6.NOS.6 Lesson 7-5-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.5 Small Group · Group 2

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

Graph on the Coordinate Plane · Coordinate plane · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do you plot a point on the coordinate plane?
1Always start at the origin (0, 0), move right/left first, then up/down — 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 plot the point (5, 4). The 5 is the x-coordinate, and the 4 is the y-coordinate.
  2. I start at the origin, which is (0, 0).
  3. First I move 5 units to the right along the x-axis.
  4. Then I move 4 units up. I place my dot. That is the point (5, 4).
3Second Model — Try it together — then prove it
  1. Now let's plot (2, 1). Where do we start? At the origin (0, 0).
  2. How far do we move right? The first number is 2, so we move 2 right.
  3. How far do we move up? The second number is 1, so we move 1 up and place the dot.
  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
  • Graph on the Coordinate Plane (Representar en el plano de coordenadas) — Plot a point by moving horizontally to its x-coordinate and vertically to its y-coordinate.
  • Coordinate plane (Plano cartesiano) — A grid with a line going across and a line going up to plot points.
  • Ordered pair (Par ordenado) — Two numbers (x, y) that tell where a point is on a grid.
  • Origin (Origen) — The point (0, 0) where the two grid lines cross.
  • Quadrant (Cuadrante) — One of the four parts of a coordinate grid, numbered I to IV.
  • Reflection (Reflexión) — A flipped, mirror image across a line.
5Watch out
  • A common mistake in Graph on the Coordinate Plane is swapping the order of the coordinates — moving up/down first instead of right/left first. For example, when plotting (5, 2), students often move up 5 and right 2, landing on the wrong point (2, 5) instead of (5, 2). Remember: the x-coordinate (first number) always tells you how far to move right or left along the x-axis; the y-coordinate (second number) tells you how far up or down along the y-axis.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MATCHING GAME

    Match each point to its quadrant or axis.

    1. (3, 2)
    2. (-4, 5)
    3. (-2, -6)
    4. (7, -1)
    5. (0, 3)
    6. (5, 0)
    • AQuadrant I
    • BQuadrant II
    • CQuadrant III
    • DQuadrant IV
    • Ey-axis
    • Fx-axis
  2. 2 MULTIPLE CHOICE

    Spot 2 — The map marks the Lookout Tower at (4, 9). What does the 4 tell you to do from the origin?

    1. AMove 4 units to the right along the x-axis
    2. BMove 4 units up along the y-axis
    3. CMove 4 units to the left
    4. DStay on the y-axis at 4
    ✏️ Workspace & Solution Steps
SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]
  1. 3 COORDINATE GRID

    Plot these points to reveal a hidden shape: (1, 1), (1, 5), (6, 5), (6, 1)

    ✏️ Workspace & Solution Steps
SECTION 3 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 4 MULTIPLE CHOICE

    Spot 3 — Vega writes: 'The Coconut Grove is 3 across and 8 up.' Which point on the map is the Coconut Grove?

    1. A(3, 8)
    2. B(8, 3)
    3. C(3, 3)
    4. D(0, 8)
    ✏️ Workspace & Solution Steps
  2. 5 MULTIPLE CHOICE

    Which ordered pair names a point 3 units right and 7 units up from the origin?

    1. A(3, 7)
    2. B(7, 3)
    3. C(3, 3)
    4. D(0, 7)
    ✏️ Workspace & Solution Steps
SECTION 4 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Level 2 Extension — Captain Vega's Misread Coordinate

    1. 1Clue:The Pirate Flag is at (3, 6).
    2. 2Read the x-coordinate:Move 3 units to the right along the x-axis.
    3. 3Read the y-coordinate:Move 1 unit up along the y-axis.
    4. 4Plot the point:Place the flag where (3, 1) would go.

    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