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

5.6 · Part II

Supported Application · Guided Entry to Today's Problem

Surface Area Using Nets · Surface area

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 5.6 · Part II
1Representing 3D Solids with Nets
2Strategy Model — step by step
  1. A net is a 2D flat pattern that folds into a 3D solid without overlapping
  2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs
  3. Surface Area is the total sum of the areas of all flat faces on the net
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?'
  1. 1 MULTIPLE CHOICE

    (Lesson 5.5) What is the volume of a rectangular prism with l = 7 in, w = 3 in, h = 4 in?

    1. A84 in³
    2. B14 in³
    3. C84 in²
    4. D42 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

    (Lesson 5.5) A time capsule box has a volume of 120 cm³. Its length is 10 cm and width is 4 cm. What is its height?

    1. A3 cm
    2. B6 cm
    3. C4 cm
    4. D12 cm
    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

    (Lesson 5.10) What is the volume of a rectangular prism with l = 4 in, w = 3 in, h = 5 in?

    1. A60 in³
    2. B12 in³
    3. C60 in²
    4. D24 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?
📐 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
6.GR.4 Lesson 5-6-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.6 · Part II

On-Level Application · Standard Rigor

Surface Area Using Nets · Surface area

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.6 · Part II
1Representing 3D Solids with Nets
2The Structural Procedure
  1. A net is a 2D flat pattern that folds into a 3D solid without overlapping
  2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs
  3. Surface Area is the total sum of the areas of all flat faces on the net
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?'
  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
  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
  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
📐 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
6.GR.4 Lesson 5-6-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.6 · Part II

Extension & Non-Routine Application

Surface Area Using Nets · Surface area

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.6 · Part II
1Representing 3D Solids with Nets
2The Structural Procedure
  1. A net is a 2D flat pattern that folds into a 3D solid without overlapping
  2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs
  3. Surface Area is the total sum of the areas of all flat faces on the net
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?'
  1. 1 MULTIPLE CHOICE

    A net folds into a rectangular prism. How many rectangular faces does that net have?

    1. A6
    2. B4
    3. C8
    4. D12
    ✏️ Workspace & Solution Steps
📐 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