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

5.3 Small Group · Group 2

Tier 1 Extension · Non-Routine Synthesis · Misconception Traps · Rigorous CER Proofs

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Solve the mathematical problem. Show all of your work and reasoning.

    TrapezoidBase 1Base 2HeightArea
    Window A
    Window B
    Window C
    Window D
    ✏️ Scratchpad / Reasoning
  2. 2 MATCHING GAME

    Match each shape to its area.

    1. Trapezoid b₁=10, b₂=6, h=4
    2. Trapezoid b₁=8, b₂=4, h=5
    3. Trapezoid b₁=12, b₂=8, h=4
    4. Triangle b=14, h=6
    5. Parallelogram b=9, h=5
    6. Rectangle 7×3
    • A32 sq units
    • B30 sq units
    • C40 sq units
    • D42 sq units
    • E45 sq units
    • F21 sq units
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    Blueprint 2: A trapezoidal skylight has bases of 9 ft and 7 ft and a height of 6 ft. What is its area?

    1. A48 sq ft
    2. B96 sq ft
    3. C63 sq ft
    4. D44 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 4 MULTIPLE CHOICE

    Two equal trapezoid windows join to form a parallelogram with area 96 sq ft. What is the area of ONE trapezoid?

    1. A48 sq ft
    2. B96 sq ft
    3. C16 sq ft
    4. D192 sq ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 5 MULTIPLE CHOICE

    A trapezoid has an area of 45 sq ft, bases of 7 ft and 11 ft. What is the height?

    1. A5 ft
    2. B9 ft
    3. C3 ft
    4. D10 ft
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Level 2 Extension — The Missing Half

    1. 1Read the blueprint:Trapezoid window: b1 = 6 ft, b2 = 10 ft, h = 4 ft
    2. 2Write the formula:A = ½ × (b1 + b2) × h
    3. 3Add the bases, then multiply by height:(6 + 10) × 4 = 16 × 4 = 64
    4. 4State the area for the glass order:A = 64 sq ft

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

    ✏️ Corrected Mathematical Work & Explanation
🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."
👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."
✍️ 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
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.
✍️ AUTHOR YOUR OWN EXTENSION CHALLENGE

Create an original multi-step word problem aligned to this standard. Include constraints, and write the complete step-by-step mathematical proof below.

✏️ Author Workspace & Complete Solution Key
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It