Difference between revisions of "Polynomials"

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==Concept #2==
 
==Concept #2==
 
===Learning objectives===
 
===Learning objectives===
 +
1. Can find the product of binomials using special Identities
 +
2. Can prove some of the important Identities
 +
3. can expand binomial terms using the Identities
 +
4. Solve problems under Identities
 +
5. can prove some of the important conditional Identities
 
===Notes for teachers===
 
===Notes for teachers===
  
 
===Activity No #1 ===
 
===Activity No #1 ===
 +
Verification the Identity (a+b)(a-b) = a2-b2
 +
{| 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
 +
10 to 15 minutes
 +
*Materials/ Resources needed
 +
Laptop, Projector, Geogebra Software
 +
*Prerequisites/Instructions, if any
 +
Should know the multiplication of Integers
 +
*Multimedia resources
  
 +
*Website interactives/ links/ / Geogebra Applets
 +
<ggb_applet width="1366" height="568" version="4.0" ggbBase64="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enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" />
 +
*Process/ Developmental Questions
 +
What is Identity?
 +
Does the Identity holds good for all the values of variables?
 
*Evaluation
 
*Evaluation
−
+
What Identity to be used to multiply (3x+2)(3x-2)
 
*Question Corner
 
*Question Corner
  
−
===Activity No #2 ===
 
−
*Evaluation
 
−
 
−
*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/ Developmental Questions
 
*Process/ Developmental Questions
−
 
 
*Evaluation
 
*Evaluation
 +
*Question Corner
  
 
*Question Corner
 
*Question Corner

Revision as of 09:29, 4 September 2013

Usage

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

Please click here for a resource creation checklist.

Concept Map

Error: Mind Map file Multiplication.mm not found


Textbook

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

NCERT Books

Class IX Chapter Polynomials

Tamilnadu Text Books

Class IX text book

Additional Information

Useful websites

multipying polynomials with tabular method is explained in a very simple manner which could help you in classroom teching

Maths is fun website here you can understand polynomial in easy way

Reference Books

Teaching Outlines

Concept #1

Learning objectives

1. Can multiply Polynomial by monomial, binomial and Trinomial

2. Can find the product of any two Polynomials by formal multiplication

Notes for teachers

Activity No #1

Multiplying Polynomials Using Algebra Tiles

  • Estimated Time
  • Materials/ Resources needed

1. Algebra Tiles activity sheet , 2. Algebra tiles

  • Prerequisites/Instructions, if any

Knowledge Of the terms monomial, binomial, trinomial, polynomial, term, degree, base, exponent, coefficient

  • Multimedia resources

  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions

1. Demonstrate multiplying polynomials using algebra tiles, as shown below:

(x x 1)(x + 6) = x2 + 7x + 6


2. Distribute algebra tiles and copies of the Multiplying Polynomials Using Algebra Tiles activity sheet. Instruct students to model each expression with the tiles, draw the model, 

                                                              simplify the expression, and write the simplified answer.
  • Evaluation

o Draw a model of the multiplication of two binomials. Simplify your expression.

o Explain why (2x)(3x) = 6x and not 6x.

  • Question Corner

Activity No #2

Multiplying Polynomials Using Tabular method

  • Estimated Time
  • Materials/ Resources needed

Whiteboard, marker pens

  • Prerequisites/Instructions, if any

Knowledge Of the terms monomial, binomial, trinomial, polynomial, term, degree, base, exponent, coefficient

  • Multimedia resources

  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions

1. Demonstrate multiplying polynomials using tabular method

(x x 1)(x + 6) = x2 + 7x + 6


2. Distribute copies of the Multiplying Polynomials Using Tabular method 

  activity sheet. Instruct students to model each expression with the tabular method , draw the table, 
  simplify the expression, and write the simplified answer.
  • Evaluation

What is the product of (2x+3y)^2

  • Question Corner

Concept #2

Learning objectives

1. Can find the product of binomials using special Identities 2. Can prove some of the important Identities 3. can expand binomial terms using the Identities 4. Solve problems under Identities 5. can prove some of the important conditional Identities

Notes for teachers

Activity No #1

Verification the Identity (a+b)(a-b) = a2-b2

  • Estimated Time

10 to 15 minutes

  • Materials/ Resources needed

Laptop, Projector, Geogebra Software

  • Prerequisites/Instructions, if any
Should know the multiplication of Integers
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets

  • Process/ Developmental Questions

What is Identity? Does the Identity holds good for all the values of variables?

  • Evaluation

What Identity to be used to multiply (3x+2)(3x-2)

  • 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
  • Question Corner

Hints for difficult problems

Project Ideas

Math Fun

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