Difference between revisions of "Factorisation"

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''[http://karnatakaeducation.org.in/KOER/index.php/ಅಪವರ್ತಿಸುವಿಕೆ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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[http://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://www.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://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
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[http://www.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/Mathematics:_Topics Topics in School Mathematics]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
 
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= Concept Map =
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[[File:Factorisation.mm|Flash]]
  
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= Concept Map =
 
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__FORCETOC__
 
 
= Textbook =
 
= Textbook =
 
To add textbook links, please follow these instructions to:  
 
To add textbook links, please follow these instructions to:  
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=Additional Information=
 
=Additional Information=
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{{#widget:YouTube|id=LitM6ERl88A}}
 
==Useful websites==
 
==Useful websites==
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*Question Corner
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#[http://www.mathsisfun.com/algebra/polynomials.html Maths is Fun]. This website contains good worksheets for factorisation.
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#[http://reference.wolfram.com/mathematica/guide/PolynomialAlgebra.html Wolfram Mathworld].  This website contains good simulations for math identities.
 +
 
==Reference Books==
 
==Reference Books==
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===NCERT Books===
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#[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=9-16 Algebraic expressions and identities]
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#[http://www.ncert.nic.in/ncerts/textbook/textbook.htm?hemh1=14-16 Factorisation]
  
 
= Teaching Outlines =
 
= Teaching Outlines =
  
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==Concept #==
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==Concept #1 Monomial expressions==
 
===Learning objectives===
 
===Learning objectives===
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To introduce expressions and the need and method of splitting
 
===Notes for teachers===
 
===Notes for teachers===
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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 #1
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#Activity #2 Demonstrate Binomial Cube
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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http://www.infomontessori.com/sensorial/montessori_binomial_cube_1.jpg
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*Estimated Time
 
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*Prerequisites/Instructions, if any
 
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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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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
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*Estimated Time
 
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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
 
  
 
==Concept #==
 
==Concept #==
 
===Learning objectives===
 
===Learning objectives===
 
===Notes for teachers===
 
===Notes for teachers===
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===Activity No # ===
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===Activity No #1 Geogebra===
 
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 
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*Estimated Time
 
*Estimated Time
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*Prerequisites/Instructions, if any
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Multimedia resources
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[[File:Geogebra_screenshot_for_identities.png|150px]]<br> This is a Geogebra screenshot for identity.<br>
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{{#widget:YouTube|id=crjItXrt43Q}}<br>
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This is a classroom demonstration of binomial cube. Show the children before you start the cubic identity.
 
*Website interactives/ links/ / Geogebra Applets
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Process/ Developmental Questions
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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= Hints for difficult problems =
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# = Hints for difficult problems =
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Question : If  x= and y= find
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Solution :
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Analysing the given condition
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 +
Step 1 : = ()()  => Using the formula : = ( )()
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 +
step 2  : = ( + )(-) => substitute the value of x and  y
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Step 3 : = x => take the L.C.M of the denominator , simplyfy using concept of addition and substaction of fraction
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Step 4: = x
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simply the above using basic concepts of addition and substraction
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Step 5 : = x
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Step 6 := x => take common term 2 ( H.C.F)
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Step 7 : = x
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Step 8 : =
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#
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=hints for difficult problem=
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If  x-= 4  prove that <math>x^{3}+6x^{2}+\frac {6}  {x^{2}}-\frac{1}  {x^{3}}=184  </math>
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=====If  x+y=a  and xy=b then prove that                                          (1+)+(1+) =
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 +
Steps for solution
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 +
step 1:  * Understanding the  problem first.
 +
    * Recalling the indentities
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 +
step  2 :  * consider the condition and squaring on both side
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    * simplify to get the value
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step 3:    *  consider  LHS
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    *  multiply the expression
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    *  substitute the value
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    *  simlpify the equqtion
 +
 
 +
 
 +
solution for the problem
 +
 
 +
consider  x+y=a
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=
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substitute x+y =a and xy=b
 +
then we get
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                    ------->(1)
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consider xy=b squaring on both side
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then we get =------->(2)
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 +
consider LHS=
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=(1+)+(1+)
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=1+
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= 1+ from eqn 1 & 2
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=
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=
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        LHS = RHS=============
  
 
= Project Ideas =
 
= Project Ideas =
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Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
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[[Category:Class 8]]
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[[Category:Algebraic expressions]]

Latest revision as of 10:41, 31 October 2019

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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

[maximize]

Textbook

To add textbook links, please follow these instructions to: (Click to create the subpage)

Additional Information

Useful websites

  • Question Corner


  1. Maths is Fun. This website contains good worksheets for factorisation.
  2. Wolfram Mathworld. This website contains good simulations for math identities.

Reference Books

NCERT Books

  1. Algebraic expressions and identities
  2. Factorisation

Teaching Outlines

Concept #1 Monomial expressions

Learning objectives

To introduce expressions and the need and method of splitting

Notes for teachers

Activities

  1. Activity #1
  2. Activity #2 Demonstrate Binomial Cube

montessori_binomial_cube_1.jpg

Concept #

Learning objectives

Notes for teachers

Activity No #1 Geogebra

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources

Geogebra screenshot for identities.png
This is a Geogebra screenshot for identity.

This is a classroom demonstration of binomial cube. Show the children before you start the cubic identity.

  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner


  1. = Hints for difficult problems =

Question : If x= and y= find


Solution :

Analysing the given condition

Step 1 : = ()() => Using the formula : = ( )()

step 2 : = ( + )(-) => substitute the value of x and y

Step 3 : = x => take the L.C.M of the denominator , simplyfy using concept of addition and substaction of fraction

Step 4: = x simply the above using basic concepts of addition and substraction

Step 5 : = x 

Step 6 := x => take common term 2 ( H.C.F)

Step 7 : = x

Step 8 : =

hints for difficult problem

If x-= 4 prove that

====If x+y=a and xy=b then prove that (1+)+(1+)

Steps for solution 

step 1:  * Understanding the  problem first.

* Recalling the indentities

step 2 : * consider the condition and squaring on both side * simplify to get the value

step 3: * consider LHS * multiply the expression * substitute the value * simlpify the equqtion


solution for the problem

consider x+y=a = substitute x+y =a and xy=b 

then we get 
                   ------->(1)

consider xy=b squaring on both side then we get =------->(2)

consider LHS= =(1+)+(1+) =1+ = 1+ from eqn 1 & 2 = = 

       LHS = RHS=============

Project Ideas

Math Fun

Usage

Create a new page and type {{subst:Math-Content}} to use this template

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