This lesson is designed to introduce students to surface area and volume.

Objectives

Upon completion of this lesson, students will:

have been introduced to the notion of surface area and volume.

have learned the terminology used with surface area and volume.

have experimented with the surface area and volume of different 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).

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.

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

Grades 3-5

Measurement

Apply appropriate techniques, tools, and formulas to determine measurements

Grades 6-8

Geometry

Use visualization, spatial reasoning, and geometric modeling to solve problems

Measurement

Apply appropriate techniques, tools, and formulas to determine measurements

Grades 9-12

Geometry

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

Measurement

Apply appropriate techniques, tools, and formulas to determine measurements

Geometry

Geometry and Measurement

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

Grade 7

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 2: The learner will understand and use measurement involving two- and three-dimensional figures.

Integrated Mathematics III

Geometry and Measurement

Competency Goal 2: The learner will use properties of geometric figures to solve problems.

Technical Mathematics I

Geometry and Measurement

Competency Goal 2: The learner will measure and apply geometric concepts to solve problems.

Technical Mathematics II

Geometry and Measurement

Competency Goal 1: The learner will use properties of geometric figures to solve problems.

5th grade

Measurement

The student will demonstrate through the mathematical processes an understanding of the units and systems of measurement and the application of tools and formulas to determine measurements.

6th Grade

Measurement

The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine unit rates; and the use of scale to determine distance.

The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine

7th Grade

Measurement

The student will demonstrate through the mathematical processes an understanding of how to use ratio and proportion to solve problems involving scale factors and rates and how to use one-step unit analysis to convert between and within the U.S. Customary System and the metric system.

The student will demonstrate through the mathematical processes an understanding of how to use ratio and proportion to solve problems involving scale factors and rates and how to use one-step unit analysis to convert between and within the U.S. Customary

8th grade

Measurement

The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and volume; and the use of conversions within and between the U.S. Customary System and the metric system.

The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and

7th Grade

Measurement

7.8 The student will investigate and solve problems involving the volume and surface area of rectangular prisms and cylinders, using concrete materials and practical situations to develop formulas.

8th Grade

Measurement

8.7 The student will investigate and solve practical problems involving volume and surface area of rectangular solids (prisms), cylinders, cones, and pyramids.

Secondary

Algebra II

AII.16 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include Σ and an.

Reason for Alignment: Surface Area and Volume lesson guides the students through relationships in geometry. The textbook does not address surface area as such at this point, but volume and area are explored, so this shouldn't be a problem if the teacher wants to take the class a little further with the worksheet used in the lesson.

Reason for Alignment: This lesson was recommended in section 1 for its use of surface area. It can be used effectively here now as well, especially because students are now working with volume too.

Reason for Alignment: Though this lesson has been recommended in other modules it would fit here as well. It accompanies the Surface Area and Volume activity.

Student Prerequisites

Arithmetic: Student must be able to:

perform integer and rational arithmetic

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

Access to a browser

pencil and paper

Copies of supplemental materials for the activities:

A measure of the number of square units needed to cover the outside of a figure

volume

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 that will be pertinent to this lesson
and/or have them begin to think about the words and ideas of this lesson:

Ask students if they recall how to find the area of a two-dimensional shape, such as a square.

Entertain a
discussion on surface area and volume of three-dimensional figures.

Objectives

Let the students know what they will be doing and learning today. Say something like this:

Today, class, we will be talking about the surface area and volume of three dimensional
figures.

We are going to use the computers to learn about surface area and volume, but please do not
turn your computers on or go to this page until I ask you to. I want to show you a little
about the program first.

Teacher Input

Open your browser to
Surface Area and Volume in order to demonstrate this activity to the students.

Show the students how to choose between a triangluar prism and a rectangular prism. You may
need to briefly discuss what these figures are.

Show students how to use the scroll bars to adjust the length, width, and height of the
prisms.

Show students how to adjust the view of the figure using the three buttons at the top of the
applet. Talk about what each view is showing. Be sure to show the students that clicking on
the figure and rotating it will allow them to view it from any angle they choose.

Point out to students the place where the surface area and volume of the figures is displayed.

Walk the students together through question 1 on the worksheet -- make sure they understand
the slider bars for controlling size.

Independent Practice

Allow the students to work independently or in small groups on the rest of the worksheet as
you monitor the room for progress.

Have the students repeat the worksheet for the triangular prism, commenting on how finding
each answer on the sheet changes from the rectangle to the triangles.

Closure

You may wish to bring the class back together for a discussion of the findings. Once the
students have been allowed to share what they found, summarize the results of the lesson. It
is important that every student know the correct answers to the worksheet in order to fully
understand surface area and volume.

Alternate Outline

This lesson can be rearranged for the one computer classroom. Have the students work through the
worksheet by directing your movements on the computer.