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

7.7 Small Group · Group 1

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

vertex · polygon · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — The coordinates already know the side lengths
1When two vertices share a coordinate, the side between them is the absolute difference of the coordinates that differ.
  • Graph the points, connect them in order, and the polygon appears. Then the same coordinates that placed the corners tell you exactly how long each side is. 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 find one side
  1. (-4.5, 3) and (5, 3) share y = 3, so the side between them is horizontal.
  2. Its length is the distance between the x-coordinates: |5 − (−4.5)| = 9.5 units.
  3. (5, 3) and (5, -3.75) share x = 5, so that side is vertical: |3 − (−3.75)| = 6.75 units.
3Mathematical Word Bank
  • vertex (vértice) — A corner point of a polygon, named by an ordered pair on the coordinate plane.
  • polygon (polígono) — A closed figure made of line segments; on the plane you draw it by plotting the vertices and connecting them in order.
  • perimeter (perímetro) — The total distance around a polygon — the sum of all its side lengths.
  • distance between vertices (distancia entre vértices) — When two vertices share an x- or y-coordinate, the distance between them is the absolute difference of the other coordinates.
  • scale (escala) — What one grid unit stands for in the real situation.
4Watch out
  • Subtracting coordinates without the absolute value — from y = 3 down to y = −3.75 the distance is 3 + 3.75 = 6.75 units, not 3.75 − 3 = 0.75. Distances that cross zero are the whole reason the absolute value is there.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each pair of vertices by the kind of side it makes.

    Target Categories: Vertical side (same x) Horizontal side (same y)
    • (5, 3) and (5, −3)
    • (−2, 1) and (−2, 6)
    • (4, −1) and (4, 7)
    • (−4, 3) and (5, 3)
    • (0, −2) and (6, −2)
    • (−3, 5) and (2, 5)
  2. 2 FILL TABLE

    Find the distance between each pair of vertices.

    VerticesShared coordinateDistance (units)
    (−4, 3) and (5, 3)
    (5, 3) and (5, −4)
    (−2, −1) and (6, −1)
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Vertices (-4.5, 3) and (5, 3) share y = 3. What is the distance between them?

    1. A9.5 units
    2. B0.5 units
    3. C8 units
    4. D1.5 units
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  2. 4 MULTIPLE CHOICE

    Vertices (5, 3) and (5, -3.75) share x = 5. What is the distance between them?

    1. A6.75 units
    2. B0.75 units
    3. C5 units
    4. D8.75 units
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  3. 5 MULTIPLE CHOICE

    What is the perimeter of the rectangle with side lengths 9.5 and 6.75 units?

    1. A32.5 units
    2. B16.25 units
    3. C64.125 units
    4. D26 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?
  4. 6 MULTIPLE CHOICE

    Why are two of the terms multiplied by 2 in the perimeter calculation?

    1. AA rectangle's opposite sides are equal, so each length appears on two sides
    2. BBecause perimeter always doubles the area
    3. CBecause there are two coordinates in each ordered pair
    4. DIt is a rounding rule
    ✏️ Workspace & Solution Steps
✍️ 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