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

Lesson 7.8Ordered Pairs in All Four Quadrants

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can plot ordered pairs in all four quadrants of the coordinate plane.

Start hereWords for this lesson

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

WordWhat it meansExample
QuadrantSpanish: Cuadrante One of the four parts of a coordinate grid, numbered I to IV. I (+, +) top-right, II (-, +) top-left, III (-, -) bottom-left, IV (+, -) bottom-right
Negative coordinateSpanish: Coordenada negativa A coordinate less than zero. It means left or below the center point. (-3, 2) means 3 left and 2 up from the origin
ReflectionSpanish: Reflexión A flipped, mirror image across a line. (3, 2) reflected over the y-axis is (-3, 2) — same distance, opposite side
AxisSpanish: Eje One of the two number lines that frame a graph: the x-axis runs across, the y-axis runs up and down. The x-axis goes left-right; the y-axis goes up-down; they cross at (0, 0)
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.

I will plot (-3, -4). I start at the origin (0, 0).

  1. The x is -3, which is negative, so I move 3 units to the LEFT.
  2. The y is -4, which is negative, so I move 4 units DOWN. I place my dot.
  3. Both coordinates are negative, so the point is in 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 (-5, 2). The x is -5, so which way do we move? Left 5 units.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • In Quadrant , the x-coordinate is and the y-coordinate is . I know (-3, -4) is in Quadrant because both coordinates are .

Word bank QuadrantNegative coordinateReflectionAxisIntegerquadrantpositivenegativex-coordinatey-coordinateleftright

Watch outA common mistake

A common mistake in Ordered Pairs in All Four Quadrants is matching each sign to the wrong axis — for example, seeing (-2, 5) and thinking "the x is negative so I move DOWN, and the y is positive so I move RIGHT," which lands the point in Quadrant IV. But the x-coordinate always controls left/right, never up/down: negative x means LEFT (not down), and positive y means UP (not right). So (-2, 5) is actually left 2, up 5 — Quadrant II. Before you submit, check that you used the x-coordinate for left/right and the y-coordinate for up/down, and never swapped them.

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

Lesson 7.8Ordered Pairs in All Four Quadrants

Version ASupported practice

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

Learning target I can plot ordered pairs in all four quadrants of the coordinate plane.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each ordered pair to its quadrant.

    1. (3, 4)
    2. (-2, 5)
    3. (-6, -1)
    4. (1, -3)
    5. (-4, 2)
    6. (5, -6)
    • AQuadrant I
    • BQuadrant II
    • CQuadrant III
    • DQuadrant IV
    • EQuadrant II
    • FQuadrant IV

    Hint Only the SIGNS matter: (+, +), (-, +), (-, -), and (+, -) each belong to one quadrant.

  2. 2Write the name of the correct group on each line.

    Order the points by quadrant: I, II, III, IV. Within the same quadrant, put the point with the greater x-coordinate first.

    Groups:
    • (-3, -2)
    • (5, 1)
    • (-1, 4)
    • (2, -6)
    • (4, 3)
    • (-5, -7)

    Hint Use the signs: (+,+) is I, (−,+) is II, (−,−) is III, and (+,−) is IV.

Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    In which quadrant is the point (-4, 5)?

    1. AQuadrant I
    2. BQuadrant III
    3. CQuadrant II
    4. DQuadrant IV

    Hint Look at the signs: x = -4 is negative and y = 5 is positive.

    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    A point has a positive x-coordinate and a negative y-coordinate. Which quadrant is it in?

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant IV
    4. DQuadrant III

    Hint Positive x pushes you RIGHT; negative y drops you DOWN.

    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Which point is located on the x-axis?

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

    Hint A point ON the x-axis never moves up or down — its height is zero.

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

    Spot the Common Mistake

    1. 1ProblemName the quadrant for the point (-2, 5).
    2. 2Student thinkingThe x is -2, so I move 2 units DOWN. The y is 5, so I move 5 units to the RIGHT.
    3. 3Student answer(-2, 5) is in Quadrant IV.

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

    Hint Which coordinate controls left/right, and which controls up/down? The x is always the left/right move.

    Correct work
    Correct answer:

Explain your thinkingHow do the signs of the x- and y-coordinates tell you which quadrant a point is in?

Sentence starter In Quadrant ___, the x-coordinate is ___ and the y-coordinate is ___. I know (-3, -4) is in Quadrant ___ because both coordinates are ___.

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.7

Lesson 7.8Ordered Pairs in All Four Quadrants

Version BCore practice

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

Learning target I can plot ordered pairs in all four quadrants of the coordinate plane.

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

    Plot one point in each quadrant: (3, 2), (-4, 1), (-2, -3), (5, -4)

    -6-4-20246-6-4-20246xy
    Show your thinking
  2. 2Complete the table. Show how you found each value.

    For each ordered pair, write the signs of x and y and name the quadrant (or axis).

    Pointx signy signQuadrant or Axis
    (6, -2)
    (-3, -5)
    (0, 7)
    (-1, 8)
    (4, 0)
    Show your work
  3. 3Write the letter of the matching item on each line.

    Match each quadrant to its coordinate sign pattern.

    1. Quadrant I
    2. Quadrant II
    3. Quadrant III
    4. Quadrant IV
    5. x-axis
    6. y-axis
    • A(+, +)
    • B(-, +)
    • C(-, -)
    • D(+, -)
    • Ey = 0
    • Fx = 0
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    Point A is at (-5, 3). If you move 8 units to the right, what are the new coordinates?

    1. A(-13, 3)
    2. B(-5, 11)
    3. C(-5, -5)
    4. D(3, 3)
    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    In which quadrant is the point (-3, 5)?

    1. AQuadrant I
    2. BQuadrant III
    3. CQuadrant IV
    4. DQuadrant II
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1ProblemName the quadrant for the point (6, -1).
    2. 2Student thinkingI'll read the coordinates as (y, x), so I treat this like (-1, 6): the first number -1 is negative (left) and the second number 6 is positive (up).
    3. 3Student answer(6, -1) is in Quadrant II.

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

    Correct work
    Correct answer:

Explain your thinkingHow do the signs of the x- and y-coordinates tell you which quadrant a point is in?

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.7

Lesson 7.8Ordered Pairs in All Four Quadrants

ChallengeExtension

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

Learning target I can plot ordered pairs in all four quadrants of the coordinate plane.

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

    Plot these 4 points and connect them in order to form a shape. Name the shape and identify which quadrants it spans: (-3, 2), (3, 2), (3, -2), (-3, -2)

    -5-4-3-2-1012345-4-3-2-101234xy
    Show your thinking
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    A point (a, b) has a < 0 and b < 0. In which quadrant does it lie?

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant IV
    4. DQuadrant III
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    Reflecting the point (3, -6) across the x-axis gives which point?

    1. A(-3, -6)
    2. B(-3, 6)
    3. C(3, 6)
    4. D(6, 3)
    Show your work
Part 3Explain and correctreasoning
  1. 4Find the mistake. Explain it, then show the correct work.

    Find the Quadrant Error

    1. 1ProblemIdentify the quadrant for (-3, -5)
    2. 2Student thinkingThe x is -3, so I go left 3. The y is -5, so I go up 5.
    3. 3Student answer(-3, -5) is in Quadrant II

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

    Correct work
    Correct answer:
  2. 5Answer in complete sentences.

    A point starts in Quadrant I at (4, 6). Describe a move that puts it in Quadrant III. What must happen to both coordinates? Can you give the exact new coordinates after your move?

    Write your answer

Explain your thinkingHow do the signs of the x- and y-coordinates tell you which quadrant a point is in?

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