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

7.7 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    To draw a polygon from a list of vertices, you:

    1. APlot each ordered pair, then connect them in order with segments
    2. BPlot only the first vertex
    3. CConnect the points in any random order
    4. DAdd all the coordinates together
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    The park's marked vertices are 3 units apart and each unit is 100 feet. What is the park's width?

    1. A300 feet
    2. B3 feet
    3. C103 feet
    4. D30 feet
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    The park's area must be 240,000 sq ft and its width is 300 ft. What is its length?

    1. A800 feet
    2. B80,000 feet
    3. C720 feet
    4. D240,300 feet
    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. 4 MULTIPLE CHOICE

    The length is 800 feet and each unit represents 100 feet. How many units long is the park on the map?

    1. A8 units
    2. B80 units
    3. C800 units
    4. D0.8 units
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

    The known vertices of the park are at (2, 4) and (5, 4), and the length runs DOWNWARD 8 units. Where are the other two vertices?

    1. A(2, -4) and (5, -4)
    2. B(2, 12) and (5, 12)
    3. C(10, 4) and (13, 4)
    4. D(2, -8) and (5, -8)
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 OPEN RESPONSE

    A square has vertices (1, 2), (6, 2), (6, -3), (1, -3). Find one side length and the perimeter.

    💬 Sentence Starter: The vertices ___ and ___ share ___ .<br>So one side is ___ , and the perimeter is ___ .
    ✏️ 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
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