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

Lesson 7.8Ordered Pairs in All Four Quadrants

Set B · Version ASecond form · supported 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.

Why This Matters Captain Vega realized her treasure map only covered one corner of the island! She needs to expand the map in all directions — north, south, east, and west of the base camp at the origin (0, 0). Now clues can have negative coordinates: (-4, 3) means 4 units west and 3 units north. A clue at (2, -5) means 2 units east and 5 units south. Which quadrant is each clue in?

RememberOrdered Pairs in All Four Quadrants

The Four Quadrants. Formula: Quadrant I: (+, +) | Quadrant II: (−, +) | Quadrant III: (−, −) | Quadrant IV: (+, −) The coordinate plane has four parts called quadrants. A negative coordinate means you move left (for x) or down (for y) from the origin instead of right or up.

  1. Quadrant I: Upper-right (+, +).
  2. Quadrant II: Upper-left (−, +).
  3. Quadrant III: Lower-left (−, −); Quadrant IV: Lower-right (+, −)

Words: Quadrant (Cuadrante)Negative coordinate (Coordenada negativa)Reflection (Reflexión)Axis (Eje)Integer (Número entero)

  1. 1Circle the letter of the best answer. Show how you know.

    What are the coordinates of a point 4 units right and 2 units down from the origin?

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

    Hint Two moves: right 4 (horizontal) and down 2 (vertical). Down means a NEGATIVE y.

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

    A rectangle has vertices (1, 1), (7, 1), (7, 4) and (1, 4). How long is the bottom side?

    1. A3 units
    2. B4 units
    3. C6 units
    4. D8 units
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    Using that same rectangle — (1, 1), (7, 1), (7, 4), (1, 4) — what is its area?

    1. A9 square units
    2. B18 square units
    3. C18 units
    4. D24 square units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  4. 4Circle the letter of the best answer. Show how you know.

    A square has vertices (−2, −2), (2, −2), (2, 2) and (−2, 2). What is its perimeter?

    1. A4 units
    2. B8 units
    3. C16 units
    4. D16 square units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  5. 5Circle the letter of the best answer. Show how you know.

    Three vertices of a rectangle are (0, 0), (5, 0) and (5, 3). What is the fourth vertex?

    1. A(0, 3)
    2. B(3, 0)
    3. C(3, 5)
    4. D(5, 5)
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A city uses a coordinate grid to map locations. City Hall is at the origin (0, 0). The library is at (-3, 4), the park is at (5, -2), the school is at (2, 3), and the hospital is at (-4, -1). Which quadrant is the library (−3, 4) in?

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

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 ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
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

Set B · Version BSecond form · core 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.

Why This Matters Captain Vega realized her treasure map only covered one corner of the island! She needs to expand the map in all directions — north, south, east, and west of the base camp at the origin (0, 0). Now clues can have negative coordinates: (-4, 3) means 4 units west and 3 units north. A clue at (2, -5) means 2 units east and 5 units south. Which quadrant is each clue in?

Part 1Understand the ideamodels and meaning
  1. 1Write the name of the correct group on each line.

    Captain Vega spotted four enemy ships. Drag each ship's coordinates into the correct quadrant of the map.

    Groups: Quadrant I Quadrant II Quadrant III Quadrant IV
    • (3, 2)
    • (-4, 1)
    • (-2, -5)
    • (6, -3)
  2. 2Write the letter of the matching item on each line.

    Match each enemy ship's coordinates to the quadrant where Captain Vega should fire.

    1. (7, 5)
    2. (-6, 2)
    3. (-1, -8)
    4. (4, -7)
    • AQuadrant I
    • BQuadrant II
    • CQuadrant III
    • DQuadrant IV
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A city uses a coordinate grid to map locations. City Hall is at the origin (0, 0). The library is at (-3, 4), the park is at (5, -2), the school is at (2, 3), and the hospital is at (-4, -1). Which quadrant is the park (5, −2) in?

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

    A city uses a coordinate grid to map locations. City Hall is at the origin (0, 0). The library is at (-3, 4), the park is at (5, -2), the school is at (2, 3), and the hospital is at (-4, -1). Which location is in Quadrant III?

    1. ACity Hall (0, 0)
    2. BThe school (2, 3)
    3. CThe library (−3, 4)
    4. DThe hospital (−4, −1)
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    A sonar ping locates an enemy submarine at (-5, -2). In which quadrant should Captain Vega aim her shot?

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant IV
    4. DQuadrant III
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    Captain Vega's lookout reports a ship in Quadrant II. What signs will its coordinates (x, y) have?

    1. A(-, +)
    2. B(+, +)
    3. C(-, -)
    4. D(+, -)
    Show your work

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

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help