6.NOS.9 Lesson 7-7-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

7.7 Small Group · Group 2

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

vertex · polygon · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — 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 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.
3Second Model — Try it together — then prove it
  1. The shape is a rectangle, so the opposite sides match: two sides of 9.5 and two of 6.75.
  2. Perimeter = 2(9.5) + 2(6.75) = 19 + 13.5 = 32.5 units.
  3. That is why two of the terms are multiplied by 2 — each length appears on two sides.
  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
  • 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.
5Watch 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

    A square has vertices (a, b) and (a, b + s) on one side. Which operation gives the side length for ANY values?

    1. ASubtract the y-coordinates and take the absolute value
    2. BAdd all four coordinates
    3. CMultiply a × b
    4. DAverage the coordinates
    ✏️ 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 OPEN RESPONSE

    The park design used width from coordinates, then length from the area, then the scale to place the missing vertices. Design your own version: pick an area and a scale, mark two vertices, and show where the other two go.

    ✏️ Mathematical Justification & Response
  2. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A rectangle has vertices (-3, 2), (4, 2), (4, -1), (-3, -1). What is its perimeter?
    2. 2A classmate at our table answered:13 units

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 OPEN RESPONSE

    A rectangle has vertices (a, b), (a + w, b), (a + w, b + h), and (a, b + h). Write expressions for its side lengths, perimeter, and area that work for ANY a, b, w, and h. Then explain why a and b never appear in your perimeter or area.

    ✏️ 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