lesson plan 4 circles

8/8/2019 Lesson Plan 4 Circles

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1. Lesson Title: Proving Pi

2. Grade/Age Level: This unit is designed for sixth grade instruction, butcan be modified for use in grades four through seven.

3. Subject Area: Mathematics, Geometry, Circles

4. Time allotted for the lesson: one class period (30 minutes)

5. Short description of lesson:

a. In this lesson, the learners will measure circumference anddiameter of several round items.

b. In this lesson, the learners will accurately calculate pi by dividingcircumference by diameter.

c. Learners will create a chart identifying circumference, diameter,and pi.

6. Massachusetts Curriculum Standards met in this lesson:

6.M.5 Identify, measure, and describe circles and therelationships of the radius,diameter, circumference, and area (e.g., d = 2r, p = C/d), and usethe concepts to solve problems.

2010 John Crescitelli Boise State University

Two-dimensional Geometry

Lesson 4 Understanding Circles

John T. Crescitelli EdTech 506 Instructional Message Design Lesson Plan


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7. Instructional Objectives (Each instructional objective [learningoutcome] for this lesson):

a. Students will identify and measure the circumference of roundobjects

b. Students will identify and measure the diameter of round objects

c. Students will create a chart comparing circumference anddiameter

d. Students will prove the concept of pi by dividing circumferenceby diameter

8. Instructional Procedures

a. Lesson SetOn each set of tables will be a collection of different circularobjects (plates, lids, lampshades, bicycle wheel, trash can,anything round that the students can measure). Also on thetables are two metric tapes measures per group of 4 students.On the board in the front of the room, the teacher has writtenProving Pi. Calculators and paper are in the classroomresource area.

b. Techniques and activities The teacher calls the class to attention and begins to eat a piece

of pie in front of the children exclaiming, I love pie, dont you? This will lead to much chatter and banter, but will begin the classdiscussion.

The lesson begins with the teacher inquiring and acknowledgingthat the students have heard of this math concept of pi, butreally dont understand what it is and how it works. The teacherasks the students to explain what they do know about themathematics pi while the teacher writes the responses on chartpaper, or the board, or overhead.

The teacher now explains that pi is a mathematical constantequal to 3.14 and that they are going to prove it. The teacherexplains through diagrams and instruction that pi is the specialrelationship between the circumference and diameter of a circle.No matter how big or how small the circle, the circumference isalways 3.14 times larger than the diameter.

This is where the teacher will want to pass out InstructionalReference Guide 4 Understanding Circles . The teacher canreinforce the instruction by showing the reference guide to



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learners. This will help them remember the steps to properlymeasure prove the concept of pi. The teacher can emphasizeterminology, and guide students to key points of instruction.

The students are then directed to measure the circumferenceand diameters of the objects at their respective tables. Allmeasurements are to the nearest millimeter. They are then to

create a three column table, identifying each measurement anddividing circumference by diameter. Students can use calculatorsfrom the classroom resource area.

Once students have measured the items at their table, they mayexchange objects with other classroom groups. The objective isto measure 6-10 objects for comparison.

c. Lesson ClosureOnce the teacher is back at the helm, he/she can conduct asummary of the day. This is where the students and teacher

work together to help summarize mastery objectives from thedays lesson. The teacher can emphasize that calculations thatdid not equal 3.14 exactly were due to measurement issues andnot that pi is a false mathematical constant. The teacher canemphasize that this constant will help them make inferences anddistance, space, and area.

At this point, the teacher picks up a bicycle tire and spins it whileholding the axel. As the kids look eagerly for the bell, the teacherquestions, Wow, how many times has this gone around? How faris that? Lets figure it out!

9. Adaptations for special learners

For those with special needs, there are several options available. Theclassroom set of round objects will have 3 discs that have themeasurements labeled on them. This can be done by adhering a tapemeasure around the circumference and the diameter. There can alsobe circles that measure to a standard number.

10. Supplemental Activities: Extension and remediation

This lesson is only the beginning of a series of examinations intounderstanding and using pi. Understanding that the product of pi anddiameter equals circumference, students can begin to estimaterevolutions and distance. Begin this activity by giving a group of students a disc that is twelve inches in diameter. With the use of acalculator, have them calculate how many revolutions it will take forthe disc to cross the classroom. Then you can have the studentsactually roll the disc across the room to check their results. This thenleads into an open response examination into bicycle wheels,revolutions, and distance.



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For those needing remediation, the teacher can provide guidedmeasurement and calculation or provide all measurements and the useof a calculator.

11. Assessment/Evaluation:

For this particular lesson, both formative and summative assessmentscan become part of the process. During initial lesson and instruction,the teacher can conduct formative assessment by classroom roaming.A checklist of instructional outcomes can be used to check classsuccesses (measured circumference and diameter correctly, created achart comparing each, correctly dividing circumference by diameter).

For summative assessment, students are presented with an openresponse question similar to what they will see on the MassachusettsComprehensive Assessment System. Students will be asked tocompare mileage between revolutions of a mountain bicycle wheel and

a bmx style bicycle wheel. The mountain bicycle wheel is twenty-sixinches in diameter, and the bmx wheel is twenty inches in diameter.

12. Learner Products

Students will create a three column chart, identifying circumference,diameter, and the division of the two. The learning objective is thateach group will show that the mathematical concept of pi exists.


lesson plan 4 circles

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