Difference between revisions of "Axioms, Postulates And Theorems"

From Karnataka Open Educational Resources
Jump to: navigation, search
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;">
+
# Concept Map
 +
# Additional Resources
 +
## OER
 +
### List web resources with a  brief description of what                  it contains; how it can be used and whether it can be                  by teacher/ student or both
 +
### Books and journals
 +
### Textbooks
 +
### Syllabus documents
 +
## Non-OER
 +
### List web resources with a  brief description of what                  it contains; how it can be used and whether it can be                  by teacher/ student or both
 +
### Books and journals
 +
### Textbooks
 +
### Syllabus documents (CBSE, ICSE, IGCSE etc)
 +
# Learning Objectives
 +
# Teaching Outlines
 +
## Concept 1:
 +
### Briefly describe the concept (2-3 sentences)
 +
## Activities
 +
### Page name - Name of activity
 +
### Template
 +
#### Objective of activity
 +
#### Pre-requisites/ prior competencies
 +
#### Resources needed (digital and non-digital)
 +
#### How to do the activity (both hands-on steps and                    discussion questions)
 +
#### Evaluation at the end of the activity
 +
## Solved problems/ key questions (earlier was hints for                problems)
 +
# Projects (can include math lab/ science lab/ language              lab)
 +
# Assessments<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]''</div>
 
''[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:
+
# List web resources with a  brief description of what                  it contains; how it can be used and whether it can be                  by teacher/ student or both
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
+
# Books and journals
 +
# Textbooks
 +
# Syllabus documents
  
=Additional Information=
+
==== Non-OER ====
this videos on axioms, postulates angles and lines
 
  
{{#widget:YouTube|id=bJVKaGqiKoE}}    {{#widget:YouTube|id=UgfSwlqi4Qg}}  {{#widget:YouTube|id=P3AOoLbA3us}}   
+
===== Web resources =====
==Useful websites==
+
# {{#widget:YouTube|id=bJVKaGqiKoE}}    {{#widget:YouTube|id=UgfSwlqi4Qg}}  {{#widget:YouTube|id=P3AOoLbA3us}}; is an introductory video on axioms, postulates angles and lines
# To know about axioms and postulates [http://www.themathpage.com/abooki/first.htm click here]
+
# Video on angles - http://study.com/academy/lesson/types-of-angles-vertical-corresponding-alternate-interior-others.html
# To know more about axioms and postulates [http://www.friesian.com/space.htm click here]
+
# Additional information on axioms and postulates
# To learn types of angles [https://www.mathsisfun.com/angles.html click here]
+
## http://www.themathpage.com/abooki/first.htm
# To see the videos on angles [http://study.com/academy/lesson/types-of-angles-vertical-corresponding-alternate-interior-others.html click here]
+
## http://www.friesian.com/space.htm
==Reference Book==
+
# __FORCETOC__To learn types of angles [https://www.mathsisfun.com/angles.html click here]
  
= Teaching Outlines =
+
===Teaching Outlines===
  
==Concept # Axioms and postulates==
+
==== Concept 1 - Introduction to planar geometry ====
===Learning objectives===
+
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
===Notes for teachers===
+
# Some statement which are taken for granted in a particular branches of mathematics is called postulates.
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 # ===
+
=====Activity 1- Introduction to angles  =====
{| style="height:10px; float:right; align:center;"
+
=====Activity 2 - Introduction to pairs of angles =====
|<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 # ===
+
==== Concept 2 - ====
{| style="height:10px; float:right; align:center;"
+
* '''s for assessment of the child)'''
|<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 =
 
 
 
= Project Ideas =
 
 
 
= Math Fun =
 
 
 
'''Usage'''
 
 
 
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 

Revision as of 05:53, 16 August 2018

  1. Concept Map
  2. Additional Resources
    1. OER
      1. List web resources with a  brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
      2. Books and journals
      3. Textbooks
      4. Syllabus documents
    2. Non-OER
      1. List web resources with a  brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
      2. Books and journals
      3. Textbooks
      4. Syllabus documents (CBSE, ICSE, IGCSE etc)
  3. Learning Objectives
  4. Teaching Outlines
    1. Concept 1:
      1. Briefly describe the concept (2-3 sentences)
    2. Activities
      1. Page name - Name of activity
      2. Template
        1. Objective of activity
        2. Pre-requisites/ prior competencies
        3. Resources needed (digital and non-digital)
        4. How to do the activity (both hands-on steps and discussion questions)
        5. Evaluation at the end of the activity
    3. Solved problems/ key questions (earlier was hints for problems)
  5. Projects (can include math lab/ science lab/ language lab)
  6. Assessments
ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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

Concept Map

Additional resources

OER

  1. List web resources with a  brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
  2. Books and journals
  3. Textbooks
  4. Syllabus documents

Non-OER

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

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.
Activity 1- Introduction to angles
Activity 2 - Introduction to pairs of angles

Concept 2 -

Retrieved from "https://karnatakaeducation.org.in/KOER/en/index.php?title=Axioms,_Postulates_And_Theorems&oldid=29508"