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Instructional Plan

Mathematics Governor’s Institute 2006

(Download as Microsoft Word Document: Instructional Plan)

 

Names of Group Members:  Diana Fesenmyer, Donna Hannick, Patricia Markowski, Merle Reinford, Georgia Rudosky

 

Topic/Theme:  Footing Around with Circumference

 

Level:  Geometry

 

Time Element:  Two 45-minute periods (includes extension activities)

 

NCTM Standards Addressed:  Algebra, Geometry, Measurement

 

PA Math Standards Addressed:  2.3.11.A, 2.3.11.C, 2.3.8.E, 2.8.11.D, 2.9.11.B, 2.9.11.F

 

Math Assessment Anchors Addressed:  M11.B.1, M11.B.2.2.4, M11.B.2.3.1, M11.C.1.1.1, M11.C.1.3, M11.D.2.1.3

 

Reading Assessment Anchors Addressed:  Open-ended response

 

Objectives:  Students will:

·         Measure circumference to the nearest 1/16th of an inch.

·         Compare and analyze the results of the change in circumference for spheres, cylinders, and prisms.

 

Instructional Strategies and Plan:

 

1.       Each student will complete the writing prompt.

 

A belt is placed snugly around the circumference of the earth at the equator and is measured (approximately 24,900 miles).  If the belt is increased by one foot, then placed uniformly around the equator, predict the distance that will exist between the earth and the belt.  Will it provide enough room for a sheet of paper, a #2 pencil, or your geometry textbook to fit between the earth and the belt?  Be specific.  Use complete sentences.

 

 

 

 

2.      Divide students into groups of three.

 

Student 1 is the recorder

Student 2 is the measurer

Student 3 is the assistant measurer

 

Each group measures the circumference of two different spherical objects.  Possibilities include marbles, golf balls, ping pong balls, tennis balls, softballs, soccer balls, and basketballs.

 

Note:  Two different groups should measure the same type of object, such as a golf ball, so that the data can be corroborated for each sphere.

 

                       Data Collection Sheet

 

                                                           

 

                                                                r     x

 

 

 

 

 

 

Object

Circumference

of Object

Circumference + 1 Foot

x

(in inches)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.      Each group will record its results on a Summary Data Collection Sheet.

 

On this sheet teachers should only include the actual objects measured.

 

 

                  Summary Data Collection Sheet

 

 

Object

 

Group Number

x

(from Data Collection Sheet)

Marble

 

 

 

 

 

Golf Ball

 

 

 

 

 

Ping  Pong Ball

 

 

 

 

 

Tennis Ball

 

 

 

 

 

Softball

 

 

 

 

 

Soccer Ball

 

 

 

 

 

Basketball

 

 

 

 

 

 

 

 

 

4.      Within their groups students will discuss:

 

·         How do the results match your original conjectures? 

(Step 1, Writing Prompt)

 

·         Based on these results, would you change your original predictions about the space between the earth and the elongated belt? 

5.      Teacher/group verifies the results algebraically.

 

                

               Algebraic Verification Worksheet

 

                                                     C2

 

                                                              C1    

       r     x

 

 

 

 

                                   

                                    If C1 = 2πr, then C2 = 2πr + 1.

 

                                    In general, to find the circumference for the outside circle:

 

                                                                    C2 = 2π (r + x)

 

                                    Find the value of x.  Convert your answer to inches.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.      Extensions for Day 2

 

Repeat Steps 1 through 5 for cylinders, cubes, and/or right prisms.

 

 

Materials/Resources:  Spherical balls, string, calculator, linear measuring instruments, worksheets (Data Collection Sheet, Summary Data Collection Sheet, Algebraic Verification Worksheet)

 

 

Interdisciplinary Connections:

·         Reading:  Open-ended responses

·         Technology:  Calculator usage

 

Assessment Strategies:

·         Formative Evaluation (checking student understanding during the lesson): 

Two groups will measure and analyze the same objects.

 

·         Summative Evaluation (How will it be determined that the objectives were achieved?):

1.       Students will be able to predict what will happen if one foot of string were added to the circumference of the earth.

      (Step 4)

 

2.      Students will be able to complete the Algebraic Verification Worksheet.  (Step 5)

 

Correctives/Remediation:  Teacher intervention, if necessary

 

Extensions/Enrichment:  See Step 6 for second day activities.

 

Special Accommodations (special needs students)

·         Description of the Special Needs student selected:  IEP

 

·         Accommodations to use with this student:

1.       Students will be told to measure to the closest tic-marks on the measuring device.

 

2.      Teacher will circulate around the room to help with measurements.

 

3.      Students will write their conclusions based on class observations, stressing why this would occur.

 

4.      Teacher will show algebraically that the common difference is approximately 1.9 inches.

 

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