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[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/Mathematics:_Topics Topics in School Mathematics]
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==concept map==
= Textbook =
[[File:polygons.mm|flash]]
== Textbook ==
To add textbook links, please follow these instructions to:
To add textbook links, please follow these instructions to:
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])
=Additional Information=
==Additional Information==
==Useful websites==
=== Resources ===
==== Resource Title ====
[http://www.mathopenref.com/tocs/polygontoc.html Polygons]
===Useful websites===
1. http://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/polygons . This website is good for referring to the theory regarding polygons.
1. http://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/polygons . This website is good for referring to the theory regarding polygons.
==Reference Books==
===Reference Books===
= Teaching Outlines =
== Teaching Outlines ==
# Introduction to polygon
# Introduction to polygon
# Characteristics of polygons.
# Characteristics of polygons.
# Types of polygons.
# Types of polygons.
==Building prior competencies==
Many student are entering Class 9 without adequate understanding of prior concepts like angles, line, etc.
Therefore, the following sequence of lessons has been suggested with a combination of hands-on activities, Geogebra work to build those concepts in students.
[[File:Polygon_prior_competencies_upload.mm|flash]]
The following Geogebra files are used with associated lessons:
#[[:File:0. Angles introduction.ggb|Angles introduction]]
#[[:File:1. Complementary angles demonstration.ggb|Complementary angles]]
#[[:File:2. Supplementary angles demonstration.ggb|Supplementary angles]]
#[[:File:3. parallellines-2.ggb|Activity with parallel line]]
#[[:File:4. Introduction to a triangle.ggb|Demonstration of triangle]]
#[[:File:5. Introduction to a polygon.ggb|Polygon]]
==Concept #1. Introduction to polygons and nomenclature.==
==Concept #1. Introduction to polygons and nomenclature.==
===Learning objectives===
===Learning objectives===
==Notes for teachers==
==Notes for teachers==
There are a countless number of polygons. Because they all differ in the number of sides that they have, this results in different angle measures at their vertices. Listed below are the names and number of sides of some polygons. The "Interior Angle Measure" column of the table only applies to regular polygons, in which all the interior angles are equal.<br>
Source: This information has been taken from the website :http://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/polygons<br>
Summary: There are a countless number of polygons. Because they all differ in the number of sides that they have, this results in different angle measures at their vertices. Listed below are the names and number of sides of some polygons. The "Interior Angle Measure" column of the table only applies to regular polygons, in which all the interior angles are equal.<br>
With the exception of the triangle and quadrilateral, notice that all polygon names end with "gon." What sets regular polygon names apart from each other are their prefixes, which speak to the number of sides that they have. For instance, the prefix for the word "hexagon" is "hexa," which essentially means "six." However, as we move down our list and the names for polygons becomes quite confusing, we need a more efficient way of naming polygons. One way is by not calling a polygon by its real name, but rather by just saying the number of sides it has, and attaching "-gon" at the end. For instance, rather than calling an 18-sided polygon an "octdecagon," we can just call it an 18-gon. Thus, a polygon with n sides is simply called an n-gon.
With the exception of the triangle and quadrilateral, notice that all polygon names end with "gon." What sets regular polygon names apart from each other are their prefixes, which speak to the number of sides that they have. For instance, the prefix for the word "hexagon" is "hexa," which essentially means "six." However, as we move down our list and the names for polygons becomes quite confusing, we need a more efficient way of naming polygons. One way is by not calling a polygon by its real name, but rather by just saying the number of sides it has, and attaching "-gon" at the end. For instance, rather than calling an 18-sided polygon an "octdecagon," we can just call it an 18-gon. Thus, a polygon with n sides is simply called an n-gon.
===Activity No # 1. Which polygon am I ? ===
===Activity No # 1. Which polygon am I ? ===
{| 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: 30 minutes.
*Estimated Time: 30 minutes.
*Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
*Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
*Prerequisites/Instructions, if any:
*Prerequisites/Instructions, if any:
# The students should know that lines intersect to form figures.
# Lines intersect to form figures.
# In other words plane closed figures have atleast 3 sides.
# Plane closed figures have atleast 3 sides.
# The intersecting points of two lines is known as a vertex and the lines are the edges/sides.
# The intersecting points of two lines is known as a vertex and the lines are the edges/sides.
# The student should know the meaning of greek numerals uni, bi, tri ....etc.
# Meaning of greek numerals uni, bi, tri ....etc.
*Multimedia resources: Laptop
*Multimedia resources: Laptop
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets: This geogebra file has been created by '''Smt Sarah Zakiya Madam, GUHS, Yellagondapalya.'''
