Difference between revisions of "Introduction to equations"

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'''Usage'''  
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<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;">
−
 
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''[http://karnatakaeducation.org.in/KOER/index.php/ಸಮೀಕರಣಗಳ_ಪರಿಚಯ see in English]''</div>
−
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
+
<!-- This portal was created using subst:box portal skeleton  -->
−
 
+
<!--        BANNER ACROSS TOP OF PAGE        -->
−
Please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
+
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
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|-
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|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]
 +
|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:_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; "|
 +
[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; "|
 +
[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; "|
 +
[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; "|
 +
[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 +
|}
 +
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
  
 
= Concept Map =
 
= Concept Map =
−
<mm>[[Introduction_to_equations.mm|Flash]]</mm>
+
[[File:Introduction_to_equations.mm|Flash]]
−
 
+
__FORCETOC__
 
= Textbook =
 
= Textbook =
 
To add textbook links, please follow these instructions to:  
 
To add textbook links, please follow these instructions to:  
Line 18: Line 34:
 
= Teaching Outlines =
 
= Teaching Outlines =
  
−
Learning Objectives
+
==Concept #1 : Generalizing the form of a linear equation from data patterns==
−
1. Recognise  a pattern in the set of data(in this class a set of coordinates)
+
===Learning objectives===
−
2. Recognise the variation(proportion/nonproportion)
 
−
3. Establish/Guess the relationship between the set of coordinates
 
−
4. Recognise varying and constant terms
 
−
5. Recognise dependency of one varible with the other
 
−
6. Establishing the relationship between a variable and a constant
 
−
7. Generalise  the relationship and expressing symbolically
 
−
8. Explore  the possibility of having  different patterns
 
−
9. Understand that every number pattern can be represented on the graph
 
−
10. Joing the coordinates leads to a straight line or sometimes to  non-Linear set
 
−
11. Interprets the relationship between  the set of points on a straight line and on the non-linear set.
 
−
12. Every pair of points when joined gives a straightline(infinite points can be located between two points
 
−
13. Relation between the coordinates of set of points which makes a straightline is a Linear Equation /Otherwise  Non-Linear
 
−
 
 
−
== Concept #1 Data Patterns ==
 
 
#Recognise  a pattern in the set of data(in this class a set of coordinates)
 
#Recognise  a pattern in the set of data(in this class a set of coordinates)
 
#Recognise the variation(proportion/nonproportion)
 
#Recognise the variation(proportion/nonproportion)
 +
#Recognise varying and constant terms
 +
#Recognise dependency of one varible with the other
 +
#Establishing the relationship between a variable and a constant
 +
#Generalise  the relationship and expressing symbolically
 
#Explore  the possibility of having  different patterns
 
#Explore  the possibility of having  different patterns
 
#Understand that every number pattern can be represented on the graph
 
#Understand that every number pattern can be represented on the graph
−
===Learning objectives===
+
#Joining the coordinates leads to a straight line or sometimes to  non-Linear set
 +
#Interprets the relationship between  the set of points on a straight line and on the non-linear set.
 +
#Every pair of points when joined gives a straightline(infinite points can be located between two points
 +
#Relation between the coordinates of set of points which makes a straightline is a Linear Equation /Otherwise  Non-Linear
 
