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| [http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics] | | [http://www.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://www.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://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics] |
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| [http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus] | | [http://www.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://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics] |
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| | | |
− | = Concept Map = | + | == Concept Map == |
− | <mm>[[Quadratic_Equations.mm|Flash]]</mm>
| + | [[File:Quadratic_Equations.mm|Flash]] |
| + | |
| __FORCETOC__ | | __FORCETOC__ |
| | | |
− | = Textbook = | + | == Textbook == |
| Please click here for Karnataka and other text books. | | Please click here for Karnataka and other text books. |
| + | #[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter09.pdf Karnataka text book for Class 10, Chapter 09 - Quadratic Equations] |
| + | #[http://nimsdxb.com/wp-content/uploads/Unit-4_Quadratic_Equations_Core.pdf/ cbse text book] |
| + | |
| + | ==Additional Information== |
| + | {{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/10549763|width=450 |height=360 |border=1 }} |
| | | |
| + | ===Useful websites=== |
| | | |
− | =Additional Information= | + | [https://in.ixl.com/search?q=quadratic+equation/ For more information about quadratic equation] |
− | ==Useful websites==
| |
− | ==Reference Books==
| |
| | | |
− | = Teaching Outlines = | + | ===Reference Books=== |
| + | [[Text_Books| relevent references]] |
| + | |
| + | === Resources === |
| + | |
| + | ==== Resource Title ==== |
| + | [http://www.mathopenref.com/quadraticexplorer.html Quadratic Function Explorer] |
| + | |
| + | ==== Description ==== |
| + | This interactive activity helps you realize the action of the three coefficients a, b, c in a quadratic equation. |
| + | |
| + | == Teaching Outlines == |
| + | |
| + | ==Concept #1 - Introduction to quadratic equations== |
| + | An equation of the form <math>ax^2+bx+c = 0</math> where a ≠ 0 and a, b, c belongs to R. |
| | | |
− | ==Concept #1 - Introduction to quadtratic equations==
| |
| ===Learning objectives=== | | ===Learning objectives=== |
| + | converting verbal statement into equations. |
| + | |
| ===Notes for teachers=== | | ===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.''
| + | #Basic knowledge of equations, linear equations,general form of linear equation, finding the rooots of equation, graphical representation of linear equations.<br> |
| + | #More importance to be given for signs while transforming the equations. |
| | | |
| ===Activities=== | | ===Activities=== |
− | #Activity No #1 '''Concept Name - Activity No.'''
| |
− | #Activity No #2 '''Concept Name - Activity No.'''
| |
| | | |
| + | #Activity No 1 '''[[Quadratic_equations_introduction_to_quadratic_equation_activity_1|Introduction to quadratic equation]]''' |
| + | #Activity No 2 '''[[Quadratic_equations_introduction_to_quadratic_equation_actvity 2| Making a rectangular garden]]''' |
| + | #Activity No 3 '''[[Quadratic_equations_introduction_to_quadratic_equation_activity 3| Understanding<math> ax^2+bx+c=0</math> geometrically]]''' |
| | | |
| + | ==Concept #2 - Types of equations== |
| + | ===Pure Quadratic Equation & Adfected Quadratic Equation=== |
| + | Quadratic equation,in the form <math>ax^2+bx+c = 0</math>, is termed as quadratic expression and the equation of the form <math>ax^2+bx+c = 0</math>, a≠0 is called quadratic equation in x. This equation is also known to be pure quadratic equation if the value of b is zero i.e. b=0. Otherwise it is said to be adfected. The letters a, b, and c are called coefficients: and c is the constant coefficient. |
| | | |
− | ==Concept #2 - Types of equations==
| |
| ===Learning objectives=== | | ===Learning objectives=== |
| + | #To distinguish between pure & adfected equations among the given equations. |
| + | #Standard forms of pure & adfected quadratic equations. |
| + | |
| ===Notes for teachers=== | | ===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.''
| + | #Knowledge of general form of quadratic equations<br> |
| + | #roots of equation<br> |
| + | #proper use of signs. |
| | | |
| ===Activities=== | | ===Activities=== |
− | #Activity No #1 '''Concept Name - Activity No.'''
| + | '''[[Identifying pure and adfected ouadratic equations- Activity No1]]''' |
− | #Activity No #2 '''Concept Name - Activity No.'''
| + | |
| + | '''[http://mathworksheets4kids.com/equations/quadratic.html/ work sheet Activity No2]''' |
| | | |
− | ==Concept #3 What is the solution of a quadratic equation?== | + | ==Concept #3 What is the solution of a quadratic equation== |
| + | The roots of the Quadratic Equation which satisfy the equation |
| ===Learning objectives=== | | ===Learning objectives=== |
| + | #x=k is a solution of the quadratic equation if k satisfies the quadratic equation |
| + | #Any quadratic equation has at most two roots. |
| + | #The roots form the solution set of quadratic equation. |
| + | |
| ===Notes for teachers=== | | ===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.''
