Grade Level: 9-12
Content Area: Mathematics
Unit Goals:
Show-Me Standards:
Performance Standards: Students will demonstrate within and integrate across all content areas the ability to
GOAL 3.2 develop and apply strategies based on ways others have prevented or solved problems
GOAL 3.4 evaluate the processes used in recognizing and solving problems
GOAL 3.5 reason inductively from a set of specific facts and deductively from general premises
Knowledge Standards: In Mathematics, students in Missouri public schools will acquire a solid foundation which includes knowledge of:
MA 2 geometric and spatial sense involving measurement (including length, area, volume), trigonometry, and similarity and transformations of shapes
MA 4 patterns and relationships within and among functions and algebraic, geometric and trigonometric concepts
Frameworks: Mathematics VI.A., VI.D., VI.G
VI.A. identify,
describe, compare, classify, and represent geometric figures
VI.D. use geometry
to describe their world
VI.G. apply the
concepts of perimeter, area, volume, angle measure, capacity, weight, and mass
Daily Objectives
Students will learn how to calculate the measurement of multi-sided objects. (Anderson and Kraftwall Taxonomy Table-Conceptual-Apply)
Materials:
Activity Sheets from Successlink unit plan: “Geometry for the Middle Grades” accessible from http://www.successlink.org/ Submitted by Ellen Gott, Chillicothe R-2
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9:00-9:15 9:15-9:18 9:18-9:25 9:25-9:27 9:27-9:30 9:30-9:50 9:50-9:55 9:55-10:00
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(Anticipatory Set) Materials Needed: Paper Implementation: Have the students draw a polyhedron on a sheet of paper to see check to see if they remember what one is. (Stating Objectives) Explain that students will investigate various polyhedrons, or multi-sided objects. They will also learn about Euler’s formula to calculate the sides of the sides of a multi-sided object. (Provide Input) Explain to the students that there are several different types of objects that have many numbers of sides and they encounter them in their daily lives. Explain that the Polyhedron is a multi-sided object and then explain how Euler’s formula works to calculate the various of a multi-sided object. (Modeling Ideal Behavior) I will then draw a polyhedron on the board and then calculate it sides using Euler’s formula. (Check for Comprehension) To check for comprehension I will as the students what a polyhedron is and ask someone to tell me how to do Euler’s formula. (Guided Practice) Activity 6 Eulers formula Materials Needed: Models of different Polyhedrons and Euler’s formula worksheet. Implementation: Hand out Euler’s formula worksheet. Students will investigate several polyhedrons. They will record the number of faces, vertices, and edges that exist in each shape. They will discover Euler’s formula by finding a pattern. (Check for Comprehension) Have the students turn in their results for grade to see how well they understood the assignment. (Closer) Explain to the students they investigated various polyhedrons. They also learned about Euler’s formula to calculate the sides of the sides of a multi-sided object.
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Alternatives for the Day:
If the students are not showing a willingness to cooperate, go to the Geometry textbook and have them complete the review exercises in chapter 4, section 8.
Remediation:
If the students do not comprehend the lessons, go back to the Geometry textbook and have them go to chapter 3, section 7 and work the problems 1- 12.
Enrichment:
If some students get done before the majority of the class, have them compute some additional types of polyhedron.
Activity Sheet 6: Eular's Formula
http://www.successlink.org/great2/g1548.html
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Polyhedron |
Faces |
Vertices |
Edges |
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Cube |
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Tetrahedron |
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Square Pyramid |
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Triangular Prism |
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5-Prism |
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Chopped-Off Cube |
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Octahedron |
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5-Pyramid |
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Soccer Ball |
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Write Euler’s Formula: