Introduction to equations

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= Concept Map =

= Textbook = To add textbook links, please follow these instructions to: ([ Click to create the subpage])

=Additional Information=

Reference Books
= Teaching Outlines =

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 #
1 Period : 40 minutes Computer(Geogebra),projector,Blackboard <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" /> (This can be done using a graph sheet also) (NOTE:Students may recognise same pattern or some may not recognise the pattern. )
 * Estimated Time
 * Materials/ Resources needed
 * 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
 * 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
 * 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

Activity No #

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

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 =

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= Math Fun =

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