6.GR.4 Lesson 5-7-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
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5.7 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

Surface Area of Prisms · Surface area · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — 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.
  • Surface area is the total area of all the faces of a solid. A rectangular prism has 6 faces; a triangular prism has 5 faces (2 triangles + 3 rectangles). Add every face to get the total. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
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.
3Mathematical 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.
4Watch 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 DRAG SORT

    Put the steps in order for finding the surface area of a triangular prism.

    Target Categories: Steps in order (first → last)
    • Find the area of one triangular base
    • Multiply the triangle area by 2 (two bases)
    • Find the area of each rectangular lateral face
    • Add all three rectangle areas together
    • Add the two triangle areas + all rectangle areas = SA
  2. 2 MATCHING GAME

    Match each solid to its description.

    1. Rectangular prism
    2. Triangular prism
    3. Cube
    4. Surface area
    5. Volume
    6. Net
    • A6 faces (all rectangles)
    • B5 faces (2 triangles + 3 rectangles)
    • C6 identical square faces
    • DUses square units (in²)
    • EUses cubic units (in³)
    • F2D pattern that folds into 3D
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    What is the surface area of a rectangular prism with l = 5 cm, w = 4 cm, h = 3 cm?

    1. A94 cm²
    2. B60 cm²
    3. C94 cm³
    4. D47 cm²
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
  2. 4 MULTIPLE CHOICE

    How many faces does a triangular prism have?

    1. A5
    2. B4
    3. C6
    4. D3
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    A triangular prism has two triangular bases each with area 12 cm² and three rectangular faces with areas 30 cm², 40 cm², and 40 cm². What is the total surface area?

    1. A134 cm²
    2. B110 cm²
    3. C122 cm²
    4. D134 cm³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Common Mistake — A Forgotten Face

    1. 1Dimensions:Rectangular prism time capsule: l = 5 in, w = 3 in, h = 2 in.
    2. 2Formula:SA = 2lw + 2lh + 2wh (add all 6 faces).
    3. 3Calculate:The student wrote SA = 2(5×3) + 2(5×2) + (3×2) = 30 + 20 + 6 = 56 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
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It