6.GR.4 Lesson 5-7-part2 Apply Day · Practice
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.7 · Part II

Application Practice for Today's Problem

Surface Area of Prisms · Surface area

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 5.7 · Part II
1Surface Area of Prisms
2Strategy Model — step by step
  1. Calculate area of Top & Bottom: 2 × (l · w)
  2. Calculate area of Front & Back: 2 × (l · h)
  3. Calculate area of Left & Right: 2 × (w · h), then sum all three pairs
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 OPEN RESPONSE

    A company ships products in two container options: a rectangular prism (8 × 6 × 4 in) or a triangular prism (triangle base 8 in, triangle height 6 in, prism length 8 in, slant sides 6.3 in each). Both must be wrapped in protective film. Which shape uses LESS film? Show your work.

    💬 Sentence Starter: Rectangular prism SA = 2(___) + 2(___) + 2(___) = ___ in². Triangular prism SA = 2(___) + ___ + ___ + ___ = ___ in². The ___ uses less film because ___.
    ✏️ 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
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