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| + | ''[http://karnatakaeducation.org.in/KOER/index.php/ಏಕಕಾಲಿಕ_ರೇಖಾತ್ಮಕ_ಸಮೀಕರಣಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div> |
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− | [http://www.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://www.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] |
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− | [http://www.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://www.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] |
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− | [http://www.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] |
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− | [http://www.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] |
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− | [http://www.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] |
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| | | |
| = Concept Map = | | = Concept Map = |
− | <mm>[[Simultaneous_Linear_Equations.mm|Flash]]</mm>
| + | [[File:Simultaneous_Linear_Equations.mm|Flash]] |
| + | |
| __FORCETOC__ | | __FORCETOC__ |
| = Textbook = | | = Textbook = |
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| = Teaching Outlines = | | = Teaching Outlines = |
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− | ==Concept #== | + | ==Concept #1 - Where do I use simultaenous equations == |
| ===Learning objectives=== | | ===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=== | | ===Notes for teachers=== |
| + | |
| ===Activity No # === | | ===Activity No # === |
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− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | + | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
| |} | | |} |
| *Estimated Time | | *Estimated Time |
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− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | + | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
| |} | | |} |
| *Estimated Time | | *Estimated Time |
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| *Question Corner | | *Question Corner |
| | | |
− | ==Concept #== | + | ==Concept #2 - Graphical Method of Simultaneous Equations== |
| ===Learning objectives=== | | ===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=== | | ===Notes for teachers=== |
− | ===Activity No # === | + | 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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− | ''[http://www.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
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− | *Prerequisites/Instructions, if any
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− | *Multimedia resources
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− | *Website interactives/ links/ / Geogebra Applets
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− | *Process/ Developmental Questions
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− | *Evaluation
| |
− | *Question Corner
| |
| | | |
| ===Activity No # === | | ===Activity No # === |
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− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | + | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
| |} | | |} |
| *Estimated Time | | *Estimated Time |
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| *Question Corner | | *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? |
| | | |
− | = Hints for difficult problems =
| + | '''How to solve''' |
| + | #These are measurements of the sides of the triangle |
| + | #Equate the three |
| + | #Substitute and solve for x and y. |
| | | |
− | == Applications of Simultaneous Linear Equations ==
| + | '''Competencies''' |
− | === Exercise 3.5.5===
| + | #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 = |
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| 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]] |