6.GR.2 Lesson 5-5-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.5 · Part II

On-Level Application · Standard Rigor

Volume with Whole-Number Edges · Volume

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.5 · Part II
1Volume of Rectangular Prisms (Whole Numbers)
2The Structural Procedure
  1. Identify the length, width, and height of the box
  2. Multiply base area (l × w) by height (h)
  3. Label answer in cubic units (e.g. in³, cm³, ft³)
3Mathematical Word Bank
  • Volume with Whole-Number Edges (Volumen con aristas de números enteros) — The number of unit cubes inside a rectangular prism. Formula: V = l × w × h.
  • Volume (Volumen) — How much space is inside a solid shape.
  • Rectangular prism (Prisma rectangular) — A solid box shape with six flat rectangle sides.
  • Cubic units (Unidades cúbicas) — The units used to measure space inside, like cubic inches.
  • Length, width, height (Largo, ancho, altura) — How long, how wide, and how tall a box is.
  • Net (Plantilla (desarrollo plano)) — A flat shape that folds up into a solid.
4Watch out
  • A common mistake in Volume with Whole Number Edges is multiplying only two of the three edges and stopping there — for example, seeing a box that is 6 in long, 4 in wide, and 3 in tall, multiplying just 6 × 4 = 24, and calling that the volume, when 24 is only the area of the bottom face (in square inches), not the volume of the whole box. The height must also be multiplied in: V = 6 × 4 × 3 = 72 cubic inches. A second common mistake is adding the three edges instead of multiplying them (6 + 4 + 3 = 13 instead of 6 × 4 × 3 = 72 cubic inches). Volume always MULTIPLIES all three edges, and the answer is always labeled in cubic units (in³), never square units (in²) or plain units (in).
  1. 1 MULTIPLE CHOICE

    Two storage bins: Bin A is 8 × 6 × 5 inches. Bin B is 9 × 4 × 7 inches. Which holds more and by how much?

    1. ABin B by 12 in³
    2. BBin A by 12 in³
    3. CBin B by 24 in³
    4. DThey hold the same
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A rectangular prism has length 8 cm, width 5 cm, and height 4 cm. What is its volume?

    1. A17 cm³
    2. B160 cm³
    3. C80 cm³
    4. D120 cm³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 3 MULTIPLE CHOICE

    A box has a volume of 72 in³. Its base is 6 in by 4 in. What is its height?

    1. A3 in
    2. B12 in
    3. C2 in
    4. D18 in
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
📐 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.2 Lesson 5-5-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.5 · Part II

Extension & Non-Routine Application

Volume with Whole-Number Edges · Volume

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.5 · Part II
1Volume of Rectangular Prisms (Whole Numbers)
2The Structural Procedure
  1. Identify the length, width, and height of the box
  2. Multiply base area (l × w) by height (h)
  3. Label answer in cubic units (e.g. in³, cm³, ft³)
3Mathematical Word Bank
  • Volume with Whole-Number Edges (Volumen con aristas de números enteros) — The number of unit cubes inside a rectangular prism. Formula: V = l × w × h.
  • Volume (Volumen) — How much space is inside a solid shape.
  • Rectangular prism (Prisma rectangular) — A solid box shape with six flat rectangle sides.
  • Cubic units (Unidades cúbicas) — The units used to measure space inside, like cubic inches.
  • Length, width, height (Largo, ancho, altura) — How long, how wide, and how tall a box is.
  • Net (Plantilla (desarrollo plano)) — A flat shape that folds up into a solid.
4Watch out
  • A common mistake in Volume with Whole Number Edges is multiplying only two of the three edges and stopping there — for example, seeing a box that is 6 in long, 4 in wide, and 3 in tall, multiplying just 6 × 4 = 24, and calling that the volume, when 24 is only the area of the bottom face (in square inches), not the volume of the whole box. The height must also be multiplied in: V = 6 × 4 × 3 = 72 cubic inches. A second common mistake is adding the three edges instead of multiplying them (6 + 4 + 3 = 13 instead of 6 × 4 × 3 = 72 cubic inches). Volume always MULTIPLIES all three edges, and the answer is always labeled in cubic units (in³), never square units (in²) or plain units (in).
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A rectangular time capsule container measures 8 inches long, 5 inches wide, and 3 inches tall. What is its volume?

    1. A120 cubic inches
    2. B16 cubic inches
    3. C40 cubic inches
    4. D158 cubic inches
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  2. 2 MULTIPLE CHOICE

    A shipping crate is 12 ft long, 3 ft wide, and 2 ft tall. How many 1-foot cubes exactly fill it?

    1. A36 cubes
    2. B144 cubes
    3. C72 cubes
    4. D17 cubes
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    A box needs to hold exactly 60 cubic inches. Give three different sets of whole-number dimensions that work. Which set would make the box closest to a cube shape? Why might that matter?

    ✏️ 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
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