6.NOS.9 Lesson 7-6-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.6 Small Group · Group 1

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

Visual Models · Distance on the Coordinate Plane · Distance · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do you find distance on the coordinate plane?
1If points are on the same side of zero, subtract; if they are on opposite sides of zero, add the absolute values.
  • Distance is how far apart two points are, and it is never negative. When two points share a row or a column, you can find the distance using their coordinates. 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 find the distance from (-3, 2) to (4, 2). Both have y = 2, so they sit on the same horizontal line.
  2. The points are on opposite sides of zero, so I add the absolute values.
  3. |-3| = 3 and |4| = 4.
  4. I add: 3 + 4 = 7. The distance between them is 7 units.
3Mathematical Word Bank
  • Distance on the Coordinate Plane (Distancia en el plano de coordenadas) — The positive space between points, found from the absolute difference of coordinates on a horizontal or vertical line.
  • Distance (Distancia) — How far apart two points are. It is never negative.
  • Absolute value (Valor absoluto) — How far a number is from zero. It is never negative.
  • Horizontal distance (Distancia horizontal) — How far apart two points are going left or right.
  • Vertical distance (Distancia vertical) — How far apart two points are going up or down.
  • Coordinate plane (Plano cartesiano) — A grid with a line going across and a line going up to plot points.
4Watch out
  • A common mistake in Distance on the Coordinate Plane is subtracting the coordinates as if both points were on the same side of zero, instead of adding their absolute values when the points are on opposite sides. For example, to find the distance between (-6, 3) and (2, 3), a student might subtract 6 − 2 = 4, but since -6 and 2 are on opposite sides of zero, the absolute values must be added instead: |-6| + |2| = 6 + 2 = 8. The correct distance is 8 units, not 4. Before you submit, ask: 'Are these two points on opposite sides of zero — and if so, did I add the absolute values instead of subtracting?'
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Find the distance between each pair of points.

    Point 1Point 2Shared CoordinateDistance
    (-5, 1)
    (2, -4)
    (-3, -2)
    (-1, 5)
    ✏️ Scratchpad / Reasoning
  2. 2 NUMBER LINE

    Plot -4 and 2 on the number line. Count the distance between them.

    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    What is the distance between (-4, 3) and (2, 3)?

    1. A2 units
    2. B4 units
    3. C6 units
    4. D8 units
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    What is the distance between (5, -2) and (5, 4)?

    1. A2 units
    2. B4 units
    3. C6 units
    4. D10 units
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    A rectangle has vertices at (1, 1), (5, 1), (5, 4), (1, 4). What is its perimeter?

    1. A14 units
    2. B12 units
    3. C20 units
    4. D8 units
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Problem:Find the distance between (2, 1) and (2, 6).
    2. 2Student thinking:Both share x = 2, so add the absolute values: |1| + |6| = 1 + 6 = 7.
    3. 3Student answer:The distance is 7 units.

    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