6.GR.4 Lesson 5-7-group2 🟣 Group 2 · Challenge & Extension
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.7 Small Group · Group 2

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

Visual Models · Surface Area of Prisms · Surface area · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do we find the surface area of a prism?
1No matter the prism, find the area of every face and add them all together — 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 triangular prism has triangle bases (base 6 in., height 4 in.), is 10 in. long, and the two slant sides are 5 in. each.
  2. Each triangle base is ½ × 6 × 4 = 12, and there are 2 of them: 2 × 12 = 24.
  3. Now the 3 rectangles: 6 × 10 = 60, 5 × 10 = 50, and 5 × 10 = 50, which add to 160.
  4. I add the bases and the rectangles: 24 + 160 = 184.
  5. So the surface area is 184 in². I counted 5 faces because it is a triangular prism.
3Second Model — Try it together — then prove it
  1. Now a rectangular prism: 5 long, 4 wide, 3 tall. How many faces does it have?
  2. Top and bottom: 5 × 4 = 20, times 2 = 40. Front and back: 5 × 3 = 15, times 2 = 30.
  3. Left and right: 4 × 3 = 12, times 2 = 24. Now add 40 + 30 + 24. What is the surface area?
  4. Yes, SA = 94 cm². Surface area always uses square units.
  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
  • Surface Area of Prisms (Área de superficie de prismas) — The total area of all bases and lateral faces of a prism. Formula: SA = 2B + lateral area.
  • Surface area (Área de superficie) — The total area of all the flat sides of a solid.
  • Rectangular prism (Prisma rectangular) — A solid box shape with six flat rectangle sides.
  • Triangular prism (Prisma triangular) — A solid with two triangle ends and three flat rectangle sides.
  • Face (Cara) — One flat side of a solid shape.
  • Net (Plantilla (desarrollo plano)) — A flat shape that folds up into a solid.
5Watch out
  • A common mistake in Surface Area of Prisms is confusing surface area with volume — multiplying l × w × h (which finds the space INSIDE the prism, in cubic units) instead of adding the areas of all the faces (SA = 2lw + 2lh + 2wh, in square units). A second common slip is forgetting to double one face pair, like writing 2(l×w) + 2(l×h) + (w×h) instead of + 2(w×h) — always count all 6 faces (or all 5 for a triangular prism) before you submit.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 FILL TABLE

    Calculate the surface area of each rectangular prism time capsule.

    CapsuleLengthWidthHeightSurface Area
    Capsule E
    Capsule F
    Capsule G
    ✏️ Scratchpad / Reasoning
  2. 2 BAR MODEL

    What is the combined area of the left and right faces?

    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A rectangular time capsule box measures 3 in by 4 in by 5 in. How much wrapping paper covers its surface (no overlap)?

    1. A94 in²
    2. B60 in²
    3. C47 in²
    4. D94 in³
    ✏️ Workspace & Solution Steps
  2. 4 MULTIPLE CHOICE

    A rectangular capsule crate is 6 cm long, 5 cm wide, and 4 cm tall. How much cardboard is needed to cover all its faces?

    1. A148 cm²
    2. B120 cm²
    3. C74 cm²
    4. D148 cm³
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    A triangular prism is 10 in long. Its triangle ends have base 8 in, height 6 in, and sides 8, 6, and 10 in. Find its surface area.

    1. A288 in²
    2. B240 in²
    3. C48 in²
    4. D288 in³
    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 — Wrapping Paper Mix-Up

    1. 1Dimensions:Rectangular capsule: l = 4 in, w = 3 in, h = 2 in. Find the wrapping paper (surface area).
    2. 2Formula:Surface area means adding the area of all 6 faces: SA = 2lw + 2lh + 2wh.
    3. 3Calculate:The student multiplied the three dimensions: 4 × 3 × 2 = 24, so they wrote SA = 24 in².
    4. 4Answer:Wrapping paper needed = 24 in²

    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