Difference between revisions of "Activity1 Pi the mathematical constant"

Revision as of 04:54, 7 May 2019

Objectives

Estimated Time

Prerequisites/Instructions, prior preparations, if any

Materials/ Resources needed

Process (How to do the activity)

Click here for Finding Pi by Archimedes Method. Archimedes approximated the value of Pi by starting with the fact that a regular hexagon inscribed in a unit circle has a perimeter of 6. He then found a method for finding the perimeter of a polygon with twice as many sides. Applying his method repeatedly, he found the perimeter of a 12, 24, 48, and 96 sided polygon. Using the perimeter as an approximation for the circumference of a circle he was able to derive an approximation for Pi equivalent to 3.14. This video uses a somewhat simpler method of doing the same thing and carries it out to polygons with millions of sides. All that is needed to understand the calculation is knowledge of the Pythagorean Theorem.
Geogebra file for explaining how 'circumference / diameter' is a constant, denoted as pi (Greek letter), using a number line
An animation of the same concept.

Process/ Developmental Questions

Open the Geogebra file. Move the slider to 'unravel' the circumference' over the number line. Since the diameter is 1 unit (measuring from -0.5 to 0.5 on number line), the circumference ends at 3.14, showing the ratio between circumference

Evaluation

Question Corner

if the diameter is increased from 1 to 2, what will the circumference be?

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-===Name of the activity===
-Brief blurb describing what the activity.  If this has been borrowed from some external web site (for example, a non OER or OER site which had this idea and based on which the activity was developed)
 === Objectives ===
-Content objectives  - what content areas
-Skill objectives - what specific skills
-Classroom objectives - to demo peer learning, to make a classroom resource, etc -
-All these kinds of objectives need not be there for every activity.  And no need to list them as different headings.  This is only for our reference when we are developing activities.
 ===Estimated Time===
@@ Line 17: / Line 9: @@
 ===Materials/ Resources needed===
 ===Process (How to do the activity)===
-How to do the different steps of the activity?
+#[https://www.youtube.com/watch?v=_rJdkhlWZVQ&feature=youtu.be Click here for Finding Pi by Archimedes Method]. Archimedes approximated the value of Pi by starting with the fact that a regular hexagon inscribed in a unit circle has a perimeter of 6. He then found a method for finding the perimeter of a polygon with twice as many sides. Applying his method repeatedly, he found the perimeter of a 12, 24, 48, and 96 sided polygon. Using the perimeter as an approximation for the circumference of a circle he was able to derive an approximation for Pi equivalent to 3.14. This video uses a somewhat simpler method of doing the same thing and carries it out to polygons with millions of sides. All that is needed to understand the calculation is knowledge of the Pythagorean Theorem.
+#[http://geogebratube.org/material/show/id/144079 Geogebra file] for explaining how 'circumference / diameter' is a constant, denoted as pi (Greek letter), using a number line
-What kinds of questions you can ask for that activity
+#An animation of the same concept.
+[[File:Pi 121.gif|400px|link=http://karnatakaeducation.org.in/KOER/en/index.php/File:Pi_121.gif]]
-What are the student follow-up activities/ questions you can give?
+*Process/ Developmental Questions
+Open the Geogebra file. Move the slider to 'unravel' the circumference' over the number line. Since the diameter is 1 unit (measuring from -0.5 to 0.5 on number line), the circumference ends at 3.14, showing the ratio between circumference
-Categories:  (Subject) (Topic) (Sub-concept/topic) (Class 6) (Resource format)
+*Evaluation
-Example -  (Mathematics) (Triangle) (Area) (Perimeter) (Class 6) (Class 8) (Geogebra) (Video)
+*Question Corner
+if the diameter is increased from 1 to 2, what will the circumference be?