Difference between revisions of "Surds"

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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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| 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]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
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= Concept Map =
 
= Concept Map =
 
__FORCETOC__
 
__FORCETOC__
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[[File:Surds in Manjesh.mm|Flash]]
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= Textbook =
 
= Textbook =
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To add textbook links, please follow these instructions to:
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Please click here for Karnataka and other text books.
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([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
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#[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter07.pdf Karnataka text book for Class 10, Chapter 07 - Surds]
  
 
=Additional Information=
 
=Additional Information=
 +
#9th_and_10th_ NCERT, ICSE and CBSE Text books, relavent websites and other books
 
==Useful websites==
 
==Useful websites==
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#[http://m.everythingmaths.co.za/grade-11/01-exponents-and-surds/01-exponents-and-surds-02.cnxmlplus Surds] starts with basic concepts,(to view the next page, please click on previous/up/next options in the bottom of the page
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#[http://en.wikipedia.org/wiki/Nth_root Please refer Wikipedia page for Surds]. This page discusses SuFNcY1z8dr6srds in detail.
 +
#[http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-surds-2009-1.pdf surds and other roots]This page discusses surds and roots in detail.
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#Video on Surds from Youtube :simplifying surds,rationalising surds,dividing and multiplying surds
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{{#widget:YouTube|id=iTt3TVjsjuY}}
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{{#widget:YouTube|id=w3PGLLT5nr4}}
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{{#widget:YouTube|id=FNcY1z8dr6s}}
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{{#widget:YouTube|id=D3SZE6zkQlM}}
  
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[http://m.everythingmaths.co.za/grade-11/01-exponents-and-surds/01-exponents-and-surds-02.cnxmlplus Surds] starts with basic concepts,(to view the next page, please click on previous/up/next options in the bottom of the page
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==Reference Questions==
 +
#what is the meaning of surds?
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#Difference between like and unlike surds.
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#Meaning of Pure and mixed surds.
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#Simplification of rationalising the denominator.
 +
 
 +
= Teaching Outlines =
 +
*Definition, examaples
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*Order and radicand of a surd
 +
*Like Surds and Unlike Surds
 +
*Addition and Subtraction of Surds
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*Multiplication of Surds.<br>i.Multiplication of Surds having same Order<br>ii. Multiplication of Surds having different Order
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*Rationalising Factor of a Surd
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*Simplifying a surd by Rationalizing denominator of a surd
  
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==Reference Books==
 
  
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= Teaching Outlines =
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==Concept 1: '''Definition of surds'''==
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Irrational root of rational number. Example:<math>\sqrt{2}, 7\sqrt{5},  \sqrt{x}</math>
  
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==Concept #==
 
 
===Learning objectives===
 
===Learning objectives===
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#know the meaning of surds
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#recognising radicand and order of surds
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===Notes for teachers===
 
===Notes for teachers===
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===Activity No # ===
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If you can't simplify a number to remove a square root (or cube root etc) then it is a surd.
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{| style="height:10px; float:right; align:center;"
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If it is a root and irrational, it is a surd.
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|<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;">
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But not all roots are surds.
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
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*Estimated Time
 
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*Materials/ Resources needed
 
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*Prerequisites/Instructions, if any
 
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*Multimedia resources
 
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*Website interactives/ links/ / Geogebra Applets
 
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*Process/ Developmental Questions
 
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*Evaluation
 
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*Question Corner
 
  
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===Activity No # ===
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===Activities===
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{| style="height:10px; float:right; align:center;"
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Activity for Definition[[Surds_definition_of_surds_activity1| click]]
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
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*Estimated Time
 
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*Materials/ Resources needed
 
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*Prerequisites/Instructions, if any
 
−
*Multimedia resources
 
−
*Website interactives/ links/ / Geogebra Applets
 
−
*Process/ Developmental Questions
 
−
*Evaluation
 
−
*Question Corner
 
  
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==Concept #==
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==Concept-2: '''Like and Unlike surds'''==
 
===Learning objectives===
 
===Learning objectives===
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#Know the meaning of surd
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#recognising the meaning of order and radicand
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#Examples of like and unlike surds
 +
#To change surd to simplest form
 +
#Addition and Multiplication og surds
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===Notes for teachers===
 
===Notes for teachers===
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===Activity No # ===
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1.Like surds: A group of surds having same order and same radicand in their simplest form.
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{| style="height:10px; float:right; align:center;"
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Example: <math>3\sqrt{5}, 7\sqrt{5}, x\sqrt{5}</math><br>
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|<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;">
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2.Unlike surds: Groups of surds having  different orders or different  radicandsor both in their simplest form.
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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Example: <math>\sqrt{a}, 3\sqrt{2}, x\sqrt{5}</math><br>
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|}
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3.Addition and sustraction  of surds.
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*Estimated Time
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Example: <math>2\sqrt{5}+3\sqrt{5}-\sqrt{5}</math><br>
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*Materials/ Resources needed
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4.Multiplication of surds.
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*Prerequisites/Instructions, if any
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Example: <math>7\sqrt{3}  X  2\sqrt{5}</math><br>
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*Multimedia resources
 
