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

Lesson 7.97.9 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can reflect points across the x-axis and y-axis on the coordinate plane, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 7.9. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

Start hereWords for this lesson

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

WordWhat it meansExample
ReflectionSpanish: Reflexión A flipped, mirror image across a line. (3, 2) reflected over the y-axis becomes (-3, 2) — x changes sign, y stays
x-axisSpanish: Eje x The line that goes across the grid. Flipping over it changes the y sign. (4, 3) → (4, -3): the y flips from +3 to -3, like folding the paper along the horizontal line
y-axisSpanish: Eje y The line that goes up the grid. Flipping over it changes the x sign. (4, 3) → (-4, 3): the x flips from +4 to -4, like folding the paper along the vertical line
SymmetrySpanish: Simetría When a shape looks the same on both sides of a line. A butterfly's wings are symmetric — fold it down the middle and both sides match
IntegerSpanish: Número entero Whole numbers and their opposites, like -2, -1, 0, 1, 2. ..., -3, -2, -1, 0, 1, 2, 3, ...
PerpendicularSpanish: Perpendicular Two lines that meet to make a square corner (90 degrees). The dashed height meets the base at a square corner — the small 90° box is what makes it perpendicular, not slanted.

How it worksWorked example

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

Point B is the reflection of point A across the x-axis. B is at (−2.5, 4). Where is point A?

  1. Name the coordinate that changes across the x-axis: y changes sign
  2. Change the sign of y again: 4 → −4
  3. Keep x the same: −2.5 → −2.5
  4. Point A is at (−2.5, −4).
  5. Reflect (2, 3) across the x-axis. Then reflect that point across the y-axis.
  6. Reflect across the x-axis. Change the sign of y: (2, 3) → (2, −3)
  7. Reflect across the y-axis. Change the sign of x: (2, −3) → (−2, −3)
  8. Compare the first and last points: (2, 3) → (−2, −3)
  9. The final point is (−2, −3). Both coordinates changed sign.

Now you trySame steps, your turn

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

Reflect the point (4, −5) across the x-axis.

Answer:

Say it and write itSentence starters

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

  • When I reflect over the x-axis, the -coordinate changes sign and the -coordinate stays the same. When I reflect over the y-axis, the -coordinate changes sign and the -coordinate stays the same.

Word bank Reflectionx-axisy-axisSymmetryIntegerPerpendicularreflectoppositesignchangesamemirror

Watch out!A common mistake

A common mistake in Reflect Points Across Axes is flipping the sign of the wrong coordinate

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

Lesson 7.97.9 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can reflect points across the x-axis and y-axis on the coordinate plane, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 7.9. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  1. 1Complete each step, then write the final answer.
    0−5−4−3−2−112345−4−3−2−11234D (3.5, −2)
    C and D are mirror images across the y-axis.

    Point D is the reflection of point C across the y-axis. D is at (3.5, −2). Where is point C?

    1. 1Which coordinate changes across the y-axis?
    2. 2Change the sign of x back. What is the x-coordinate of C?
    3. 3What is the y-coordinate of C?
    Final answer:
  2. 2Complete each step, then write the final answer.
    0−5−4−3−2−112345−3−2−1123(−4, 1)
    Two flips, one across each axis.

    Reflect (−4, 1) across the y-axis. Then reflect that point across the x-axis.

    1. 1What is the x-coordinate after the first reflection?
    2. 2What is the y-coordinate after the second reflection?
    3. 3Why did both signs change from (−4, 1) to (4, −1)?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Reflect (0.5, −9) across the x-axis. What is the new y-coordinate?

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

    Point M is reflected across the x-axis. Its image is at (−6, −3). What is the y-coordinate of M?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    0−6−5−4−3−2−1123456−112345chest

    A pirate chest is buried at (−5, 4). A decoy chest is its reflection across the y-axis. How many units apart are the two chests?

    Show your work
    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    Lu reflects (−8, 2) across the y-axis. She changes both signs. Which point is the correct reflection?

    1. A(8, 2)
    2. B(8, −2)
    3. C(−8, −2)
    4. D(2, −8)
    Show your work

Explain your thinkingLu changed both signs for one reflection. When does changing both signs work? Use a point and both axes to explain.

ChallengeWrite your own problem

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

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