Difference between revisions of "Simultaneous Linear Equations"

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''[http://karnatakaeducation.org.in/KOER/index.php/ಏಕಕಾಲಿಕ_ರೇಖಾತ್ಮಕ_ಸಮೀಕರಣಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
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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://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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[http://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/Mathematics:_Topics Topics in School Mathematics]
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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 =
 +
[[File:Simultaneous_Linear_Equations.mm|Flash]]
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 +
__FORCETOC__
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= Textbook =
 +
To add textbook links, please follow these instructions to:
 +
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
 +
 
 +
=Additional Information=
 +
==Useful websites==
 +
==Reference Books==
 +
 
 +
= Teaching Outlines =
 +
 
 +
==Concept #1 - Where do I use simultaenous equations ==
 +
===Learning objectives===
 +
 +
#There are two quantities/ parameters that are used together to describe something.
 +
#This is of the forms ax+by = c
 +
#You need two sets of equations to find the solutions.
 +
#Extend this understanding for different sets of variables.
 +
 
 +
===Notes for teachers===
 +
 
 +
===Activity No # ===
 +
{| style="height:10px; float:right; align:center;"
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|<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;">
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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|}
 +
*Estimated Time
 +
*Materials/ Resources needed
 +
*Prerequisites/Instructions, if any
 +
*Multimedia resources
 +
*Website interactives/ links/ / Geogebra Applets
 +
*Process/ Developmental Questions
 +
*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://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
 +
*Evaluation
 +
*Question Corner
 +
 
 +
==Concept #2 - Graphical Method of Simultaneous Equations==
 +
===Learning objectives===
 +
#State a given problem in algebraic terms
 +
#Identifying the variables
 +
#Interpret a linear equation as a line
 +
#Understand that the solution is a point on both the lines, they intersect
 +
===Notes for teachers===
 +
It is better to use the graphical method before the algebraic manipulation.<br>
 +
{{#widget:YouTube|id=MRAIgJmRmag}}
 +
 
 +
===Activity No 1: [[Simultaneous linear equation activity|Simultaneous linear equation]] ===
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{| style="height:10px; float:right; align:center;"
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|<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;">
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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|}
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*
 +
 
 +
===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://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
 +
*Evaluation
 +
*Question Corner
 +
 
 +
= Hints for difficult problems =
 +
 
 +
== Applications of Simultaneous Linear Equations - Exercise 3.5.5 ==
 +
 
 +
===Problem #5, Exercise 3.5.5, Page 213 ===
 +
The measure of the sides (in cms) of a triangle are :<br>
 +
<math>\frac{5}{3}x+y+\frac{1}{2}</math><br>
 +
<math>2x+\frac{1}{2}y</math><br>
 +
<math>\frac{2}{3}x+2y+\frac{5}{2}</math>
 +
When does it becomhttp://karnatakaeducation.org.in/KOER/en/skins/common/images/button_bold.pnge an equilateral triangle?
 +
 
 +
'''How to solve'''
 +
#These are measurements of the sides of the triangle
 +
#Equate the three
 +
#Substitute and solve for x and y.
 +
 
 +
'''Competencies'''
 +
#Equilateral triangle must have all sides equal
 +
#The sides of a triangle are line (segments) and can be expressed as a linear equation.  Though this is not used for solving this problem
 +
#Infer that if the sides are same, the expressions must be the same numerical value
 +
#If that is true, I can use combine the expressions to express one in terms of the other
 +
#Rearranging terms and combining expressions to form equations
 +
#Solve
 +
 
 +
= Project Ideas =
 +
 
 +
= Math Fun =
 +
 
 +
'''Usage'''
 +
 
 +
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 +
 
 +
[[Category:Simultaneous Linear Equations]]

Latest revision as of 20:09, 19 December 2020

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

Teaching Outlines

Concept #1 - Where do I use simultaenous equations

Learning objectives

  1. There are two quantities/ parameters that are used together to describe something.
  2. This is of the forms ax+by = c
  3. You need two sets of equations to find the solutions.
  4. Extend this understanding for different sets of variables.

Notes for teachers

Activity No #

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

Concept #2 - Graphical Method of Simultaneous Equations

Learning objectives

  1. State a given problem in algebraic terms
  2. Identifying the variables
  3. Interpret a linear equation as a line
  4. Understand that the solution is a point on both the lines, they intersect

Notes for teachers

It is better to use the graphical method before the algebraic manipulation.

Activity No 1: Simultaneous linear equation

Activity No #

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

Hints for difficult problems

Applications of Simultaneous Linear Equations - Exercise 3.5.5

Problem #5, Exercise 3.5.5, Page 213

The measure of the sides (in cms) of a triangle are :


When does it becomhttp://karnatakaeducation.org.in/KOER/en/skins/common/images/button_bold.pnge an equilateral triangle?

How to solve

  1. These are measurements of the sides of the triangle
  2. Equate the three
  3. Substitute and solve for x and y.

Competencies

  1. Equilateral triangle must have all sides equal
  2. The sides of a triangle are line (segments) and can be expressed as a linear equation. Though this is not used for solving this problem
  3. Infer that if the sides are same, the expressions must be the same numerical value
  4. If that is true, I can use combine the expressions to express one in terms of the other
  5. Rearranging terms and combining expressions to form equations
  6. Solve

Project Ideas

Math Fun

Usage

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

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