6.NOS.7 Lesson 7-8-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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7.8 Small Group · Group 1

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

Ordered Pairs in All Four Quadrants · Quadrant · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do you plot points in all four quadrants?
1The signs of (x, y) tell you the quadrant: (+,+) is I, (-,+) is II, (-,-) is III, (+,-) is IV.
  • The coordinate plane has four parts called quadrants. A negative coordinate means you move left (for x) or down (for y) from the origin instead of right or up. 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 plot (-3, -4). I start at the origin (0, 0).
  2. The x is -3, which is negative, so I move 3 units to the LEFT.
  3. The y is -4, which is negative, so I move 4 units DOWN. I place my dot.
  4. Both coordinates are negative, so the point is in Quadrant III.
3Mathematical Word Bank
  • Ordered Pairs in All Four Quadrants (Pares ordenados en los cuatro cuadrantes) — Points written as (x, y) whose positive or negative coordinates place them in one of four quadrants.
  • Quadrant (Cuadrante) — One of the four parts of a coordinate grid, numbered I to IV.
  • Negative coordinate (Coordenada negativa) — A coordinate less than zero. It means left or below the center point.
  • Reflection (Reflexión) — A flipped, mirror image across a line.
  • Axis (Eje) — One of the two number lines that frame a graph: the x-axis runs across, the y-axis runs up and down.
  • Integer (Número entero) — Whole numbers and their opposites, like -2, -1, 0, 1, 2.
4Watch out
  • A common mistake in Ordered Pairs in All Four Quadrants is matching each sign to the wrong axis — for example, seeing (-2, 5) and thinking "the x is negative so I move DOWN, and the y is positive so I move RIGHT," which lands the point in Quadrant IV. But the x-coordinate always controls left/right, never up/down: negative x means LEFT (not down), and positive y means UP (not right). So (-2, 5) is actually left 2, up 5 — Quadrant II. Before you submit, check that you used the x-coordinate for left/right and the y-coordinate for up/down, and never swapped them.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MATCHING GAME

    Match each ordered pair to its quadrant.

    1. (3, 4)
    2. (-2, 5)
    3. (-6, -1)
    4. (1, -3)
    5. (-4, 2)
    6. (5, -6)
    • AQuadrant I
    • BQuadrant II
    • CQuadrant III
    • DQuadrant IV
    • EQuadrant II
    • FQuadrant IV
  2. 2 DRAG SORT

    Sort these points by their quadrant: I first, then II, III, IV.

    Target Categories: Group 1 Group 2
    • (-3, -2)
    • (5, 1)
    • (-1, 4)
    • (2, -6)
    • (4, 3)
    • (-5, -7)
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    In which quadrant is the point (-4, 5)?

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant III
    4. DQuadrant IV
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    A point has a positive x-coordinate and a negative y-coordinate. Which quadrant is it in?

    1. AQuadrant I
    2. BQuadrant II
    3. CQuadrant III
    4. DQuadrant IV
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Which point is located on the x-axis?

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

    Spot the Common Mistake

    1. 1Problem:Name the quadrant for the point (-2, 5).
    2. 2Student thinking:The x is -2, so I move 2 units DOWN. The y is 5, so I move 5 units to the RIGHT.
    3. 3Student answer:(-2, 5) is in Quadrant IV.

    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