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

5.6 Small Group · Group 1

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

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 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MATCHING GAME

    Match each concept about rectangular prisms.

    1. Top & Bottom faces
    2. Front & Back faces
    3. Left & Right faces
    4. Surface area formula
    5. Volume formula
    6. Number of faces
    • Al × w (two of them)
    • Bl × h (two of them)
    • Cw × h (two of them)
    • DSA = 2lw + 2lh + 2wh
    • EV = l × w × h
    • F6 faces total
  2. 2 DRAG SORT

    Put these steps in order for finding the surface area of a 5 × 3 × 2 box.

    Target Categories: Group 1 Group 2
    • Identify the three face pairs: 5×3, 5×2, 3×2
    • Find area of each: 15, 10, 6
    • Multiply each by 2: 30, 20, 12
    • Add all pairs: 30 + 20 + 12
    • SA = 62 in²
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    A rectangular prism has l = 6 in, w = 4 in, h = 2 in. What is its surface area?

    1. A88 in²
    2. B48 in²
    3. C88 in³
    4. D44 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?
  2. 4 MULTIPLE CHOICE

    How many faces does a rectangular prism have?

    1. A6
    2. B4
    3. C8
    4. D12
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Surface area is measured in which type of unit?

    1. ASquare units (in², cm², ft²)
    2. BCubic units (in³, cm³, ft³)
    3. CLinear units (in, cm, ft)
    4. DNo units needed
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 6 ERROR ANALYSIS

    Spot the Mistake — A Counted Face Was Skipped

    1. 1Read:A time capsule box from the net is l = 6 in, w = 4 in, h = 2 in. Find the surface area.
    2. 2Label the faces:Top/Bottom: 6×4 = 24, Front/Back: 6×2 = 12, Left/Right: 4×2 = 8
    3. 3Add the faces:SA = 24 + 24 + 12 + 8 + 8 = 76 in² (only one front/back face counted)

    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