Packing the Box: Volume of Rectangular Prisms

About This Resource

A complete Grade 5 math lesson pack on the volume of rectangular prisms: counting unit cubes, cubic units, the formulas V = l × w × h and V = B × h, finding a missing dimension, volume of composite figures made of two prisms and real-world packing problems. Includes slides with worked examples, a timed lesson plan, flashcards, worksheet, quiz, homework, rubric and answer key.

Overview

Students learn that volume is the amount of space inside a solid figure, measured in cubic units. They start by counting unit cubes in layers, discover that the number of cubes in one layer is the area of the base, and build the formulas V = l × w × h and V = B × h. They then find volumes of boxes in cubic centimeters, find a missing length when the volume is known, add the volumes of two prisms joined together and solve packing and storage problems. Worked examples on the slides show every step.

Resource Details

Subject: Math
Topic: Volume of Rectangular Prisms
Category: Measurement
File Type: PDF
File Size: 317.9 KB
Published: 01 Nov 2026
Downloads: 0

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Grade 5 (ages 10–11) 60 minutes Measurement geometry multiplication problem solving reasoning

Learning Objectives

Explain volume as the number of unit cubes that fill a solid and measure it in cubic units.
Find the volume of a rectangular prism using V = l × w × h and V = B × h.
Solve real-world problems, including missing dimensions and composite figures made of two prisms.

How to Use This Resource

Start with slide 1: show two boxes and ask which holds more. Fill a small box with cubes to introduce cubic units.
Teach layers, the two formulas, missing dimensions and composite figures with the slides, letting students try each worked example on whiteboards first.
Students complete the worksheet, then use the quiz to check and the homework for practice. Answers are in the answer key.

Classroom Activity Ideas

Build it: groups use 24 unit cubes to build as many different prisms as they can and record length, width and height for each.
Classroom boxes: measure a tissue box, a shoe box and a lunch box in centimeters and find each volume.
Design a box: students design a gift box with a volume of exactly 60 cubic centimeters and draw it with labels.

Differentiation

Support: give centimeter cubes and grid paper, and let students count layers before multiplying. Challenge: find all the prisms with a volume of 36 cubic units, solve two-step composite problems and explain what happens to the volume when every side is doubled.

Assessment

Worksheet activities and the quiz check finding volume, missing dimensions and composite figures (answer key included). Explanations and the rubric assess understanding of why the formula works.

Teacher Tips

Build understanding before the formula: show one layer of cubes, count it, then stack layers. When students see that the base layer is l × w and the number of layers is h, the formula makes sense and they remember it. Always insist on cubic units in the answer.

What's Included

11-page printable PDF lesson pack: teacher lesson plan with timings, materials and differentiation
Key vocabulary list (7 words with meanings and examples)
Student worksheet (6 activities)
Quiz / assessment (3 parts)
Homework practice page
Printable flashcards: 7 A5 picture cards (separate PDF)
Assessment rubric (4 levels)
Lesson slides (editable PowerPoint)
Editable Word version of all student pages
Complete answer key (also as a separate PDF)