===Notes for teachers===
 
===Notes for teachers===
 +
#Every Linear Equation represents a straightline .If the relationship(pattern)between two quantities can be represented as straightline then the relationship is in the form of linear equation
 +
#A teacher can develop a lesson on Linear Equation with Geogebra application
 +
===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://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 +
|}
 +
*Estimated Time <br>
 +
1 Period : 40 minutes<br>
 +
*Materials/ Resources needed<br>
 +
Computer(Geogebra),projector,Blackboard<br>
 +
<ggb_applet width="1366" height="568" version="4.2" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" />
 +
*Prerequisites/Instructions, if any<br>
 +
#Students have been  introduced to graph(pictographs,bargraph,Histograms..)
 +
#Students can  make  the difference (Relationship)between axes and quadrants
 +
#Refer to the Teaching Outline of Introduction to Coordinates
 +
#Students are able to locate a given  point on the graph if a set of coordinates are given
 +
#Students are able to  recognise coordinates of a given point on the graph
 +
#Students can differentiate position of a point on the (NL)and also on the Quadrants
 +
*Multimedia resources
 +
*Website interactives/ links/ / Geogebra Applets
 +
*Process/ Developmental Questions<br>
 +
(This can be done using a graph sheet also)
 +
#Start with a Geogebra Drawing pad
 +
#Give /ask students to give a set of coordinates
 +
#You may get different patterns(assaign a group task)
 +
#Ask the students to recognise  coordinates of same  pattern
 +
#Ask them to extend the pattern to say many more coordinates following the same pattern
 +
(NOTE:Students may recognise same pattern or some may not recognise the pattern. ) 
 +
#Ask the students visualise the points and visualise the pattern on the grap.
 +
#Ask them to join the points (teacher can help student to join the points by using Straight line tool in Geogebra which is more meaningfull)
 +
#This can be extended to say that Relation between the coordinates of set of points which gives/makes/results  a straightline is a Linear Equation
 +
#Continue with some more points with line joing the points and establishing the relation ship between variables also.
 +
#Introduction to the degree of an equation may be discussed in subsequent lessons.
 +
 +
*Evaluation
 +
#Show them the graph of an equation and ask students to predict the pattern
 +
*Question Corner
 +
 
===Activity No # ===
 
===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://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 +
|}
 +
*Estimated Time
 
*Materials/ Resources needed
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Prerequisites/Instructions, if any
Line 49: Line 102:
 
*Question Corner
 
*Question Corner
  
−
 
+
==Concept #2 Solution of an equation==
−
== Concept #2 : Generalizing equations from data patterns ==  
 
 
===Learning objectives===
 
===Learning objectives===
−
#Establish/Guess the relationship between the set of coordinates
 
−
#Recognise varying and constant terms
 
−
#Recognise dependency of one varible with the other
 
−
#Establishing the relationship between a variable and a constant
 
−
#Generalise  the relationship and expressing symbolically
 
 
===Notes for teachers===
 
===Notes for teachers===
 
===Activity No # ===
 
===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://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 +
|}
 +
*Estimated Time
 
*Materials/ Resources needed
 
*Materials/ Resources needed
 
*Prerequisites/Instructions, if any
 
*Prerequisites/Instructions, if any
 
*Multimedia resources
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Website interactives/ links/ / Geogebra Applets
−
*Process/ Developmental Questions
+
 
 +
[[File:algebragame.png|400px|alt text:Click here for a game to introduce algebra]]
 +
[http://www.math-play.com/One-Step-Equation-Game.html Math Play]
 +
<br>*Process/ Developmental Questions
 
*Evaluation
 
*Evaluation
 
*Question Corner
 
*Question Corner
  
−
== Concept #3 : Form of a linear equation ==
 
−
===Learning objectives===
 
−
#Analyzing a linear equation
 
−
===Notes for teachers===
 
−
Note for the Teachers
 
−
# Every Linear Equation represents a straightline .If the relationship(pattern)between two quantities can be represented as straightline then the relationship is in the form of linear equation
 
−
# A teacher can develop a lesson on Linear Equation with Geogebra application
 
−
Analysing a Linear Equation
 
−
Class Interaction(with activity)
 
 
===Activity No # ===
 
===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://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
 +
|}
 +
*Estimated Time
 
*Materials/ Resources needed
 
*Materials/ Resources needed
−
Computer(Geogebra),projector,Blackboard
 
−
(Lesson can be developed using graph sheets also)
 
 
*Prerequisites/Instructions, if any
 
*Prerequisites/Instructions, if any
−
#Students have been  introduced to graph(pictographs,bargraph,Histograms..)
 
