Abstract
This lesson is designed to introduce students to the concept of surface area and generalize the formula for all prisms.
This lesson is designed to follow the Surface Area of a Rectangular Prism lesson.
Objectives
Upon completion of this lesson, students will:
- have a better understanding of surface area.
- 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 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
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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
- Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Sixth Grade
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Geometry
- Solve real-world and mathematical problems involving area, surface area, and volume.
Seventh Grade
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Geometry
- Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Geometry
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Geometric Measurement and Dimension
- 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
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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
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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
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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
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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
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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
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Module 1 - Amazing Feats, Facts and Fictions
- Section 4: Finding Volumes
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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 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
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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)
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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.
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Teacher Input
- Lead students in a discussion about generalizing the formula for surface area of all types of prisms.
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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.
- 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.
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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.
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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.