head 1.1; access; symbols; locks; strict; comment @# @; 1.1 date 2018.03.14.15.43.24; author root; state Exp; branches; next ; desc @This document (3.1 Need for Proof) is re-created by administrator on 17 May 2017 @ 1.1 log @Initial revision @ text @{ "_id": { "$oid": "59425eb44975ac013bf0f5a9" }, "_type": "GSystem", "access_policy": "PUBLIC", "altnames": "3.1 Need for Proof", "annotations": [], "attribute_set": [], "author_set": [ 1 ], "collection_set": [], "comment_enabled": null, "content": "
\r\nGEOMETRIC REASONING\r\n
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Need for Proof

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Task 1

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\r\n

In your notebook mark 2 distinct points on a circle and join them. Note how many separate regions the circle is divided into
\r\n
\r\n(Click here to write)
\r\n\"Enter\"
\r\n 

\r\n\r\n\r\n \r\n\r\n

\"me_U05A04Q01_en_img01\"

\r\n \r\n\r\n
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Task 2

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Now draw another circle. Mark 3 distinct points on it. Join all possible pairs of points.
\r\nHow many separate regions is the circle divided into?

\r\n\r\n\r\n\"me_U05A04Q02_en_img02\"
\r\n
\r\n \r\n
Task 3\r\n\r\n
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Mark 4 distinct points on one circle, join all possible pairs of points.
\r\nNote the number of (separate) regions. In the other circle, do the same with 5 distinct points.
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\r\n
\r\nFor four distinct points on the circle-
\r\n 

\r\n\r\n\r\n\r\n

For five distinct points on the circle-
\r\n 

\r\n\r\n\r\n\r\n

\"u5\"
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\r\n 

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Task 4

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Now record your observations from Tasks 1-3 in the table given below.

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\"u6\"
\r\n(Click here to write)
\r\n\"Enter\"
\r\n 

\r\n\r\n
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Task 5

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What is the pattern you observe? Write it down. (You could write it as a \u2018rule\u2019 about the relationship between the number of points taken on the circle, and the number of separate regions the circle is divided into.)

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\r\n(Click here to write)
\r\n\"Enter\"
\r\n 

\r\n\r\n
\r\n

Task 6

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Do you think your \u2018rule\u2019 will hold true for ANY number of points taken on the circle? Why or why not ?

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(Click here to write)

\r\n\"Enter\"
\r\n \r\n
Task 7\r\n\r\n
\r\n

Verify your \u2018rule\u2019 by taking:
\r\n
\r\ni) 1 point on a circle
\r\nNumber of separate regions: ___
\r\n(Click here to write)
\r\n\"Enter\"
\r\n 

\r\n\r\n

ii) 6 points on a circle
\r\nNumber of separate regions: ____
\r\n(Click here to write)
\r\n\"Enter\"
\r\n 

\r\n\r\n
\r\n

Task 8

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Does your rule hold true? Based on this, would you like to change your response to Task 7?
\r\nIf yes, put the new response here.
\r\n(Click here to write)
\r\n\"Enter\"

\r\n\r\n
\r\n 
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a How many examples do you think are \u2018enough\u2019 to prove a conjecture?
\r\n(Click here to write)
\r\n\"Enter\"
\r\n
\r\nb How many examples do you think are \u2018enough\u2019 to disprove a conjecture?
\r\n(Click here to write)
\r\n\"Enter\"

\r\n", "content_org": "
\r\nGEOMETRIC REASONING\r\n
\r\n\r\n

\u200bNeed for Proof

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\r\n

Task 1

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Mark 2 distinct points on a circle and join them.
\r\nNote how many separate regions the circle is divided into
\r\n 

\r\n\r\n\r\n
\r\n\"Img1l13\"\r\n

 

\r\n\r\n
\r\n

Task 2

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\r\nNow draw another circle. Mark 3 distinct points on it. Join all possible pairs of points.
\r\nHow many separate regions is the circle divided into?\r\n\r\n\r\n\"l13img2\"
\r\n \r\n
\r\n

Task 3

\r\n\r\n
\r\n

 

\r\n\r\n

Mark 4 distinct points on one circle, join all possible pairs of points.
\r\nNote the number of (separate) regions. In the other circle, do the same with 5 distinct points.
\r\n
\r\n
\r\nFor four distinct points on the circle-
\r\n 

\r\n\r\n\r\n\r\n

For five distinct points on the circle-
\r\n 

\r\n\r\n\r\n\r\n

\"l13img3\"

\r\n\r\n
\r\n

Task 4

\r\n\r\n
\r\n

 

\r\n\r\n
\r\n

Now record your observations from Tasks 1-3 in the table given below.

\r\n
\r\n\r\n

\"l13img4\"
\r\n 

\r\n\r\n
\r\n

Task 5

\r\n\r\n
\r\n


\r\nWhat is the pattern you observe? Write it down. (You could write it as a \u2018rule\u2019 about the relationship between the number of points taken on the circle, and the number of separate regions the circle is divided into.) 
\r\n 

\r\n\r\n
\r\n_____________________________________________________________\r\n\r\n_____________________________________________________________
\r\n\r\n
\r\n

Task 6

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\r\nDo you think your \u2018rule\u2019 will hold true for ANY number of points taken on the circle? Why or why not ?_____________________________________________________________
\r\n
\r\n_____________________________________________________________
\r\n \r\n
\r\n

Task 7

\r\n\r\n
\r\n

 

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Verify your \u2018rule\u2019 by taking:
\r\n
\r\ni) 1 point on a circle
\r\nNumber of separate regions: ___

\r\n\r\n

ii) 6 points on a circle
\r\nNumber of separate regions: ____
\r\n
\r\n 

\r\n\r\n
\r\n

Task 8

\r\n\r\n
\r\n


\r\nDoes your rule hold true? Based on this, would you like to change your response to Task 7?
\r\nIf yes, put the new response here.
\r\n 

\r\n\r\n
\r\n_____________________________________________________________\r\n\r\n_____________________________________________________________\u200b
\r\n\r\n

 

\r\n\r\n
\r\n

\"Think\" Think about this!
\r\nHow many examples do you think are \u2018enough\u2019 to prove a conjecture?
\r\nHow many examples do you think are \u2018enough\u2019 to disprove a conjecture?

\r\n
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