Free Printable WorksheetMathGrade 5Math Curriculum5.MD.C.5

5.104 Decompose Composite Rectangular Prisms Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 5 Math worksheet provides structured practice on 5.104 Decompose Composite Rectangular Prisms. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Skill description: Select the correct decomposition and total volume for a composite solid made of rectangular prisms. Choose the answer that uses the correct units and conversion factors and matches the context. Corresponding standards: CCSS 5.MD.C.5.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 5

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 5.104 Decompose Composite Rectangular Prisms skill assessments:

Problem 1Difficulty: Mastery

A student needs the volume of a festival booth model. The solid can be split into a counter block measuring 10 inches by 4 inches by 3 inches, a storage block measuring 4 inches by 4 inches by 5 inches, an awning block measuring 8 inches by 2 inches by 2 inches, and a menu block measuring 3 inches by 2 inches by 4 inches. Which choice is correct?

A(10 × 4 × 3) + (4 × 4 × 5) + (8 × 2 × 2) + (3 × 2 × 4) = 256 square inches

B(10 × 4 × 3) + (4 × 4 × 5) + (8 × 2 × 2) = 232 cubic inches

C(10 × 4 × 3) + (4 × 4 × 5) + (8 × 2 × 2) + (3 × 2 × 4) = 363 cubic inches

D(10 × 4 × 3) + (4 × 4 × 5) + (8 × 2 × 2) + (3 × 2 × 4) = 256 cubic inches

Solution & Explanation:Find each prism's volume, then add: counter block: 10 × 4 × 3 = 120; storage block: 4 × 4 × 5 = 80; awning block: 8 × 2 × 2 = 32; menu block: 3 × 2 × 4 = 24. The total is 256 cubic inches, so the units must be cubic.

Problem 2Difficulty: Mastery

A robot charging station has been decomposed into floor pad, battery block, screen block, and cable block. The measurements are a floor pad measuring 15 centimeters by 6 centimeters by 2 centimeters, a battery block measuring 5 centimeters by 4 centimeters by 4 centimeters, a screen block measuring 4 centimeters by 2 centimeters by 6 centimeters, and a cable block measuring 3 centimeters by 2 centimeters by 2 centimeters. Which decomposition and total volume are correct?

A(15 + 6 + 2) + (5 + 4 + 4) + (4 + 2 + 6) + (3 + 2 + 2) = 55 cubic centimeters

B(15 × 6 × 2) + (5 × 4 × 4) + (4 × 2 × 6) + (3 × 2 × 2) = 426 cubic centimeters

C(15 × 6 × 2) + (5 × 4 × 4) + (4 × 2 × 6) + (3 × 2 × 2) = 320 cubic centimeters

D(15 × 6) + (5 × 4) + (4 × 2) + (3 × 2) = 124 cubic centimeters

Solution & Explanation:Find each prism's volume, then add: floor pad: 15 × 6 × 2 = 180; battery block: 5 × 4 × 4 = 80; screen block: 4 × 2 × 6 = 48; cable block: 3 × 2 × 2 = 12. The total is 320 cubic centimeters, so the units must be cubic.

Problem 3Difficulty: Mastery

Use the planned diagram of a park model entrance. It shows these non-overlapping rectangular prisms: a walkway base measuring 11 feet by 3 feet by 1 foot, a left pillar measuring 2 feet by 2 feet by 5 feet, a right pillar measuring 2 feet by 2 feet by 5 feet, and a top beam measuring 6 feet by 2 feet by 1 foot. Which choice gives the total volume?

A(11 × 3 × 1) + (2 × 2 × 5) + (2 × 2 × 5) = 73 cubic feet

B(11 × 3 × 1) + (2 × 2 × 5) + (2 × 2 × 5) + (6 × 2 × 1) = 85 cubic feet

C(11 × 3) + (2 × 2) + (2 × 2) + (6 × 2) = 53 cubic feet

D(11 × 3 × 1) + (11 × 3 × 1) + (2 × 2 × 5) + (2 × 2 × 5) + (6 × 2 × 1) = 118 cubic feet

Solution & Explanation:Find each prism's volume, then add: walkway base: 11 × 3 × 1 = 33; left pillar: 2 × 2 × 5 = 20; right pillar: 2 × 2 × 5 = 20; top beam: 6 × 2 × 1 = 12. The total is 85 cubic feet, so the units must be cubic.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 5 Math students. It aligns with educational standard 5.MD.C.5 (Primary standard selected for prompt fields in this prompt cell: CCSS 5.MD.C.5. Skill statement in this prompt cell: Select the correct decomposition and total volume for a composite solid made of rectangular prisms. Choose the answer that uses the correct units and conversion factors and matches the context. Associated standards listed with this skill in this prompt cell: CCSS 5.MD.C.5. Use this prompt-provided wording as the supporting standard description for this workflow.).