Difference between revisions of "Surds"
m (removed Category:Algebra using HotCat) |
|||
(78 intermediate revisions by 7 users 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/ಕರಣಿಗಳು 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;" | {| 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; "| | + | | 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:_History The Story of Mathematics] | + | [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://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:_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; "| | + | | 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:_Pedagogy Teaching of Mathematics] | + | [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; "| | + | | 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/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus] | + | [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; "| | + | | 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:_Topics Topics in School Mathematics] | + | [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; "| | + | | 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/Text_Books#Mathematics_-_Textbooks Textbooks] | + | [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; "| | + | | 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/Maths:_Question_Papers Question Bank] | + | [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''']. | ||
Line 21: | Line 24: | ||
= Concept Map = | = Concept Map = | ||
__FORCETOC__ | __FORCETOC__ | ||
+ | |||
+ | [[File:Surds in Manjesh.mm|Flash]] | ||
+ | |||
= Textbook = | = Textbook = | ||
− | + | Please click here for Karnataka and other text books. | |
− | + | #[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== | ||
+ | #[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 | ||
+ | #[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. | ||
+ | #Video on Surds from Youtube :simplifying surds,rationalising surds,dividing and multiplying surds | ||
+ | {{#widget:YouTube|id=iTt3TVjsjuY}} | ||
+ | {{#widget:YouTube|id=w3PGLLT5nr4}} | ||
+ | {{#widget:YouTube|id=FNcY1z8dr6s}} | ||
+ | {{#widget:YouTube|id=D3SZE6zkQlM}} | ||
− | + | ==Reference Questions== | |
+ | #what is the meaning of surds? | ||
+ | #Difference between like and unlike surds. | ||
+ | #Meaning of Pure and mixed surds. | ||
+ | #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.<br>i.Multiplication of Surds having same Order<br>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:<math>\sqrt{2}, 7\sqrt{5}, \sqrt{x}</math> | ||
− | + | ===Learning objectives=== | |
− | + | #know the meaning of surds | |
+ | #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[[Surds_definition_of_surds_activity1| click]] | ||
− | ==Concept | + | ==Concept-2: '''Like and Unlike surds'''== |
===Learning objectives=== | ===Learning objectives=== | ||
− | + | #Know the meaning of surd | |
− | # | + | #recognising the meaning of order and radicand |
− | # | + | #Examples of like and unlike surds |
− | # | + | #To change surd to simplest form |
− | + | #Addition and Multiplication og surds | |
===Notes for teachers=== | ===Notes for teachers=== | ||
− | + | 1.Like surds: A group of surds having same order and same radicand in their simplest form. | |
− | { | + | Example: <math>3\sqrt{5}, 7\sqrt{5}, x\sqrt{5}</math><br> |
− | + | 2.Unlike surds: Groups of surds having different orders or different radicandsor both in their simplest form. | |
− | + | Example: <math>\sqrt{a}, 3\sqrt{2}, x\sqrt{5}</math><br> | |
− | + | 3.Addition and sustraction of surds. | |
− | + | Example: <math>2\sqrt{5}+3\sqrt{5}-\sqrt{5}</math><br> | |
− | + | 4.Multiplication of surds. | |
− | + | Example: <math>7\sqrt{3} X 2\sqrt{5}</math><br> | |
− | |||
− | |||
− | |||
− | |||
− | |||
− | === | + | ===Activities=== |
− | + | Activity for like and unlike surds [[Surds_like_and_unlike_surds_activity_1|click here]] | |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | ==Concept | + | == Concept-3: Addition of Surds == |
− | # | + | #simplify the surds |
− | + | <math>3\sqrt{45}+2\sqrt{20}-\sqrt{5}</math> | |
− | |||
− | |||
− | |||
+ | <math>=3\sqrt{3X3X5}+2\sqrt{2X2X5}-\sqrt{5}</math> | ||
+ | =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 = | = Hints for difficult problems = | ||
+ | Please click[http://karnatakaeducation.org.in/KOER/en/index.php?title=Class10_surds_problems&action=submit here\]here | ||
= Project Ideas = | = Project Ideas = | ||
+ | |||
+ | [[KOER_Mathematics_2014-15#Resources_and_handouts]] | ||
= Math Fun = | = Math Fun = | ||
Line 130: | Line 120: | ||
Teachers contributions for this page | Teachers contributions for this page | ||
# Tharanath Achar Sir, Graduate Assistant. Govt. P U College, Belthangady | # Tharanath Achar Sir, Graduate Assistant. Govt. P U College, Belthangady | ||
+ | |||
+ | = Math Fun = | ||
+ | |||
+ | [[Category:Surds]] |
Latest revision as of 07:41, 7 November 2019
Philosophy of Mathematics |
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.
Additional Information
- 9th_and_10th_ NCERT, ICSE and CBSE Text books, relavent websites and other books
Useful websites
- Surds starts with basic concepts,(to view the next page, please click on previous/up/next options in the bottom of the page
- Please refer Wikipedia page for Surds. This page discusses SuFNcY1z8dr6srds in detail.
- surds and other rootsThis page discusses surds and roots in detail.
- Video on Surds from Youtube :simplifying surds,rationalising surds,dividing and multiplying surds
Reference Questions
- what is the meaning of surds?
- Difference between like and unlike surds.
- Meaning of Pure and mixed surds.
- 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
- know the meaning of surds
- 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
- Know the meaning of surd
- recognising the meaning of order and radicand
- Examples of like and unlike surds
- To change surd to simplest form
- 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
- 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
Math Fun
Teachers contributions for this page
- Tharanath Achar Sir, Graduate Assistant. Govt. P U College, Belthangady