Difference between revisions of "Ratio and Proportion"

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''[http://karnatakaeducation.org.in/KOER/index.php/ಅನುಪಾತ_ಮತ್ತು_ಸಮಾನುಪಾತ ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
 
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= Concept Map =
 
= Concept Map =
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<mm>[[Ratio .mm]]</mm>
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[[File:Ratio .mm]]
 
__FORCETOC__
 
__FORCETOC__
  
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==Useful websites==
 
==Useful websites==
 
==Reference Books==
 
==Reference Books==
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1. Cabinet of mathematical curiosities - Ian Stewart
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1. Cabinet of mathematical curiosities - Ian Stewart<br>
 
2. Cabinet of mathematical curiosities - Ian Stewart
 
2. Cabinet of mathematical curiosities - Ian Stewart
  
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===Learning objectives===
 
===Learning objectives===
 
===Notes for teachers===
 
===Notes for teachers===
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For Solved Problems Click [http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion here]
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For Solved Problems Click [http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion]
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[[http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion here]]
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[http://www.mathsisfun.com Maths is Fun]
  
 
===Activity No # ===
 
===Activity No # ===
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* '''Evaluation (Questions for assessment of the child)'''
 
* '''Evaluation (Questions for assessment of the child)'''
 
* '''Question Corner'''
 
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===Activity No # ===
 
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= Hints for difficult problems =
 
= Hints for difficult problems =
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==Ratio and Proportionality=
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===Exercise 2.4.2===
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In the adjacent figure, two triangles are similar. Find the length of the missing side
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This problem can be solved with the following steps.
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#Prerequisites: students should know the concept of similarity and proportionality
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        *Proportionality : two ratios are equal then four quantities are in proportional
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                *Similar Triangles : If two triangles are said to be similar 1. if they are equiangular 2. the corresponding side are proportional
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# Understanding/ analysing the given problem
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## Identifying/ Naming the triangles
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## Identifying the sides whose length is not given
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## comparing two sides of triangles (visualising that 1st triangle is smaller than 2 nd triagle and viceversa
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## should identify the corresponding sides (sides having same allignment)
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#  Procedure
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## find the ratio between the corresponding sides whose length is known <math>13 / 39 = 13 * 1 / 13  *3 = 1/3</math>
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## express proportional corresponding sides (using the property of similarity)
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    AC/DF = AB/DE
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13/39  =  5/x
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13 : 39  = 5 : x  (use the property of proportionality i.e Product of extremes is equal to product of means)
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13 * x = 39 * 5
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        x = 39* 5 /13
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Use the following Geogebra applet to understand proportion
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= Project Ideas =
 
= Project Ideas =

Latest revision as of 15:36, 17 May 2017

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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Activity No #

  • 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

=Ratio and Proportionality

Exercise 2.4.2

In the adjacent figure, two triangles are similar. Find the length of the missing side This problem can be solved with the following steps.

  1. Prerequisites: students should know the concept of similarity and proportionality

*Proportionality : two ratios are equal then four quantities are in proportional 

               *Similar Triangles : If two triangles are said to be similar 1. if they are equiangular 2. the corresponding side are proportional
  1. Understanding/ analysing the given problem
    1. Identifying/ Naming the triangles
    2. Identifying the sides whose length is not given
    3. comparing two sides of triangles (visualising that 1st triangle is smaller than 2 nd triagle and viceversa
    4. should identify the corresponding sides (sides having same allignment)
  2. Procedure
    1. find the ratio between the corresponding sides whose length is known
    2. express proportional corresponding sides (using the property of similarity)
   AC/DF = AB/DE

13/39 = 5/x 13 : 39 = 5 : x (use the property of proportionality i.e Product of extremes is equal to product of means) 13 * x = 39 * 5 

       x = 39* 5 /13

Use the following Geogebra applet to understand proportion

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