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

7.5 Small Group · Group 2

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

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 MULTIPLE CHOICE

    A point is at (6, 2). What does the 6 tell you?

    1. AMove 6 units to the right
    2. BMove 6 units up
    3. CMove 6 units to the left
    4. DThe point is in Quadrant 6
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    What are the coordinates of the origin?

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

    Fix our table's thinking

    1. 1The problem:What are the coordinates of the origin?
    2. 2A classmate at our table answered:(1, 0)

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 4 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Clue:Plot the point (4, 0).
    2. 2Move right:Move 4 units to the right along the x-axis. Good.
    3. 3Move up:Move 4 units up, because the pair has a 4 in it.
    4. 4Plot the point:Place the dot at (4, 4).

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 5 ERROR ANALYSIS

    Miscounted Grid Lines

    1. 1Ordered pair:(7, 3)
    2. 2Move along the x-axis:Start at the origin (0, 0) and count 7 units to the right.
    3. 3Move along the y-axis:Count up from the x-axis: 1, 2, 3, 4 — stop on 4.
    4. 4Plot the point:Place the dot at (7, 4).

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 6 OPEN RESPONSE

    A student says that (3, 5) and (5, 3) are the same point because they use the same numbers. Is the student correct? Explain why or why not, and describe where each point is located on the coordinate plane.

    ✏️ Mathematical Justification & Response
📐 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