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

5.6 Small Group · Group 1

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

Surface Area Using Nets · 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 box?
1A box has 3 pairs of matching faces, so add up all 6 faces to get the surface area.
  • Surface area is the total area of all the flat faces of a solid. A net unfolds the box flat so you can see and add all 6 faces. The answer uses square units. 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 box is 8 in. long, 5 in. wide, and 3 in. tall. I unfold it into a net and see 3 pairs of faces.
  2. Top and bottom: each is 8 × 5 = 40, and there are 2 of them, so 2 × 40 = 80.
  3. Front and back: each is 8 × 3 = 24, so 2 × 24 = 48.
  4. Left and right: each is 5 × 3 = 15, so 2 × 15 = 30.
  5. I add all the pairs: 80 + 48 + 30 = 158. The surface area is 158 in².
3Mathematical Word Bank
  • Surface Area Using Nets (Área de superficie usando redes) — The total area of all the faces of a solid. A net unfolds the solid flat so you can see every face and add their areas.
  • Surface area (Área de superficie) — The total area of all the flat sides of a solid.
  • Net (Plantilla (desarrollo plano)) — A flat shape that folds up into a solid.
  • Face (Cara) — One flat side of a solid shape.
  • Two-dimensional (Bidimensional) — A flat shape with length and width, but no thickness.
  • Edge (Arista) — The line where two flat sides of a solid meet.
4Watch out
  • A common mistake in Surface Area Using Nets is finding the area of only one face from each of the 3 matching pairs and forgetting to double it, instead of counting all 6 faces. For a box that is 9 in × 4 in × 5 in, a student might add just one face from each pair: (9×4) + (9×5) + (4×5) = 36 + 45 + 20 = 101 in², but the net actually has two of each face, so the correct total is 2(36) + 2(45) + 2(20) = 72 + 90 + 40 = 202 in² — exactly double. Before you submit, ask: 'Did I count both matching faces in each pair, or only one from each pair?'
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A cube has edges of 5 cm. What is its surface area?

    1. A150 cm²
    2. B125 cm²
    3. C150 cm³
    4. D30 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. 2 MULTIPLE CHOICE

    You unfold a time capsule that is a cube. Its net shows 6 equal squares, and each square has an area of 4 cm². What is the cube's total surface area?

    1. A24 cm²
    2. B10 cm²
    3. C16 cm²
    4. D12 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?
  3. 3 MULTIPLE CHOICE

    Your team unfolds a rectangular time capsule box into a flat net. How many faces (flat sides) will the net show in all?

    1. A6
    2. B4
    3. C5
    4. D8
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    A time capsule box measures 2 in × 3 in × 4 in. Using its net, you add up all six faces. What is the total surface area?

    1. A52 in²
    2. B24 in²
    3. C26 in²
    4. D48 in²
    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 Mistake — One Pair Was Not Doubled

    1. 1Read:A time capsule box from the net is l = 7 in, w = 5 in, h = 4 in. Find the surface area.
    2. 2Find each face pair:Top/Bottom: 7×5 = 35, Front/Back: 7×4 = 28, Left/Right: 5×4 = 20
    3. 3Apply the formula:SA = 2(35) + 2(28) + 20 = 70 + 56 + 20 = 146 in² (left/right pair not doubled)
    4. 4Answer:Surface Area = 146 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 — The Missing Back Face

    1. 1Box from the net:A time capsule box: l = 8 in, w = 3 in, h = 2 in
    2. 2Label the faces:Top/Bottom: 8×3 = 24, Front/Back: 8×2 = 16, Left/Right: 3×2 = 6
    3. 3Add the faces:SA = 24 + 24 + 16 + 6 + 6 = 76 in² (only one front face counted)
    4. 4Answer:Surface Area = 76 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