Learn on PengienVision, Mathematics, Grade 5Chapter 11: Understand Volume Concepts

Lesson 1: Model Volume

In this Grade 5 lesson from enVision Mathematics Chapter 11, students learn to find the volume of solid figures by counting and multiplying unit cubes packed into rectangular prisms without gaps or overlaps. Students explore key vocabulary including volume and cubic units, building physical models to calculate how many cubic units fill a given three-dimensional shape. The lesson connects hands-on cube models to numerical reasoning, preparing students to measure the space inside solid figures.

Section 1

Introduction to Volume and Cubic Units

Property

Volume is a measure of how much space is inside a three-dimensional object or how much it takes to fill a container.
Volume is always measured in cubic units such as cubic inches (in3\text{in}^3), cubic feet (ft3\text{ft}^3), cubic centimeters (cm3\text{cm}^3), or cubic meters (m3\text{m}^3).

Examples

Section 2

Calculating Volume by Layers

Property

The volume of a rectangular prism can be found by multiplying the number of unit cubes in a single layer by the total number of layers.

V=(cubes in one layer)×(number of layers)V = (\text{cubes in one layer}) \times (\text{number of layers})

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Introduction to Volume and Cubic Units

Property

Volume is a measure of how much space is inside a three-dimensional object or how much it takes to fill a container.
Volume is always measured in cubic units such as cubic inches (in3\text{in}^3), cubic feet (ft3\text{ft}^3), cubic centimeters (cm3\text{cm}^3), or cubic meters (m3\text{m}^3).

Examples

Section 2

Calculating Volume by Layers

Property

The volume of a rectangular prism can be found by multiplying the number of unit cubes in a single layer by the total number of layers.

V=(cubes in one layer)×(number of layers)V = (\text{cubes in one layer}) \times (\text{number of layers})