6.NOS.7 Lesson 7-9-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
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7.9 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Find the reflection of each point over the given axis.

    Original PointAxisReflected Point
    (3, -7)
    (-5, 2)
    (8, -1)
    (-4, -6)
    (0, 9)
    (-3, 0)
    ✏️ Scratchpad / Reasoning
SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 2 COORDINATE GRID

    Plot (1, 4) and its reflections: over the x-axis, over the y-axis, and over both axes

    ✏️ Workspace & Solution Steps
SECTION 3 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 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
  2. 4 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
  3. 5 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 4 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 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
🗣️ 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
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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It