6.GR.2 Lesson 5-10-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.10 · Part II

Supported Application · Guided Entry to Today's Problem

Volume of Rectangular Prisms · Volume

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 5.10 · Part II
1Volume of Rectangular Prisms with Fractional Edges
2Strategy Model — step by step
  1. Convert mixed numbers to improper fractions before multiplying
  2. Multiply numerators across, multiply denominators across: V = (l · w · h)
  3. Simplify the fraction and label with cubic units
3Mathematical Word Bank
  • Volume of Rectangular Prisms (Volumen de prismas rectangulares) — The space inside a rectangular prism. Formula: V = Bh = 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.
  • Dimensions (Dimensiones) — How long, how wide, and how tall a shape is.
  • Base area (Área de la base) — The area of the bottom of a solid. Volume = base area × height.
4Watch out
  • A common mistake in Volume of Rectangular Prisms is rounding a fractional edge length to the nearest whole number before multiplying, instead of using the exact fraction or decimal. For a box that is 2 ft × 1.5 ft × 1 ft, a student might round 1.5 down to 1 and compute 2 × 1 × 1 = 2 ft³, but the correct volume uses the exact edge length: 2 × 1.5 × 1 = 3 ft³ — a full cubic foot larger. Before you submit, ask: 'Did I multiply using the exact fractional or decimal edge length, or did I round it off first?'
  1. 1 MULTIPLE CHOICE

    (Lesson 5.4) An L-shaped room is made of two rectangles: 10 ft × 6 ft and 4 ft × 3 ft. What is the total area?

    1. A12 sq ft
    2. B60 sq ft
    3. C72 sq ft
    4. D72 ft
    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 5.4) A rectangular patio is 15 ft × 10 ft with a 5 ft × 4 ft rectangular flower bed cut out. What is the remaining area?

    1. A20 sq ft
    2. B130 sq ft
    3. C150 sq ft
    4. D170 sq ft
    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 5.5) What is the volume of a rectangular prism with l = 7 in, w = 3 in, h = 4 in?

    1. A14 in³
    2. B42 in³
    3. C84 in³
    4. D84 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?
📐 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.2 Lesson 5-10-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.10 · Part II

On-Level Application · Standard Rigor

Volume of Rectangular Prisms · Volume

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.10 · Part II
1Volume of Rectangular Prisms with Fractional Edges
2The Structural Procedure
  1. Convert mixed numbers to improper fractions before multiplying
  2. Multiply numerators across, multiply denominators across: V = (l · w · h)
  3. Simplify the fraction and label with cubic units
3Mathematical Word Bank
  • Volume of Rectangular Prisms (Volumen de prismas rectangulares) — The space inside a rectangular prism. Formula: V = Bh = 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.
  • Dimensions (Dimensiones) — How long, how wide, and how tall a shape is.
  • Base area (Área de la base) — The area of the bottom of a solid. Volume = base area × height.
4Watch out
  • A common mistake in Volume of Rectangular Prisms is rounding a fractional edge length to the nearest whole number before multiplying, instead of using the exact fraction or decimal. For a box that is 2 ft × 1.5 ft × 1 ft, a student might round 1.5 down to 1 and compute 2 × 1 × 1 = 2 ft³, but the correct volume uses the exact edge length: 2 × 1.5 × 1 = 3 ft³ — a full cubic foot larger. Before you submit, ask: 'Did I multiply using the exact fractional or decimal edge length, or did I round it off first?'
  1. 1 MULTIPLE CHOICE

    Two boxes: Box A is 10 × 5 × 4 inches. Box B is 8 × 6 × 5 inches. Which has more volume and by how much?

    1. ABox B by 40 in³
    2. BBox A by 40 in³
    3. CBox B by 60 in³
    4. DThey're equal
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    What is the volume of a prism with edge lengths 1/2 m, 3 m, and 4 m?

    1. A3 m³
    2. B6 m³
    3. C7.5 m³
    4. D12 m³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
  3. 3 MULTIPLE CHOICE

    A cube has an edge length of 5 cm. What is its volume?

    1. A15 cm³
    2. B25 cm³
    3. C75 cm³
    4. D125 cm³
    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 5-10-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

5.10 · Part II

Extension & Non-Routine Application

Volume of Rectangular Prisms · Volume

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 5.10 · Part II
1Volume of Rectangular Prisms with Fractional Edges
2The Structural Procedure
  1. Convert mixed numbers to improper fractions before multiplying
  2. Multiply numerators across, multiply denominators across: V = (l · w · h)
  3. Simplify the fraction and label with cubic units
3Mathematical Word Bank
  • Volume of Rectangular Prisms (Volumen de prismas rectangulares) — The space inside a rectangular prism. Formula: V = Bh = 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.
  • Dimensions (Dimensiones) — How long, how wide, and how tall a shape is.
  • Base area (Área de la base) — The area of the bottom of a solid. Volume = base area × height.
4Watch out
  • A common mistake in Volume of Rectangular Prisms is rounding a fractional edge length to the nearest whole number before multiplying, instead of using the exact fraction or decimal. For a box that is 2 ft × 1.5 ft × 1 ft, a student might round 1.5 down to 1 and compute 2 × 1 × 1 = 2 ft³, but the correct volume uses the exact edge length: 2 × 1.5 × 1 = 3 ft³ — a full cubic foot larger. Before you submit, ask: 'Did I multiply using the exact fractional or decimal edge length, or did I round it off first?'
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A container measures 1½ feet long, 2 feet wide, and 3 feet tall. What is its volume?

    1. A6 cubic feet
    2. B6½ cubic feet
    3. C9 cubic feet
    4. D18 cubic feet
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A fish tank measures 2 1/2 ft by 2 ft by 3 ft. What is its volume?

    1. A7.5 ft³
    2. B12 ft³
    3. C15 ft³
    4. D30 ft³
    Formula
    Put the numbers in
    Work it out
    Answer with its unit
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    A toy company ships action figures in boxes that are 4 × 3 × 6 inches. A shipping crate is 24 × 12 × 18 inches. How many action figure boxes fit in the crate? Explain your reasoning step by step.

    ✏️ 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