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| + | ''[http://karnatakaeducation.org.in/KOER/index.php/ಅಪವರ್ತಿಸುವಿಕೆ 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] |
| |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/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] |
| |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/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://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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− |
| |
− | <mm>[[Factorisation of Polynomials.mm|Flash]]</mm>
| |
| = Concept Map = | | = Concept Map = |
− | | + | [[File:Factorisation.mm|Flash]] |
− | | |
− | __FORCETOC__
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| | | |
| = Textbook = | | = Textbook = |
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| | | |
| =Additional Information= | | =Additional Information= |
| + | |
| + | {{#widget:YouTube|id=LitM6ERl88A}} |
| ==Useful websites== | | ==Useful websites== |
| + | *Question Corner |
| + | |
| + | |
| + | #[http://www.mathsisfun.com/algebra/polynomials.html Maths is Fun]. This website contains good worksheets for factorisation. |
| + | #[http://reference.wolfram.com/mathematica/guide/PolynomialAlgebra.html Wolfram Mathworld]. This website contains good simulations for math identities. |
| + | |
| ==Reference Books== | | ==Reference Books== |
| ===NCERT Books=== | | ===NCERT Books=== |
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| = Teaching Outlines = | | = Teaching Outlines = |
| | | |
− | ==Concept #== | + | ==Concept #1 Monomial expressions== |
| ===Learning objectives=== | | ===Learning objectives=== |
| + | To introduce expressions and the need and method of splitting |
| ===Notes for teachers=== | | ===Notes for teachers=== |
− | ===Activity No # === | + | ===Activities=== |
− | {| style="height:10px; float:right; align:center;"
| + | #Activity #1 |
− | |<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;">
| + | #Activity #2 Demonstrate Binomial Cube |
− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
| + | http://www.infomontessori.com/sensorial/montessori_binomial_cube_1.jpg |
− | |}
| |
− | *Estimated Time
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− | *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
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− | *Question Corner
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− | | |
− | ===Activity No # ===
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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://www.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
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− | *Question Corner
| |
| | | |
| ==Concept #== | | ==Concept #== |
| ===Learning objectives=== | | ===Learning objectives=== |
| ===Notes for teachers=== | | ===Notes for teachers=== |
− | ===Activity No # === | + | ===Activity No #1 Geogebra=== |
| {| 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://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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| *Prerequisites/Instructions, if any | | *Prerequisites/Instructions, if any |
| *Multimedia resources | | *Multimedia resources |
| + | [[File:Geogebra_screenshot_for_identities.png|150px]]<br> This is a Geogebra screenshot for identity.<br> |
| + | {{#widget:YouTube|id=crjItXrt43Q}}<br> |
| + | This is a classroom demonstration of binomial cube. Show the children before you start the cubic identity. |
| *Website interactives/ links/ / Geogebra Applets | | *Website interactives/ links/ / Geogebra Applets |
| *Process/ Developmental Questions | | *Process/ Developmental Questions |
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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;"> | | |<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://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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| | | |
− | = Hints for difficult problems = | + | # = Hints for difficult problems = |
| + | Question : If x= and y= find |
| + | |
| + | |
| + | Solution : |
| + | |
| + | Analysing the given condition |
| + | |
| + | Step 1 : = ()() => Using the formula : = ( )() |
| + | |
| + | step 2 : = ( + )(-) => substitute the value of x and y |
| + | |
| + | Step 3 : = x => take the L.C.M of the denominator , simplyfy using concept of addition and substaction of fraction |
| + | |
| + | Step 4: = x |
| + | simply the above using basic concepts of addition and substraction |
| + | |
| + | Step 5 : = x |
| + | |
| + | Step 6 := x => take common term 2 ( H.C.F) |
| + | |
| + | Step 7 : = x |
| + | |
| + | Step 8 : = |
| + | # |
| + | =hints for difficult problem= |
| + | |
| + | If x-= 4 prove that <math>x^{3}+6x^{2}+\frac {6} {x^{2}}-\frac{1} {x^{3}}=184 </math> |
| + | |
| + | =====If x+y=a and xy=b then prove that (1+)+(1+) = |
| + | |
| + | Steps for solution |
| + | |
| + | step 1: * Understanding the problem first. |
| + | * Recalling the indentities |
| + | |
| + | step 2 : * consider the condition and squaring on both side |
| + | * simplify to get the value |
| + | |
| + | step 3: * consider LHS |
| + | * multiply the expression |
| + | * substitute the value |
| + | * simlpify the equqtion |
| + | |
| + | |
| + | solution for the problem |
| + | |
| + | consider x+y=a |
| + | = |
| + | substitute x+y =a and xy=b |
| + | then we get |
| + | ------->(1) |
| + | consider xy=b squaring on both side |
| + | then we get =------->(2) |
| + | |
| + | consider LHS= |
| + | =(1+)+(1+) |
| + | =1+ |
| + | = 1+ from eqn 1 & 2 |
| + | = |
| + | = |
| + | LHS = RHS============= |
| | | |
| = 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:Class 8]] |
| + | [[Category:Algebraic expressions]] |