6.GR.4 Lesson 5-6-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.6 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Visual Models · Surface Area Using Nets · Surface area · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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.
3Second Model — Try it together — then prove it
  1. Now a smaller box: 4 long, 3 wide, 2 tall. How many pairs of faces does it have?
  2. Top and bottom: 4 × 3 = 12, times 2 = 24. Front and back: 4 × 2 = 8, times 2 = 16.
  3. Left and right: 3 × 2 = 6, times 2 = 12. Now add 24 + 16 + 12. What is the surface area?
  4. Yes, SA = 52 in². Remember to use square units.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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 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
  2. 2 MULTIPLE CHOICE

    How many faces does a rectangular prism have?

    1. A6
    2. B4
    3. C8
    4. D12
    ✏️ Workspace & Solution Steps
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem: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?
    2. 2A classmate at our table answered:26 in²

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 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
  3. 6 ERROR ANALYSIS

    Find the Surface Area Error

    1. 1Dimensions:l = 10 in, w = 4 in, h = 3 in
    2. 2Formula:SA = 2lw + 2lh + 2wh
    3. 3Calculate:SA = 2(10×4) + 2(10×3) + (4×3) = 80 + 60 + 12 = 152 in²
    4. 4Answer:Surface Area = 152 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
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It