6.GR.4 Lesson 5-7-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.7 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

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 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A triangular prism has triangular bases with base 6 in and height 4 in. The prism is 10 in long and the two slant sides of the triangle are each 5 in. What is the surface area?

    1. A184 in²
    2. B160 in²
    3. C124 in²
    4. D184 in³
    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. 2 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
  3. 3 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
  4. 4 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
    1. 1Name itWhich measure is asked?
    2. 2Write the formulaBefore any numbers.
    3. 3SubstituteMatch each letter.
    4. 4Unitunits, sq units, or cubic?
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Common Mistake — Surface Area or Volume?

    1. 1Dimensions:Rectangular prism time capsule: l = 7 in, w = 4 in, h = 3 in. Find the surface area.
    2. 2Formula:Surface area adds all 6 faces: SA = 2lw + 2lh + 2wh.
    3. 3Calculate:The student multiplied the three dimensions: 7 × 4 × 3 = 84, so they wrote SA = 84 in².

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 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
📐 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