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Line 24: − <mm>[[Types of progressions.mm|Flash]]</mm>+ + − Please click here for Karnataka and other text books.+ − + + + + + + + + + − + + + + + + + + + + + + + + + − ''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.''+ + + + − #Activity No #1 '''Concept Name - 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://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 (How to do the activity)''' − * '''Developmental Questions (What discussion questions)''' − * '''Evaluation (Questions for assessment of the child)''' − * '''Question Corner''' − #Activity No #2 '''Concept Name - 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://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 (How to do the activity)''' − * '''Developmental Questions (What discussion questions)''' − * '''Evaluation (Questions for assessment of the child)''' − * '''Question Corner''' − − == Headline text == + + + + + + + − ''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.''+ − − + − + − '' − − == Headline text == + + + + + + + − ''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.''+ − + − + − + − '' − − == Headline text == + + + + − ''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.''+ − + + + − + − + − '' − − == Headline text == + + + + + + + +
Types of progressions (view source)
Revision as of 04:01, 12 November 2019
, 04:01, 12 November 2019no edit summary
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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]
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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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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
[http://www.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]
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= Concept Map =
= Concept Map =
__FORCETOC__
__FORCETOC__
[[File:Types of progressions.mm|Flash]]
= Textbook =
= Textbook =
#[http://gujarat-education.gov.in/textbook/Images/maths10-eng/chap5.pdf Gujarat textbook for class 10 : Chapter 5 Arithmetic progression]<br>
#[http://www.scert.kerala.gov.in/images/text_books/chapter_01m.pdf Kerala state textbook for class 10 : Chapter 01 Arithmetic Sequences]<br>
#[http://ncert.nic.in/NCERTS/textbook/textbook.htm?jemh1=5-14 NCERT text book : Aarithmetic progression]
=Additional Information=
=Additional Information=
==Useful websites==
==Useful websites==
#[http://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html Maths is fun for Arithmetic progressions]
#[http://www.mathsisfun.com/algebra/sequences-sums-geometric.html Maths is fun for Geometric progressions]
#[http://www.mathisfunforum.com/viewtopic.php?id=3305 maths is fun all three types progression]
Quiz Websites
#[http://www.projectmaths.ie/students/cd-strand3LC/arithmeticsequence.htm Quiz for Arithmetic Progressions]
#[http://www.cliffsnotes.com/math/algebra/algebra-ii/sequences-and-series/quiz-arithmetic-sequence Quiz for AP and GP]
==Reference Books==
==Reference Books==
= Teaching Outlines =
= Teaching Outlines =
#Identify the types of progression in the given sequence
#Meaning of three types of progression
#General form of three types of progression
#Difference between three types of progression
#Terms related to A.P , H.P and G.P
# Formula's of three types progression
#Mean of three types of progression and their relation
# Problems of three types of progression
==Concept #1 Arithmetic Progression==
==Concept #1 Arithmetic Progression==
===Learning objectives===
===Learning objectives===
#Definition of Arithmetic progression
#Writing the general form of an A.P
#Terms used in A.P
#Finding 'a', common difference, 'n' th of A.P
#Framing formula to find the sum of a finite arithmetic series.
#Finding the sum of a finite arithmetic series.
===Notes for teachers===
===Notes for teachers===
#An arithmetic progression is a sequence in which each term is obtained by adding a fixed number to the preceding term.
#General form : a , a+d , a+2d , a+3d, . . . . ., a+(n-1)d
#Common Difference (d) : Difference between any term and its preceding term
# Formula's of Arithmetic progression
===Activities===
===Activities===
#Activity No #1 activity for arithmetic progression
#Activity No #2 activity for arithmetic progression
==Concept #2 Harmonic progression==
==Concept #2 Harmonic progression==
===Learning objectives===
===Learning objectives===
#Defining an Harmonic progression
#The General form of Harmonic Progression
#Compare H.P with other type of progression
#Identifying H.P among a given set of progression
===Notes for teachers===
===Notes for teachers===
A sequence in which , the reciprocals of the terms form an arithmetic progression is called a Harmonic progression.
===Activities===
===Activities===
#Activity No #1 '''Concept Name - Activity No.'''
#Activity No #1 acivity for Harmonic progression
#Activity No #2 '''Concept Name - Activity No.'''
#Activity No #2 acivity for Harmonic progression
==Concept #3 Geometric progression==
==Concept #3 Geometric progression==
===Learning objectives===
===Learning objectives===
#Defining G.P by recognizing common ratios
#General form of G.P
#Terms used in G.P
#Identifying next term and precedig term of an 'n' th term of G.P
#Finding the common ratio, a specific term and the last term of G.P
#Formulating the formula 'n'th term of G.P , sum formula based on 'r', Sum of infinite formula,
===Notes for teachers===
===Notes for teachers===
# A geometric progression is a sequence in which each succeeding term is obtained by multiplying the preceding term by a fixed number.
#The ratio of a term and its preceeding term is called common ratio (r).
===Activities===
===Activities===
#Activity No #1 '''Concept Name - Activity No.'''
#Activity No #1 activity for Geometric progression
#Activity No #2 '''Concept Name - Activity No.'''
#Activity No #2 activity for Geometric progression
==Concept #4 Relation between A.M, G.M, H.M==
==Concept #4 Relation between A.M, G.M, H.M==
===Learning objectives===
===Learning objectives===
#Formulating the formula for A.M, G.M and H.M
#Using formula to find mean of any two terms in A.P , G.P and H.P
#Relation between A.M , G.M and H.M
===Notes for teachers===
===Notes for teachers===
#Arithmetic mean of two numbers is equal to half of their sum.
#The harmonic mean of any two numbers is equal to twice their product divided by their sum.
#The Geometric mean of any numbers is square root of their product.
#Geometric mean is equal to square root of their product of arithmetic mean and harmonic mean/
===Activities===
===Activities===
#Activity No #1 '''Concept Name - Activity No.'''
#Activity No #1 activity to show relation between A.M, G.M, H.M
#Activity No #2 '''Concept Name - Activity No.'''
#Activity No #2 activity to show relation between A.M, G.M, H.M
=Assessment activities for CCE=
=Assessment activities for CCE=
= Hints for difficult problems =
= Hints for difficult problems =
1. A company employed 400 persons in the year 2001 and each year increased by 35 persons. In which year the number of employees in the company will be 785?
[[Class10_progressions_problems#Problem_1_from_Exercise_3.2_.28_Q.N.11_-_page_No._37.29|click here for Solution]]<br>
2. The sum of 6 terms which form an A.P is 345. The difference between the first and last terms is 55. Find the terms.
[[Class10_progressions_problems#Problem_2_from_Exercise_3.3_.28_Q.N.12_-_page_No._43.29|click here for solution]]<br>
3. Find two numbers whose arithmetic mean exceeds their geometric mean by 2, and whose harmonic mean is one-fifth of the larger number .[[Class10_progressions_problems#Problem 3|click here for solution]]<br>
4. If 'a' be the arithmetic mean between 'b' and 'c', and 'b' the geometric mean between 'a' and 'c', then prove that 'c' will be the harmonic mean between 'a' and 'b'.[[Class10_progressions_problems#Problem 4|click here for solution]]
= Project Ideas =
= Project Ideas =
= Math Fun =
= Math Fun =
[[Category:Progressions]]