6.NOS.7 Lesson 7-9-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.9 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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).
3Second Model — Try it together — then prove it
  1. Now let's reflect (4, -5) over the x-axis. Which coordinate changes over the x-axis? The y-coordinate.
  2. What does -5 become when it changes sign? It becomes 5.
  3. The x stays 4, so the reflection is what point? It is (4, 5).
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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

    What is the reflection of (4, -3) over the x-axis?

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

    What is the reflection of (-2, 6) over the y-axis?

    1. A(2, 6)
    2. B(-2, -6)
    3. C(2, -6)
    4. D(6, -2)
    ✏️ Workspace & Solution Steps
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:What is the reflection of (4, -3) over the x-axis?
    2. 2A classmate at our table answered:(-4, 3)

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:Reflect the point (-3, -8) over the x-axis.
    2. 2Attempt:Both coordinates are negative, so I will flip the x-coordinate: -3 becomes 3. The answer is (3, -8).
    3. 3Check:Folding over the horizontal x-axis should send the point up across the axis, but this answer kept it below the axis.

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 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
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It