6.NOS.7 Lesson 7-9-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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7.9 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MATCHING GAME

    Match each point and axis to its reflection.

    1. (2, 5) over y-axis
    2. (-3, 1) over y-axis
    3. (4, -6) over x-axis
    4. (-1, -4) over x-axis
    5. (5, 2) over x-axis
    6. (-6, 3) over y-axis
    • A(-2, 5)
    • B(3, 1)
    • C(4, 6)
    • D(-1, 4)
    • E(5, -2)
    • F(6, 3)
  2. 2 DRAG SORT

    Put the steps in order for reflecting (5, -3) over the y-axis.

    Target Categories: Group 1 Group 2
    • Start with the point (5, -3)
    • Identify the axis of reflection: y-axis
    • The y-axis is vertical, so the x-coordinate changes sign
    • Change x from 5 to -5, keep y as -3
    • The reflection is (-5, -3)
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 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. 4 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. 5 MULTIPLE CHOICE

    Which point is on the y-axis?

    1. A(0, 5)
    2. B(5, 0)
    3. C(3, 3)
    4. D(-2, 4)
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:Reflect the point (6, 4) over the y-axis.
    2. 2Attempt:The y-axis is vertical, so I will change the y-coordinate: 4 becomes -4. The answer is (6, -4).
    3. 3Check:The point only moved up and down, but a fold over the vertical y-axis should move it left and right.

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

    ✏️ Corrected Mathematical Work & Explanation
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.
BUT An estimate provides a quick benchmark, but an exact proof is required for precision.
SO The quantities follow the standard rule, so the final result is verified with certainty.
📐 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