understand how to solve problems for the volume of triangular prisms.

understand a generalization for solving for the volume 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.

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

Area of shapes (rectangles, triangles, circles, etc)

Basic concept of volume

Volume of rectangular prisms

Objectives

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

Today we are going to be extending our discussion from yesterday about volume. Instead of
looking at the volume of rectangular prisms, we are going to be generalizing the process for
all prisms.

We will continue to use the
Surface Area and Volume applet, but please don't open your computers until I instruct you to do so.

Teacher Input

Lead students in a
discussion about a generalized approach to finding the volume of all prisms.

Be prepared to show students physical models of different prisms and identify the base shape.

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.

Before students begin working on the applet, be sure to point out the Slant Height component
on the applet and explain that this measurement is not necessary for today's activity.

Note: If students will be using the
Compute mode for finding only the volume of the prisms and not the Surface Area and Slant Height,
show the students the pop-up box that will appear indicating that the Surface Area input is
incorrect.

Independent Practice

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

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

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.

You can also ask students to brainstorm definitions for surface area as a lead in to future
lessons.

Alternate Outline

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

Instead of having students complete Record Sheet 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. When students have computed the volume, have one
student enter the number to check answer.