Volume of Rectangular Prisms

Abstract

This lesson is designed to introduce students to the concept of volume and how to find the volume of rectangular prisms.

Objectives

Upon completion of this lesson, students will:

  • have been introduced to the concept of volume.
  • understand how to solve for the volume of rectangular prisms.

Standards Addressed

Grade 6

  • Geometry

    • The student solves problems (including real-world situations) using perimeter, area, or volume.

Grade 7

  • Geometry

    • The student solves problems (including real-world situations).

Grade 8

  • Geometry

    • The student solves problems (including real-world situations).

Grade 9

  • Geometry

    • The student solves problems (including real-world situations).

Grade 10

  • Geometry

    • The student solves problems (including real-world situations).

Grades 8-12

  • Geometry

    • 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
    • 9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.

Third Grade

  • Measurement and Data

    • Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Fifth Grade

  • Measurement and Data

    • Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Sixth Grade

  • Geometry

    • Solve real-world and mathematical problems involving area, surface area, and volume.

Seventh Grade

  • Geometry

    • Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Geometry

  • Geometric Measurement and Dimension

    • Explain volume formulas and use them to solve problems
    • Visualize relationships between two-dimensional and three- dimensional objects

Grades 9-12

  • Geometry

    • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Geometry

  • Geometry and Measurement

    • Competency Goal 2: The learner will use geometric and algebraic properties of figures to solve problems and write proofs.

Geometry

  • Geometry

    • Standard G-7: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects.

7th Grade

  • Geometry

    • The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.

8th Grade

  • Geometry

    • The student will develop an understanding of geometric concepts and relationships as the basis for geometric modeling and reasoning to solve problems involving one-, two-, and three-dimensional figures.

Geometry

  • Measurement

    • Students will apply appropriate units of measurement; develop effective estimation and computation strategies for solving real world problems involving length, area, and volume; and choose appropriate techniques and tools to measure quantities in order to

Geometry

  • Congruence and the Geometry of Size

    • 8. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations.

Secondary

  • Geometry

    • G.13 The student will use formulas for surface area and volume of three-dimensional objects to solve practical problems. Calculators will be used to find decimal approximations for results.

Textbooks Aligned

Grade Seven

  • Filling and Wrapping

    • Investigation Three: Finding Volumes of Boxes
    • Investigation Seven: Finding Volumes of Irregular Objects

Book 1

  • Module 7 - Wonders of the World

    • Section 2: Volumes of Prisms

Book 2

  • Module 6 - Flights of Fancy

    • Section 2: Surface Area of Prisms
    • Section 5: Volume of a Prism

Book 3

  • Module 1 - Amazing Feats, Facts and Fictions

    • Section 4: Finding Volumes

  • Module 3 - The Mystery of Blacktail Canyon

    • Section 1: Volume

  • Module 5 - Inventions

    • Section 1: Volume

  • Module 6 - Architects and Engineers

    • Section 3: Surface Area of Prisms and Pyramids
    • Section 3: Volumes of Prisms

7th

  • Module 7 - MATH-Thematical Mix

    • Section 1: Measurement and Volume

8th

  • Module 5 - Architects and Engineers

    • Section 4: Surface Area and Volume

Grade 7

  • Packages and Polygons

    • Geometric Shapes

Student Prerequisites

  • Arithmetic: Students must be able to:
    • perform integer and rational arithmetic
    • find the area of squares and rectangles
  • Technological: Students must be able to:
    • perform basic mouse manipulations such as point, click and drag
    • use a browser for experimenting with the activities

Teacher Preparation

Key Terms

height of the triangular prism

the distance between the two bases

volume

A measure of the number of cubic units needed to fill the space inside an object

Lesson Outline

  1. Focus and Review

    Remind students of what they learned in previous lessons:

    • Area of squares, rectangles, and triangles
    • Basic properties of three-dimensional figures
    • Examples of three dimensional figures

  2. Objectives

    Let students know what they will being doing today and also what you hope they will learn through the lesson.

    • Today we will be focusing on finding the volume of rectangular prisms so we know "how much it can hold."
    • We will be using the computers later, but for now I want you to leave them closed and participate in our discussion.

  3. Teacher Input

    • Ask students if they know what volume is and engage students in a discussion about the definition of this term.
    • Show several example three-dimensional figures to the students (either physical models or from the Surface Area and Volume activity) and ask them to rank them from biggest volume to smallest volume.
    • Have students share their rankings and discuss how they determined "how much it could hold."
    • Begin a discussion on how to find the volume of a rectangular prism. By the end of this discussion students should understand that you need three measurements (length, width, and depth) to find the volume of the prism.

  4. Guided Practice

    • Open your browser to the Surface Area and Volume applet and introduce students to the applet and how to manipulate the measurements of rectangular prisms.
    • Have students work in pairs and use the Surface Area and Volume applet and the first sheet of the accompanying worksheet to see the relationship between the width, height, and depth of rectangular prisms.
    • After students have completed the first page of the worksheet, bring the class together to review the formula for the volume of a rectangular prism.
    • Introduce students to the Compute mode in the applet.
    • Note: If students will be finding only the volume of the prism and not the surface area, be sure to show the error message that will appear when you attempt to check answers.

  5. Independent Practice

    • Have students work in pairs using the Compute mode in the applet to correctly solve for the volume. Monitor the room for questions and be sure that the students are on the correct web site.

  6. Closure

    • You may wish to bring the class back together to discuss any problems that were especially hard for students to solve. Once the students have been allowed to share what they found, summarize once more the main points of the lesson.
    • Students should have a strong grasp of the volume of a rectangular prism and be prepared for assessment.

Alternate Outline

The lesson can be arranged in several ways based on computer availability:

  • The class could work together to complete the chart on the first page of the worksheet by asking the teacher or a student to manipulate the applet while all students record.
  • While in Compute mode, students could direct another student or the teacher to manipulate the measurements of the prism and then all students can record their guess for the volume on their paper or an individual whiteboard. One student answer can be checked in the applet.

Suggested Follow-Up

  • This lesson can be followed by the Volume of Prism lesson, which covers generalizing the formula for volume for all prisms.