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

Lesson 7.97.9 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can reflect points across the x-axis and y-axis on the coordinate plane — one step at a time, with support.

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.

Reflect the point (3, 2) across the y-axis.

  1. Find the axis you reflect across: y-axis
  2. Change the sign of x: 3 → −3
  3. Keep y the same: 2 → 2
  4. The reflection of (3, 2) across the y-axis is (−3, 2).

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 outA common mistake

A common mistake in Reflect Points Across Axes is flipping the sign of the wrong coordinate — changing the x-coordinate when reflecting over the x-axis, instead of the y-coordinate (or vice versa for the y-axis). For example, to reflect (3, -5) over the x-axis, a student might flip the x-coordinate and write (-3, -5), but reflecting over the x-axis only changes the sign of the y-coordinate: (3, -5) becomes (3, 5). Before you submit, ask: 'Did I flip the sign of the coordinate that matches the axis I'm reflecting over — y for the x-axis, x for the y-axis?'

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

Lesson 7.97.9 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, I can reflect points across the x-axis and y-axis on the coordinate plane — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    −7−5−3−11357−3−2−1123(6, 1)
    Both points are 6 units from the y-axis.

    Reflect the point (6, 1) across the y-axis.

    1. 1Which coordinate changes when you reflect across the y-axis?
    2. 2What does 6 become when it changes sign?
    3. 3The y stays 1. What is the new point?
    Final answer:
  2. 2Complete each step, then write the final answer.
    −3−2−1123−5−4−3−2−112345(−1, −4)
    This time we flip across the x-axis.

    Reflect the point (−1, −4) across the x-axis.

    1. 1Which coordinate changes when you reflect across the x-axis?
    2. 2What does −4 become when it changes sign?
    3. 3The x stays −1. What is the new point?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Reflect (6, 4) across the x-axis. The new point is (6, ?). What is the missing y-coordinate?

    Show your work

    Hint Across the x-axis, the y-coordinate changes sign.

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

    Reflect (−7, −2.5) across the y-axis. The new point is (?, −2.5). What is the missing x-coordinate?

    Show your work

    Hint Across the y-axis, the x-coordinate changes sign.

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

    Captain Vega folds her map along the x-axis. A palm tree at (−3, 8) lands on its mirror image. What is the y-coordinate of the mirror image?

    Show your work

    Hint Folding along the x-axis is a reflection across the x-axis. Which coordinate changes?

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

    Rosa reflects (4, −6) across the x-axis. She writes (−4, −6). Is she right? What is the correct y-coordinate?

    Show your work

    Hint Rosa changed x. Which coordinate should change across the x-axis?

    Final answer:

Explain your thinkingRosa changed the wrong coordinate. How can you tell which coordinate changes when you reflect?

Sentence starter Across the x-axis, the ___ changes because ___. · Rosa should have changed ___.

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