Difference between revisions of "Simultaneous Linear Equations"

From Karnataka Open Educational Resources
Jump to navigation Jump to search
 
(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/ಏಕಕಾಲಿಕ_ರೇಖಾತ್ಮಕ_ಸಮೀಕರಣಗಳು 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        -->
 
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
 
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
 
|-
 
|-
−
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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:_History The Story of Mathematics]
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
−
|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]
+
| 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]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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:_Pedagogy Teaching of Mathematics]
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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:_Topics Topics in School Mathematics]
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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/Text_Books#Mathematics_-_Textbooks Textbooks]
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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/Maths:_Question_Papers Question Bank]
 
[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
|}
 
|}
Line 20: Line 22:
  
 
= Concept Map =
 
= Concept Map =
−
<mm>[[Simultaneous_Linear_Equations.mm|Flash]]</mm>
+
[[File:Simultaneous_Linear_Equations.mm|Flash]]
 +
 
 
__FORCETOC__
 
__FORCETOC__
 
= Textbook =
 
= Textbook =
Line 80: Line 83:
 
{{#widget:YouTube|id=MRAIgJmRmag}}
 
{{#widget:YouTube|id=MRAIgJmRmag}}
  
−
===Activity No # ===
+
===Activity No 1: [[Simultaneous linear equation activity|Simultaneous linear equation]] ===
 
{| style="height:10px; float:right; align:center;"
 
{| 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;">
 
|<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>
 
''[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
 
  
 
===Activity No # ===
 
===Activity No # ===
Line 113: Line 109:
  
 
===Problem #5, Exercise 3.5.5, Page 213 ===
 
===Problem #5, Exercise 3.5.5, Page 213 ===
−
The measure of the sides (in cms) of a triangle are :
+
The measure of the sides (in cms) of a triangle are :<br>
−
<math>frac{5}{3}x</math>
+
<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 =
 
= Project Ideas =
Line 123: Line 135:
  
 
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
 +
 +
[[Category:Simultaneous Linear Equations]]

Latest revision as of 14:39, 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

Retrieved from "https://karnatakaeducation.org.in/KOER/en/index.php?title=Simultaneous_Linear_Equations&oldid=34934"