Abstract
This lesson is designed to introduce students to the concept of volume and how to find the volume of triangular and other shape prisms.
This lesson is designed to follow the Volume of a Rectangular Prism lesson.
Objectives
Upon completion of this lesson, students will:
- have reinforced the concept of volume.
- 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 6
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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
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Measurement and Data
- Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
Fifth Grade
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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
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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
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Module 7 - Wonders of the World
- Section 2: Volumes of Prisms
Book 2
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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
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Module 5 - Inventions
- Section 1: Volume
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Module 6 - Architects and Engineers
- Section 3: Surface Area of Prisms and Pyramids
- Section 3: Volumes of Prisms
7th
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Module 7 - MATH-Thematical Mix
- Section 1: Measurement and Volume
8th
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Module 5 - Architects and Engineers
- Section 4: Surface Area and Volume
Grade 7
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Packages and Polygons
- Geometric Shapes
Student Prerequisites
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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
- Physical manipulative objects as examples of triangular prisms
- Access to browser for pairs of students
- Paper and pencil
- Student copies of Record Sheets
Key Terms
volume
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
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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.
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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.
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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.
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Independent Practice
- Have students open Surface Area and Volume applet to Compute mode and choose Triangular Prism from the drop-down menu.
- Students should work in pairs to complete the Volume of a Triangular Prism Record Sheet.
- Teacher should monitor the room for questions and make sure that students are on the correct website.
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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.
Suggested Follow-Up
- This lesson can be followed by a series of lessons on the Surface Area of prisms: Surface Area of Rectangular Prisms and Surface Area of Prisms
- Alternately, this lesson could be followed-up by lessons on volume of other three-dimensional figures such as pyramids, cones, cylinders, and spheres.