Difference between revisions of "Axioms, Postulates And Theorems"

From Karnataka Open Educational Resources
Jump to: navigation, search
(3 intermediate revisions by the same user not shown)
Line 1: Line 1:
<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;">
+
''[http://karnatakaeducation.org.in/KOER/index.php/ಸ್ವಯಂ_ಸಿದ್ಧಗಳು_,_ಆಧಾರ_ಪ್ರತಿಜ್ಞೆಗಳು_ಮತ್ತು_ಪ್ರಮೇಯಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''
''[http://karnatakaeducation.org.in/KOER/index.php/ಸ್ವಯಂ_ಸಿದ್ಧಗಳು_,_ಆಧಾರ_ಪ್ರತಿಜ್ಞೆಗಳು_ಮತ್ತು_ಪ್ರಮೇಯಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
 
 
<!-- This portal was created using subst:box portal skeleton  -->
 
<!-- This portal was created using subst:box portal skeleton  -->
 
<!--        BANNER ACROSS TOP OF PAGE        -->
 
<!--        BANNER ACROSS TOP OF PAGE        -->
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
+
 
|-
 
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
 
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
|}
 
 
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
 
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
  
= Concept Map =
+
=== Concept Map ===
[[File: Axioms, postulates and theorems.mm|Flash]]
 
  
__FORCETOC__
+
=== Additional resources ===
  
= Textbook =
+
==== OER ====
To add textbook links, please follow these instructions to:
+
==== Non-OER ====
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
 
  
=Additional Information=
+
===== Web resources =====
this videos on axioms, postulates angles and lines
+
# Video on angles - http://study.com/academy/lesson/types-of-angles-vertical-corresponding-alternate-interior-others.html
 
+
# Additional information on axioms and postulates
{{#widget:YouTube|id=bJVKaGqiKoE}}    {{#widget:YouTube|id=UgfSwlqi4Qg}}  {{#widget:YouTube|id=P3AOoLbA3us}} 
+
## http://www.themathpage.com/abooki/first.htm
==Useful websites==
+
## http://www.friesian.com/space.htm
# To know about axioms and postulates [http://www.themathpage.com/abooki/first.htm click here]
+
# __FORCETOC__To learn types of angles [https://www.mathsisfun.com/angles.html click here]
# To know more about axioms and postulates [http://www.friesian.com/space.htm click here]
+
#The following videos provide an introduction to axioms, postulates and lines
# To learn types of angles [https://www.mathsisfun.com/angles.html click here]
+
{| class="wikitable"
# To see the videos on angles [http://study.com/academy/lesson/types-of-angles-vertical-corresponding-alternate-interior-others.html click here]
+
|{{#widget:YouTube|id=bJVKaGqiKoE}}
==Reference Book==
+
|-
 
+
|{{#widget:YouTube|id=UgfSwlqi4Qg}}
= Teaching Outlines =
+
|-
 
+
|{{#widget:YouTube|id=P3AOoLbA3us}}
==Concept # Axioms and postulates==
 
===Learning objectives===
 
#
 
===Notes for teachers===
 
First teacher can talk about Euclid and his great contribution to Mathematics. The below two statements helps to understand and prove the theorems in geometry.
 
# certain statements which are valid in all branches of mathematics whose validity is taken for granted without seeking mathematical proofs is called axioms
 
# some statement which are taken for granted in a particular branches of mathematics is called postulates.
 
 
 
===Activity No # ===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
* '''Estimated Time'''
 
* '''Materials/ Resources needed'''
 
* '''Prerequisites/Instructions, if any'''
 
* '''Multimedia resources'''
 
* '''Website interactives/ links/ Geogebra Applets'''
 
* '''Process (How to do the activity)'''
 
* '''Developmental Questions (What discussion questions)'''
 
* '''Evaluation (Questions for assessment of the child)'''
 
* '''Question Corner'''
 
 
 
===Activity No # ===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
* '''Estimated Time'''
 
* '''Materials/ Resources needed'''
 
* '''Prerequisites/Instructions, if any'''
 
* '''Multimedia resources'''
 
* '''Website interactives/ links/ Geogebra Applets'''
 
* '''Process (How to do the activity)'''
 
* '''Developmental Questions (What discussion questions)'''
 
* '''Evaluation (Questions for assessment of the child)'''
 
* '''Question Corner'''
 
 
 
==Concept #==
 
===Learning objectives===
 
===Notes for teachers===
 
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
 
 
 
===Activity No # ===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
|}
 
* '''Estimated Time'''
 
* '''Materials/ Resources needed'''
 
* '''Prerequisites/Instructions, if any'''
 
* '''Multimedia resources'''
 
* '''Website interactives/ links/ Geogebra Applets'''
 
* '''Process (How to do the activity)'''
 
* '''Developmental Questions (What discussion questions)'''
 
* '''Evaluation (Questions for assessment of the child)'''
 
* '''Question Corner'''
 
 
 
 
 
===Activity No # ===
 
{| style="height:10px; float:right; align:center;"
 
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
 
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
 
|}
 
|}
* '''Estimated Time'''
 
* '''Materials/ Resources needed'''
 
* '''Prerequisites/Instructions, if any'''
 
* '''Multimedia resources'''
 
* '''Website interactives/ links/ Geogebra Applets'''
 
* '''Process (How to do the activity)'''
 
* '''Developmental Questions (What discussion questions)'''
 
* '''Evaluation (Questions for assessment of the child)'''
 
* '''Question Corner'''
 
  
= Hints for difficult problems =
+
===Teaching Outlines===
  
= Project Ideas =
+
==== Concept 1 - Introduction to planar geometry ====
 +
It is useful to discuss with students  about Euclid and his great contribution to Mathematics. The below two statements helps to understand and prove the theorems in geometry.  Also, through a combination of activities, help the students understand results in the nature of axioms and postulates.
 +
# Certain statements which are valid in all branches of mathematics whose validity is taken for granted without seeking mathematical proofs is called axioms
 +
# Some statement which are taken for granted in a particular branches of mathematics is called postulates.
  
= Math Fun =
+
===== Activities =====
  
'''Usage'''
+
======Activity 1- Introduction to angles  ======
 +
======Activity 2 - Introduction to pairs of angles ======
  
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
+
===== Solved problems =====

Revision as of 11:48, 16 August 2018

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

While creating a resource page, please click here for a resource creation checklist.

Concept Map

Additional resources

OER

Non-OER

Web resources
  1. Video on angles - http://study.com/academy/lesson/types-of-angles-vertical-corresponding-alternate-interior-others.html
  2. Additional information on axioms and postulates
    1. http://www.themathpage.com/abooki/first.htm
    2. http://www.friesian.com/space.htm
  3. To learn types of angles click here
  4. The following videos provide an introduction to axioms, postulates and lines

Teaching Outlines

Concept 1 - Introduction to planar geometry

It is useful to discuss with students about Euclid and his great contribution to Mathematics. The below two statements helps to understand and prove the theorems in geometry. Also, through a combination of activities, help the students understand results in the nature of axioms and postulates.

  1. Certain statements which are valid in all branches of mathematics whose validity is taken for granted without seeking mathematical proofs is called axioms
  2. Some statement which are taken for granted in a particular branches of mathematics is called postulates.
Activities
Activity 1- Introduction to angles
Activity 2 - Introduction to pairs of angles
Solved problems