6.GR.1 Lesson 5-3-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.3 Small Group · Group 2

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

Area of Trapezoids · Trapezoid · 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 trapezoid?
1Area of a trapezoid = ½ × (base 1 + base 2) × height. We add the two bases first, then take half — 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 trapezoid window has a top base of 4 feet, a bottom base of 8 feet, and a height of 5 feet.
  2. I write the formula: A = ½ × (b1 + b2) × h.
  3. I add the bases first: 4 + 8 = 12.
  4. I multiply by the height: 12 × 5 = 60.
  5. I take half: ½ × 60 = 30. So the area is 30 square feet.
3Second Model — Try it together — then prove it
  1. Now a smaller trapezoid: bases 3 cm and 5 cm, height 2 cm.
  2. First, what is 3 + 5? Yes, 8.
  3. Next, what is 8 × 2? Yes, 16.
  4. Now take half: ½ × 16 = 8, so the area is 8 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 Trapezoids (Área de trapecios) — The space inside a trapezoid. Formula: A = 1/2(b₁ + b₂)h.
  • Trapezoid (Trapecio) — A four-sided shape with just one pair of parallel sides.
  • Parallel (Paralelas) — Two lines or sides that stay the same distance apart and never meet.
  • Base 1 (b1) (Base 1 (b1)) — One of the two parallel sides of a trapezoid.
  • Base 2 (b2) (Base 2 (b2)) — The other parallel side of a trapezoid.
  • Height (Altura) — The straight-up distance between the two parallel sides.
5Watch out
  • A common mistake in Area of Trapezoids is forgetting the ½ in A = ½ × (b1 + b2) × h. After adding the bases and multiplying by the height, students stop there instead of taking half — for example, with bases 6 ft and 10 ft and a height of 4 ft, they compute (6 + 10) × 4 = 64 sq ft instead of taking half to get the correct 32 sq ft. That unhalved number is really the area of the parallelogram made from two trapezoids, not the area of one trapezoid. Before you submit, always ask: "Did I take half of my last answer?"
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Blueprint 1: A trapezoidal lobby window has bases of 6 ft and 10 ft and a height of 4 ft. What is its area for the glass order?

    1. A32 sq ft
    2. B40 sq ft
    3. C16 sq ft
    4. D60 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    Design a trapezoid whose area is exactly 24 sq ft, where one base is 4 ft LONGER than the other. Give both bases and the height, and show your design checks out. Could a classmate's correct design use different numbers than yours?

    ✏️ Mathematical Justification & Response
  2. 3 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Blueprint 1: A trapezoidal lobby window has bases of 6 ft and 10 ft and a height of 4 ft. What is its area for the glass order?
    2. 2A classmate at our table answered:60 sq ft

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 4 ERROR ANALYSIS

    Using the Wrong Height

    1. 1Read the blueprint:A trapezoid window has b1 = 7 ft and b2 = 13 ft. The slanted side measures 10 ft, and the straight-up height between the bases is 6 ft.
    2. 2Write the formula:A = ½ × (b1 + b2) × h
    3. 3Substitute values:A = ½ × (7 + 13) × 10
    4. 4Calculate:A = ½ × 20 × 10 = 100 sq ft

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

    ✏️ Corrected Mathematical Work & Explanation
  4. 5 ERROR ANALYSIS

    Find the Area Error

    1. 1Identify the bases and height:b₁ = 10 m, b₂ = 6 m, h = 7 m
    2. 2Write the formula:A = ½ × (b₁ + b₂) × h
    3. 3Substitute values:A = ½ × (10 + 6) × 7
    4. 4Calculate:A = (10 + 6) × 7 = 112 sq m

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

    ✏️ Corrected Mathematical Work & Explanation
  5. 6 OPEN RESPONSE

    A trapezoid and a parallelogram both have a height of 8 ft. The trapezoid has bases of 5 ft and 11 ft. The parallelogram has a base of 7 ft. Which shape has the greater area? Explain your reasoning using the formulas.

    ✏️ 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