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

Lesson 7.87.8 Small Group · Group 2

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, explain what each part stands for, and build one for a situation I have not seen before.

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.

Point A is 4 units left of the y-axis and 2.5 units down from the x-axis. Name point A and its quadrant.

  1. Turn left 4 into an x-coordinate: left 4 → x = −4
  2. Turn down 2.5 into a y-coordinate: down 2.5 → y = −2.5
  3. Write the ordered pair, x first: (−4, −2.5)
  4. Use the signs to name the quadrant: (−, −) → Quadrant III
  5. Point A is (−4, −2.5). It is in Quadrant III.
  6. Which quadrant is the point (0, −5) in?
  7. Read x. Do not move left or right: x = 0
  8. Read y. Move down 5 units: y = −5 → down 5
  9. Decide if the point is in a quadrant: on the y-axis → no quadrant
  10. (0, −5) is on the y-axis. It is not in any quadrant.

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 (−5, 2). Name the quadrant it is in.

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 7.87.8 Small Group · Group 2

Group 2Challenge 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, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    −5−4−3−2−112345−5−4−3−2−112345B
    Point B, right and down from the origin.

    Point B is 3.5 units right of the y-axis and 4 units down from the x-axis. Name point B and its quadrant.

    1. 1Turn right 3.5 into an x-coordinate.
    2. 2What is the y-coordinate of B?
    3. 3Which quadrant is B in?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −5−4−3−2−112345−4−3−2−11234(−4, 0)
    The point sits on an axis.

    Plot the point (−4, 0). Which quadrant is it in?

    1. 1Which way do we move for x = −4? For y = 0?
    2. 2Every point on the x-axis has the same y-coordinate. What is it?
    3. 3Why is (−4, 0) not in Quadrant II or Quadrant III?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Which quadrant is the point (−0.5, 8) in?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    Point R is in Quadrant IV. It is 7 units from the y-axis and 2 units from the x-axis. What is the y-coordinate of R?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A diver starts at a dock at (0, 0). She swims 4 units west, then 3 units east, then 6 units south. East and north are positive. Which quadrant is she in now?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Max says: "If x and y have different signs, the point is in Quadrant II." Test his rule on (3, −7). Which quadrant is (3, −7) really in?

    Show your work
    Final answer:

Explain your thinkingMax only checked if the signs were different. What else must you check? Compare (3, −7) and (−3, 7).

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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