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*Website interactives/ links/ / Geogebra Applets
 
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*Process/ Developmental Questions
 
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*Evaluation
 
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*Question Corner
 
  
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===Activity No # ===
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===Activities===
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{| style="height:10px; float:right; align:center;"
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Activity for like and unlike surds [[Surds_like_and_unlike_surds_activity_1|click here]]
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|<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;">
 
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
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|}
 
−
*Estimated Time
 
−
*Materials/ Resources needed
 
−
*Prerequisites/Instructions, if any
 
−
*Multimedia resources
 
−
*Website interactives/ links/ / Geogebra Applets
 
−
*Process/ Developmental Questions
 
−
*Evaluation
 
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*Question Corner
 
  
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== Concept-3: Addition of Surds ==
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#simplify the surds
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<math>3\sqrt{45}+2\sqrt{20}-\sqrt{5}</math>
  
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<math>=3\sqrt{3X3X5}+2\sqrt{2X2X5}-\sqrt{5}</math>
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=Assessment activities for CCE=
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Solving problems with  same order and same radicand, same order and different radicand, different order and different radicand also different order and same order.
 +
Examples:
 +
[[Surds_CCE_Activity]] click here
  
 
= Hints for difficult problems =
 
= Hints for difficult problems =
  
 
= Project Ideas =
 
= Project Ideas =
 +
= Hints for difficult problems =
 +
Please click[http://karnatakaeducation.org.in/KOER/en/index.php?title=Class10_surds_problems&action=submit here\]here
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 +
= Project Ideas =
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 +
[[KOER_Mathematics_2014-15#Resources_and_handouts]]
  
 
= Math Fun =
 
= Math Fun =
  
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'''Usage'''
 
  
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Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
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Teachers contributions for this page
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# Tharanath Achar Sir, Graduate Assistant. Govt. P U College, Belthangady
 +
 
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= Math Fun =
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[[Category:Surds]]

Latest revision as of 13:11, 7 November 2019

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

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

Concept Map

Textbook

Please click here for Karnataka and other text books.

  1. Karnataka text book for Class 10, Chapter 07 - Surds

Additional Information

  1. 9th_and_10th_ NCERT, ICSE and CBSE Text books, relavent websites and other books

Useful websites

  1. Surds starts with basic concepts,(to view the next page, please click on previous/up/next options in the bottom of the page
  2. Please refer Wikipedia page for Surds. This page discusses SuFNcY1z8dr6srds in detail.
  3. surds and other rootsThis page discusses surds and roots in detail.
  4. Video on Surds from Youtube :simplifying surds,rationalising surds,dividing and multiplying surds

Reference Questions

  1. what is the meaning of surds?
  2. Difference between like and unlike surds.
  3. Meaning of Pure and mixed surds.
  4. Simplification of rationalising the denominator.

Teaching Outlines

  • Definition, examaples
  • Order and radicand of a surd
  • Like Surds and Unlike Surds
  • Addition and Subtraction of Surds
  • Multiplication of Surds.
    i.Multiplication of Surds having same Order
    ii. Multiplication of Surds having different Order
  • Rationalising Factor of a Surd
  • Simplifying a surd by Rationalizing denominator of a surd


Concept 1: Definition of surds

Irrational root of rational number. Example: 

Learning objectives

  1. know the meaning of surds
  2. recognising radicand and order of surds

Notes for teachers

If you can't simplify a number to remove a square root (or cube root etc) then it is a surd. If it is a root and irrational, it is a surd. But not all roots are surds.

Activities

Activity for Definition click

Concept-2: Like and Unlike surds

Learning objectives

  1. Know the meaning of surd
  2. recognising the meaning of order and radicand
  3. Examples of like and unlike surds
  4. To change surd to simplest form
  5. Addition and Multiplication og surds

Notes for teachers

1.Like surds: A group of surds having same order and same radicand in their simplest form. Example:  
2.Unlike surds: Groups of surds having different orders or different radicandsor both in their simplest form. Example:  
3.Addition and sustraction of surds. Example:  
4.Multiplication of surds. Example:  

Activities

Activity for like and unlike surds click here

Concept-3: Addition of Surds

  1. simplify the surds

 

 

Assessment activities for CCE

Solving problems with same order and same radicand, same order and different radicand, different order and different radicand also different order and same order. Examples: Surds_CCE_Activity click here

Hints for difficult problems

Project Ideas

Hints for difficult problems

Please clickhere\here

Project Ideas

KOER_Mathematics_2014-15#Resources_and_handouts

Math Fun

Teachers contributions for this page

  1. Tharanath Achar Sir, Graduate Assistant. Govt. P U College, Belthangady

Math Fun

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