6.GR.1 Lesson 5-9-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.9 Small Group · Group 2

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

Area of Regular Polygons · Regular Polygon · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do we find the area of a regular polygon?
1A regular polygon splits into the same number of triangles as it has sides, so total area = (one triangle's area) × (number of sides) — 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. My hexagon has 6 equal sides. Each side is 6 feet, and each center triangle has a height of 5.2 feet.
  2. First I find one triangle: A = ½ × base × height = ½ × 6 × 5.2.
  3. I multiply: 6 × 5.2 = 31.2, then ½ × 31.2 = 15.6 square feet.
  4. A hexagon has 6 sides, so it has 6 equal triangles.
  5. I multiply: 6 × 15.6 = 93.6. So the total area is 93.6 square feet.
3Second Model — Try it together — then prove it
  1. Now a smaller regular pentagon: each of its 5 triangles has base 4 cm and height 3 cm.
  2. First find one triangle: ½ × 4 × 3. What is 4 × 3? Yes, 12, and half of 12 is 6 sq cm.
  3. A pentagon has 5 sides, so how many triangles? Yes, 5.
  4. Multiply: 5 × 6 = 30, so the total area is 30 square centimeters.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • Area of Regular Polygons (Área de polígonos regulares) — The space a regular polygon covers. Split it from the center into identical triangles, find one triangle's area, then multiply by how many there are.
  • Regular Polygon (Polígono regular) — A closed flat shape made of straight sides, where every side is the same length and every angle is the same size.
  • Decompose (Descomponer) — To break a shape into smaller, simpler shapes.
  • Triangle (Triángulo) — A shape with three sides.
  • Composite (Compuesto) — Made by putting two or more simple shapes together.
  • Formula (Fórmula) — A math rule written with symbols.
5Watch out
  • A common mistake in Area of Regular Polygons is stopping after finding the area of ONE triangle and reporting that as the total area — or adding the number of triangles instead of multiplying. Remember: total area = (one triangle's area) × (number of sides), not (one triangle's area) + (number of sides).
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Using the triangle from the previous question, what is the total area of the hexagonal skylight?

    1. A93.6 sq ft
    2. B15.6 sq ft
    3. C187.2 sq ft
    4. D62.4 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2 MULTIPLE CHOICE

    A regular hexagon is split into 6 triangles, each with base 4 cm and height 3.5 cm. What is the total area?

    1. A42 sq cm
    2. B21 sq cm
    3. C84 sq cm
    4. D14 sq cm
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Using the triangle from the previous question, what is the total area of the hexagonal skylight?
    2. 2A classmate at our table answered:15.6 sq ft

    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. 1Decompose the pentagon:A regular pentagon = 5 congruent triangles
    2. 2Identify one triangle:base = 6 ft, height = 4 ft
    3. 3Find the area of one triangle:A = 6 × 4 = 24 sq ft
    4. 4Find total area:Total area = 5 × 24 = 120 sq ft

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 5 ERROR ANALYSIS

    Find the Area Error

    1. 1Decompose the hexagon:A regular hexagon = 6 triangles
    2. 2Find area of one triangle:b = 5 m, h = 4.3 m
    3. 3Calculate one triangle:A = ½ × 5 × 4.3 = 10.75 sq m
    4. 4Find total area:Total = 10.75 + 6 = 16.75 sq m

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 6 OPEN RESPONSE

    A regular hexagon and a regular pentagon both have triangles with the same base (6 ft) and the same height (5 ft). Which polygon has the greater total area? Explain why the number of sides matters.

    ✏️ 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