't move in that direction.

Part 2Apply itreal-world problems
  1. 4Circle 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?

    1. A(0, 7)
    2. B(3, 7)
    3. C(3, 3)
    4. D(7, 3)

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

    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    What are the coordinates of the origin?

    1. A(0, 0)
    2. B(0, 1)
    3. C(1, 1)
    4. D(1, 0)

    Hint The origin is the exact spot where the x-axis and y-axis cross. Picture that crossing point.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1CluePlot the point (5, 2).
    2. 2StartStart at the origin (0, 0). Good.
    3. 3Move upMove 5 units UP along the y-axis.
    4. 4Move rightMove 2 units to the right. Place the dot at (2, 5).

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Which direction does the first number in (x, y) tell you to move — right or up?

    Correct work
    Correct answer:

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 ___.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.5Represent Rational Numbers on the Coordinate Plane

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can plot and identify points on the coordinate plane using ordered pairs.

Part 1Understand the ideamodels and meaning
  1. 1Plot and label each point on the grid.

    Plot these points to reveal a hidden shape: (1, 1), (1, 5), (6, 5), (6, 1)

    01234567801234567xy
    Show your thinking
  2. 2Write the letter of the matching item on each line.

    Match each point to its quadrant or axis.

    1. (3, 2)
    2. (-4, 5)
    3. (-2, -6)
    4. (7, -1)
    5. (0, 3)
    6. (5, 0)
    • AQuadrant I
    • BQuadrant II
    • CQuadrant III
    • DQuadrant IV
    • Ey-axis
    • Fx-axis
  3. 3Complete the table. Show how you found each value.

    Complete the table. Write the ordered pair for each description.

    DescriptionOrdered Pair
    Right 7, Up 2
    Right 0, Up 5
    Right 4, Up 0
    Right 3, Up 3
    Show your work
  4. 4Write the name of the correct group on each line.

    Sort these ordered pairs by their x-coordinate from smallest to largest.

    Groups:
    • (5, 3)
    • (1, 7)
    • (3, 2)
    • (0, 4)
    • (7, 1)
Part 2Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1CluePlot the point (4, 0).
    2. 2Move rightMove 4 units to the right along the x-axis. Good.
    3. 3Move upMove 4 units up, because the pair has a 4 in it.
    4. 4Plot the pointPlace the dot at (4, 4).

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingYou plotted a triangle. How did the ordered pairs tell you exactly where to place each point?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 7: Integers, Rational Numbers, and the Coordinate PlaneStandard 6.NOS.6

Lesson 7.5Represent Rational Numbers on the Coordinate Plane

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can plot and identify points on the coordinate plane using ordered pairs.

Part 1Understand the ideamodels and meaning
  1. 1Plot and label each point on the grid.

    Plot the points (2, 3), (2, 7), (6, 7), (6, 3). Connect them. Name the shape and find its perimeter using the coordinates.

    0123456780123456789xy
    Show your thinking
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Miscounted Grid Lines

    1. 1Ordered pair(7, 3)
    2. 2Move along the x-axisStart at the origin (0, 0) and count 7 units to the right.
    3. 3Move along the y-axisCount up from the x-axis: 1, 2, 3, 4 — stop on 4.
    4. 4Plot the pointPlace the dot at (7, 4).

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A student says that (3, 5) and (5, 3) are the same point because they use the same numbers. Is the student correct? Explain why or why not, and describe where each point is located on the coordinate plane.

    Write your answer

Explain your thinkingYou plotted a triangle. How did the ordered pairs tell you exactly where to place each point?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help