<span> </span>
<span></span><div id="ggbContainerfbad5ae84c119793e6125f6c6fe3c642"></div><span></span>
*Process:
*Process:
# The teacher can tell the students that they are surrounded by many different kinds of shapes every day.
# The teacher can tell the students that they are surrounded by many different kinds of shapes every day.
# What is a polygon with 12 sides called ?
# What is a polygon with 12 sides called ?
# You have a collection of sides from triangles and decagons. The total number of sides is 100 and you have 4 decagons. How many triangles do you have ?
# You have a collection of sides from triangles and decagons. The total number of sides is 100 and you have 4 decagons. How many triangles do you have ?
===Activity No # ===
===Activity No # ===
{| 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
(This image has been taken from:http://www.mathsisfun.com/geometry/regular-polygons.html)
===Notes for teachers===
===Notes for teachers===
===Activity No # Polygon's table of values.===
===Activity No # 1. Polygon's table of values.===
{| 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>
|}
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*Estimated Time:
*Estimated Time: 90 minutes.
*Materials/ Resources needed:
*Materials/ Resources needed:
# Sheets of paper, scale, compass, protractor, pencil.
*Prerequisites/Instructions, if any:
*Prerequisites/Instructions, if any:
# Knowledge of different polygons and their names.
# Requisite formulae needed to do the calculations.
# Skills to perform and tabulate calculations accurately.
*Multimedia resources:
*Multimedia resources:
*Website interactives/ links/ / Geogebra Applets:
*Website interactives/ links/ / Geogebra Applets:
Please refer to this website for more clarity on this activity : http://www.mathsisfun.com/geometry/regular-polygons.html
*Process:
*Process:
# Use the formulas listed in learning objectives above to make a table of Side, Apothem and Area, compared to a Radius of "1":
# Use the formulas listed in learning objectives above to make a table of Side, Apothem and Area, compared to a Radius of "1":
# Let the table have the following columns.
# Let the table have the following columns.
[[File:Table.jpeg|800px]]
*Developmental Questions:
*Developmental Questions:
# Name the types of polygons based on their sides.
# What is a regular polygon ?
# How many sides does a ______________ have ?
# What is an interior angle ?
# Is there any relationship between the number of sides and number of angles ?
# What radius has been mentioned here as common for all ?
# What is an apothem ?
# How do you get the central point of a polygon ?
# What is the formula to find the area of a polygon ?
*Evaluation:
*Evaluation:
*Question Corner:
# Which measuring parameter do you think is the deciding factor for the area of a polygon ?
*Question Corner
# Can you find the listed measures like interior angle, area without using the formula ? How ? Discuss.
===Activity No # ===
===Activity No # ===
{| 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
{| 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>
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[[File:Tangram.jpg|300px]]
[[File:Tangram.jpg|300px]]
*Materials/ Resources needed: Chart papers, scissors, pencil, scale.
*Materials/ Resources needed: Chart papers, scissors, pencil, scale.
*Prerequisites/Instructions, if any
*Prerequisites/Instructions, if any
# The students should have understanding of basic shapes like square, rectangle, parallelogram, triangle and trapezium.
# An understanding of basic shapes like square, rectangle, parallelogram, triangle and trapezium.
# They should be able to draw mentioned shapes accurately and cut exactly on boundaries.
# Ability to draw mentioned shapes accurately and cut exactly on boundaries.
*Multimedia resources
*Multimedia resources
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets
{| 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:
{| 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
= Hints for difficult problems =
= Hints for difficult problems =
[[:File:polygon problem.odt]]
==Angle sum property==
CLASS IX TOPIC POLYGONS
ADDITIONAL PROBLEMS (problem no 3 )
A polygon has 'n' sides .Two of it's angles are right angles and each of remaining angle isFind the value of 'n'.
Step 1;(Students must understand the problem)
In a polygon of side 'n' two angles are and other angles are each.We must find out value of 'n'.
Step 2(Students know the formula for sum of angles of polygon of side 'n')
(2n-4)right angles.
Step 3(Sum of the angles is equal to what?)
There are 'n' angles in a polygon of side 'n'.Out of 'n' angles 2 angles are right anles and other (n-2) angles are each.
(2n-4) <math>90^0</math> = (n-2)<nowiki><math>\144^0+(2)(90^0)how to open the bracket and substitute the values)</nowiki>
2n x - 4 x =
= (Brings similar terms at one side of the equation)
= (Add and substract and simplify)
=
n = (Devide and simplify)
n = 7
= Project Ideas =
= Project Ideas =
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:Polygons]]