Difference between revisions of "Ratio and Proportion"

From Karnataka Open Educational Resources
Jump to navigation Jump to search
m (Text replacement - "</mm>" to "")
 
(15 intermediate revisions by 4 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/ಅನುಪಾತ_ಮತ್ತು_ಸಮಾನುಪಾತ 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        -->
Line 20: Line 22:
  
 
= Concept Map =
 
= Concept Map =
−
<mm>[[Ratio.mm|Flash]]</mm>
+
[[File:Ratio .mm]]
 
__FORCETOC__
 
__FORCETOC__
  
Line 30: Line 32:
 
==Useful websites==
 
==Useful websites==
 
==Reference Books==
 
==Reference Books==
 +
1. Cabinet of mathematical curiosities - Ian Stewart<br>
 +
2. Cabinet of mathematical curiosities - Ian Stewart
  
 
= Teaching Outlines =
 
= Teaching Outlines =
Line 36: Line 40:
 
===Learning objectives===
 
===Learning objectives===
 
===Notes for teachers===
 
===Notes for teachers===
−
For Solved Problems Click [http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion here]
+
For Solved Problems Click [http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion]
 +
 
 +
[[http://karnatakaeducation.org.in/KOER/en/index.php/Solved_problems_on_Ratio_proportion here]]
 +
 
 +
[http://www.mathsisfun.com Maths is Fun]
  
 
===Activity No # ===
 
===Activity No # ===
Line 52: Line 60:
 
* '''Evaluation (Questions for assessment of the child)'''
 
* '''Evaluation (Questions for assessment of the child)'''
 
* '''Question Corner'''
 
* '''Question Corner'''
 +
 +
*'''How to make text bold'''
 +
*''How to make text italic''
  
 
===Activity No # ===
 
===Activity No # ===
Line 106: Line 117:
  
 
= Hints for difficult problems =
 
= 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.
 +
#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
 +
 +
# Understanding/ analysing the given problem
 +
## Identifying/ Naming the triangles
 +
## Identifying the sides whose length is not given
 +
## comparing two sides of triangles (visualising that 1st triangle is smaller than 2 nd triagle and viceversa
 +
## should identify the corresponding sides (sides having same allignment)
 +
#  Procedure
 +
## find the ratio between the corresponding sides whose length is known <math>13 / 39 = 13 * 1 / 13  *3 = 1/3</math>
 +
## 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
 +
 +
<ggb_applet width="800" height="400" version="4.4" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />
  
 
= Project Ideas =
 
= Project Ideas =

Latest revision as of 21:06, 17 May 2017

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

Reference Books

1. Cabinet of mathematical curiosities - Ian Stewart
2. Cabinet of mathematical curiosities - Ian Stewart

Teaching Outlines

Concept #

Learning objectives

Notes for teachers

For Solved Problems Click [1]

[here]

Maths is Fun

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
  • How to make text bold
  • How to make text italic

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


Concept #

Learning objectives

Notes for teachers

These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.

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


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

Project Ideas

Math Fun

Usage

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

Retrieved from "https://karnatakaeducation.org.in/KOER/en/index.php?title=Ratio_and_Proportion&oldid=27338"