6.NOS.7 Lesson 7-9-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.9 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Reflect Points Across Axes · Reflection · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do you reflect a point across an axis?
1Reflect over the x-axis: the y-coordinate changes sign. Reflect over the y-axis: the x-coordinate changes sign.
  • A reflection is a flip of a point over a line, like a mirror image. The axis you flip over decides which coordinate changes its sign. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me
  1. I will reflect (3, 2) over the y-axis.
  2. The y-axis is the vertical line, so the point flips left or right. That changes the x-coordinate.
  3. The x changes sign: 3 becomes -3. The y stays the same: 2 stays 2.
  4. So the reflection of (3, 2) over the y-axis is (-3, 2).
3Mathematical Word Bank
  • Reflect Points Across Axes (Reflejar puntos sobre los ejes) — Flip a point across an axis so it stays the same perpendicular distance from that axis.
  • Reflection (Reflexión) — A flipped, mirror image across a line.
  • x-axis (Eje x) — The line that goes across the grid. Flipping over it changes the y sign.
  • y-axis (Eje y) — The line that goes up the grid. Flipping over it changes the x sign.
  • Symmetry (Simetría) — When a shape looks the same on both sides of a line.
  • Integer (Número entero) — Whole numbers and their opposites, like -2, -1, 0, 1, 2.
4Watch out
  • 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?'
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Point A is at (-3, 5). It is reflected over the x-axis to A', then A' is reflected over the y-axis to A''. What are the coordinates of A''?

    1. A(3, -5)
    2. B(-3, -5)
    3. C(3, 5)
    4. D(-3, 5)
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Captain Vega folds the map along the x-axis. A marker at (7, 2) lands on its mirror image. What are the new coordinates?

    1. A(7, -2)
    2. B(-7, 2)
    3. C(-7, -2)
    4. D(2, 7)
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    A buried chest is marked at (-5, 3). Vega folds the map along the y-axis to find its mirror twin. Where is the twin?

    1. A(5, 3)
    2. B(-5, -3)
    3. C(5, -3)
    4. D(3, -5)
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Vega reflects a palm-tree marker at (8, -6) across the x-axis. Which coordinate changes its sign?

    1. AThe y-coordinate
    2. BThe x-coordinate
    3. CBoth coordinates
    4. DNeither coordinate
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Level 2 Extension — Vega's Fold Mix-Up

    1. 1Problem:Reflect the marker (6, 4) across the x-axis.
    2. 2Step 1:The x-axis is the fold line, so flip the sign of the x-coordinate.
    3. 3Step 2:Change 6 to -6 and keep y as 4.
    4. 4Answer:(-6, 4)

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Find the Reflection Error

    1. 1Problem:Reflect (-3, 5) over the y-axis
    2. 2Student thinking:The y-axis is vertical, so I change the y-coordinate
    3. 3Student answer:(-3, -5)

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It