6.NOS.7 Lesson 7-8-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.8 Small Group · Group 2

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

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — 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 (-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.
3Second Model — Try it together — then prove it
  1. Now let's plot (-5, 2). The x is -5, so which way do we move? Left 5 units.
  2. The y is 2, which is positive, so which way? Up 2 units.
  3. Left and up lands us in which quadrant? Quadrant II.
  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
  • 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.
5Watch 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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A sonar ping locates an enemy submarine at (-5, -2). In which quadrant should Captain Vega aim her shot?

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

    Captain Vega's lookout reports a ship in Quadrant II. What signs will its coordinates (x, y) have?

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

    Point A is at (-5, 3). If you move 8 units to the right, what are the new coordinates?

    1. A(3, 3)
    2. B(-13, 3)
    3. C(-5, 11)
    4. D(-5, -5)
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Captain Vega's lookout reports a ship in Quadrant II. What signs will its coordinates (x, y) have?
    2. 2A classmate at our table answered:(+, +)

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 OPEN RESPONSE

    A point is reflected across the x-axis, and then that image is reflected across the y-axis. Predict which quadrant it lands in for a start in EACH of the four quadrants, then state the rule for what happens to the coordinates (x, y). Does the order of the two reflections matter?

    ✏️ Mathematical Justification & Response
  3. 6 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:Name the quadrant for the point (6, -1).
    2. 2Student thinking:I'll read the coordinates as (y, x), so I treat this like (-1, 6): the first number -1 is negative (left) and the second number 6 is positive (up).
    3. 3Student answer:(6, -1) is in Quadrant II.

    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