| + | #different methods of solving quadratic equation |
| + | #knowledge of suitable formula to be used to solve specific problem. |
| + | #identify the type of quadratic equation. |
| | | |
| ===Activities=== | | ===Activities=== |
− | #Activity No #1 '''Concept Name - Activity No.''' | + | #Activity No #1 #Activity No 3-[http://www.projectmaths.ie/students/strand4JC/student-activity-quadratic-formula.pdf| quadratic formula]<br> |
− | #Activity No #2 '''Concept Name - Activity No.''' | + | #Activity No #2 '''Concept Name - Activity No''' |
| | | |
| ==Concept #4Methods of solution== | | ==Concept #4Methods of solution== |
| + | Different methods of finding the solution to a quadratic equation |
| + | #Factorisation method |
| + | #Completing the square method |
| + | #Formula method |
| + | #Graphical method. |
| ===Learning objectives=== | | ===Learning objectives=== |
| + | #Solving quadratic equation by factorisation method |
| + | #Solving quadratic equation by completing the square method |
| + | #Deriving formula to find the roots of quadratic equation. |
| + | #Solving quadratic equation by using formula.<br> |
| + | #Solving quadratic equation graphically.<br> |
| + | #To find the sum and product of the roots of the quadratic equations. |
| + | |
| ===Notes for teachers=== | | ===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.''
| + | *Students need to know factorisation |
| + | *substitution of values and simplification |
| + | *Identifying suitable method |
| | | |
| ===Activities=== | | ===Activities=== |
− | #Activity No #1 '''Concept Name - Activity No.''' | + | #Activity No 1 -[https://www.geogebratube.org/material/iframe/id/8357/width/968/height/487/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/preferhtml5| geogebra] |
− | #Activity No #2 '''Concept Name - Activity No.''' | + | #Activity No 2-[http://www.wikihow.com/Solve-Quadratic-Equations/ learn more how to solve Q.E] |
| + | #Activity 3-[http://www.learnnc.org/lp/pages/2981| learn quadratics] |
| + | #Activity 4- [[Quadratic Equation solution activity1|Quadratic Equation solution]] |
| | | |
| ==Concept #5'''Nature of roots'''== | | ==Concept #5'''Nature of roots'''== |
| + | The roots of a quadratic equation can be real & equal, real & distinct or imaginary. |
| + | Nature of roots depends on the values of b^-4ac. |
| ===Learning objectives=== | | ===Learning objectives=== |
| + | #To find the discriminant & interpret the nature of the roots of the given quadratic equation. |
| + | |
| ===Notes for teachers=== | | ===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.''
| + | Guiding in Identifying the nature based on the value of discriminant |
| | | |
| ===Activities=== | | ===Activities=== |
− | #Activity No #1 '''Concept Name - Activity No.''' | + | #Activity No #1 '''Concept Name - Activity No.'''[http://interpret the nature of roots/ interpret the nature of the roots] |
| + | |
| #Activity No #2 '''Concept Name - Activity No.''' | | #Activity No #2 '''Concept Name - Activity No.''' |
− |
| |
| | | |
| ==Concept #6'''applications'''== | | ==Concept #6'''applications'''== |
| + | Solving problems based on quadratic equations. |
| ===Learning objectives=== | | ===Learning objectives=== |
| + | By applying the methods of solving quadratic equations, finding the solutions to real life situations. |
| + | |
| ===Notes for teachers=== | | ===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.''
| + | Help the students in Identifying parameters and suitable methods for solving application problems. |
| | | |
| ===Activities=== | | ===Activities=== |
− | #Activity No #1 '''Concept Name - Activity No.''' | + | #Activity No #1 [https://www.youtube.com/watch?v=IGGnn9oa4QYz| more word problems] |
− | #Activity No #2 '''Concept Name - Activity No.''' | + | #Activity 2:[http://www.ehow.com/info_8502727_applications-quadratic-equations.html| quadratics in real life] |
− | | |
| =Assessment activities for CCE= | | =Assessment activities for CCE= |
| + | .[Http://Tube.geogebra.org/m/105393c|quadratic quiz] |
| | | |
− | = Hints for difficult problems = | + | =Hints for difficult problems = |
− | | + | 1.If P & q are the roots of the equation <math>2a^2-4a+1=0</math> find the value of |
− | = Project Ideas = | + | <math>p^3+q^3</math><br> |
| + | [[solution]]<br> |
| + | 2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base.<br> |
| + | [[solution]]<br> |
| + | 3.Solve <math>x^2-4x-8=0</math> By completing the square. <br> |
| + | [[solution]] |
| | | |
− | = Math Fun =
| + | [[Category:Class 10]] |
| + | [[Category:Quadratic Equations]] |