−
#Students can  make  the difference (Relationship)between axes and quadrants
 
−
Refer to the Teaching Outline of Introduction to Coordinates
 
−
#Students are able to locate a given  point on the graph if a set of coordinates are given
 
−
#Students are able to  recognise coordinates of a given point on the graph
 
−
#Students can differentiate position of a point on the (NL)and also on the Quadrants
 
 
*Multimedia resources
 
*Multimedia resources
 
*Website interactives/ links/ / Geogebra Applets
 
*Website interactives/ links/ / Geogebra Applets
 
*Process/ Developmental Questions
 
*Process/ Developmental Questions
−
1. Start with a Geogebra Drawing pad
 
−
2. Give /ask students to give a set of coordinates
 
−
You may get different patterns(assaign a group task)
 
−
3. ask the students to recognise  coordinates of same  pattern
 
−
4. ask them to extend the pattern to say many more coordinates following the same pattern
 
−
(NOTE:Students may recognise same pattern or some may not recognise the pattern. ) 
 
−
5. Ask the students visualise the points and visualise the pattern on the grap.
 
−
6. Ask them to join the points (teacher can help student to join the points by using Straight line tool in Geogebra which is more meaningfull)
 
−
7. This can be extended to say that
 
−
Relation between the coordinates of set of points which gives/makes/results  a straightline is a Linear Equation
 
−
8. Continue with some more points with line joing the points and establishing the relation ship between variables also.
 
−
9. Introduction to the degree of an equation may be discussed in subsequent lessons.
 
−
 
 
*Evaluation
 
*Evaluation
 
*Question Corner
 
*Question Corner
Line 111: Line 141:
  
 
= Math Fun =
 
= Math Fun =
 +
 +
'''Usage'''
 +
 +
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template
 +
 +
[[Category:Introduction to Equations]]

Latest revision as of 05:07, 20 November 2019

see in English

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 : Generalizing the form of a linear equation from data patterns

Learning objectives

  1. Recognise a pattern in the set of data(in this class a set of coordinates)
  2. Recognise the variation(proportion/nonproportion)
  3. Recognise varying and constant terms
  4. Recognise dependency of one varible with the other
  5. Establishing the relationship between a variable and a constant
  6. Generalise the relationship and expressing symbolically
  7. Explore the possibility of having different patterns
  8. Understand that every number pattern can be represented on the graph
  9. Joining the coordinates leads to a straight line or sometimes to non-Linear set
  10. Interprets the relationship between the set of points on a straight line and on the non-linear set.
  11. Every pair of points when joined gives a straightline(infinite points can be located between two points
  12. Relation between the coordinates of set of points which makes a straightline is a Linear Equation /Otherwise Non-Linear

Notes for teachers

  1. Every Linear Equation represents a straightline .If the relationship(pattern)between two quantities can be represented as straightline then the relationship is in the form of linear equation
  2. A teacher can develop a lesson on Linear Equation with Geogebra application

Activity No #

  • Estimated Time

1 Period : 40 minutes

  • Materials/ Resources needed

Computer(Geogebra),projector,Blackboard

  • Prerequisites/Instructions, if any
  1. Students have been introduced to graph(pictographs,bargraph,Histograms..)
  2. Students can make the difference (Relationship)between axes and quadrants
  3. Refer to the Teaching Outline of Introduction to Coordinates
  4. Students are able to locate a given point on the graph if a set of coordinates are given
  5. Students are able to recognise coordinates of a given point on the graph
  6. Students can differentiate position of a point on the (NL)and also on the Quadrants
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions

(This can be done using a graph sheet also)

  1. Start with a Geogebra Drawing pad
  2. Give /ask students to give a set of coordinates
  3. You may get different patterns(assaign a group task)
  4. Ask the students to recognise coordinates of same pattern
  5. Ask them to extend the pattern to say many more coordinates following the same pattern

(NOTE:Students may recognise same pattern or some may not recognise the pattern. )

  1. Ask the students visualise the points and visualise the pattern on the grap.
  2. Ask them to join the points (teacher can help student to join the points by using Straight line tool in Geogebra which is more meaningfull)
  3. This can be extended to say that Relation between the coordinates of set of points which gives/makes/results a straightline is a Linear Equation
  4. Continue with some more points with line joing the points and establishing the relation ship between variables also.
  5. Introduction to the degree of an equation may be discussed in subsequent lessons.
  • Evaluation
  1. Show them the graph of an equation and ask students to predict the pattern
  • 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 Solution of an equation

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets

alt text:Click here for a game to introduce algebra Math Play
*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

Hints for difficult problems

Project Ideas

Math Fun

Usage

Create a new page and type {{subst:Math-Content}} to use this template

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