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 10

Geometry

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

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).

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.

Fifth Grade

Measurement and Data

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

Geometry

Geometric Measurement and Dimension

Explain volume formulas and use them to solve problems

Visualize relationships between two-dimensional and three- dimensional objects

Seventh Grade

Geometry

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

Sixth Grade

Geometry

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

Third Grade

Measurement and Data

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

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

Lesson Outline

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

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.

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.

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.

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.

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.