understand how to solve for the surface area of triangular prisms

understand the meaning of the slant height of triangular prisms

understand a generalization for finding the surface area of all 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.

Geometry

Geometric Measurement and Dimension

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

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

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.

find the area of shapes (squares, rectangles, triangles)

Teacher Preparation

Physical manipulative objects of different shaped prisms

Access to a browser for pairs of students

Paper and pencil

Key Terms

surface area

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

Lesson Outline

Focus and Review

Remind students of what has been covered in previous lessons and have students review the
following:

Basic concept of surface area as covered in previous lesson

Process for finding surface area of a rectangular prism

Area of shapes (squares, rectangles, triangles, and circles)

Objectives

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

Today we are going to be extending yesterday's lesson on surface area to all types of prisms.

We will be using the
Surface Area and Volume applet again today, but please do not open your computers until I instruct you to do so.

Teacher Input

Lead students in a
discussion about generalizing the formula for surface area of all types of prisms.

Guided Practice

Introduce
Surface Area and Volume applet to any students who are unfamiliar with the applet.

Make sure that students are using
Triangular Prism from the drop-down menu.

Engage students in a discussion about
slant height and have students practice finding the slant height of the triangle.

Note: If students will be using the Compute mode for finding only the surface area of the
triangular prisms and not the volume, show the students the pop-up box that will appear
indicating that the Volume input is incorrect.

Independent Practice

Have students open the
Surface Area and Volume applet to
Compute mode and choose
Triangular Prism from the drop-down menu.

Students should work in pairs to find the volume and surface area of triangular prisms using the
applets.

At the end of the lesson, students should open the applet scoreboard and copy the percantage of
problems answered correctly of each type (volume, surface area, slant height). Students can
indicate to the instructor the type of problem on which they received the lowest percentage and
this information can be used for remediation and review.

Teacher should monitor the classroom for questions and make sure that students are on the
correct website.

Closure

You may wish to bring the students 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 the previous lessons about surface area and volume for prisms.

Alternate Outline

This lesson can be rearranged if there is only one available computer:

Instead of having students use the applet in pairs, display the Compute mode on a classroom
computer, record the dimensions on the whiteboard, and have students work independently to solve
for the volume, surface area, and slant height. When students have computed the volume, surface
area, and slant height, have one student enter the numbers to check the answers.

Suggested Follow-Up

After students have mastered the volume and surface area of prisms, you can begin to discuss the
volume and surface area of other three-dimensional figures including pyramids, cones, and
spheres.