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Line 1: − = Concept Plan = − <mm>[[angles.mm|Flash]]</mm> − <!-- This portal was created using subst:box portal skeleton --> − <!-- BANNER ACROSS TOP OF PAGE --> − + − + − + − + − + − + − + − + − + − + − + − + − + + + + + + Line 33:
Line 34: − + − ===Learning objectives===+ − + − ===Activity No # === − + − + − *Materials/ Resources needed − *Prerequisites/Instructions, if any − *Multimedia resources − *Website interactives/ links/ / Geogebra Applets − *Process/ Developmental Questions − *Evaluation − *Question Corner − − ===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/ Developmental Questions − *Evaluation − *Question Corner Line 70:
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→Concept # 5. Angle bisector-Its construction
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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://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]
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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://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]
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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://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]
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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://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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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
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 Plan ===
[[File:Angles.mm]]
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__FORCETOC__
__FORCETOC__
= Teaching Outlines =
= Teaching Outlines =
==Concept #1.What is an angle ? ==
====Concept #1.What is an angle ? ====
===Activities===
===Notes for teachers===
Foramtion of
{| 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
*
==Concept #2. Using a Protractor- Measuring an angle ==
==Concept #2. Using a Protractor- Measuring an angle ==
{| 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;">
''[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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*Estimated Time
*Estimated Time
===Learning objectives===
===Learning objectives===
===Notes for teachers===
===Notes for teachers===
===Activity No # ===
===Activity No #1.Crazy Angles using 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;">
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
|}
|}
*Estimated Time
*Estimated Time: 40 minutes
*Materials/ Resources needed
*Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.
*Prerequisites/Instructions, if any
*Prerequisites/Instructions, if any:
*Multimedia resources
# The students should have a basic understanding about point, rays, line segments and vertex.
# They should know how angles are formed.
# They should know that angles are measured in units called degrees. 360 ° is a full rotation (a circle)
# They should know to use a protractor and measure the angles.
# They should know the meaning of terms acute, obtuse, straight, reflex, and complete angles.
*Multimedia resources; Laptop
*Website interactives/ links/ / Geogebra Applets
*Website interactives/ links/ / Geogebra Applets
<span> </span>
<span></span><div id="ggbContainer4a44ef2dc4b78417b74d34b3b537830b"></div><span></span>
*Process:
# The teacher should recaptulate the concept of a point, line segment, ray, vertex and angles.
# The teacher should show how angles are formed.
# Discuss the concept of cartesian plane, X and Y axes, rotation, and how it relates to angles.
# Demonstrate how to measure angles using a protractor.
# Define and illustrate the classification of the types of angles—acute, obtuse, right, straight zero and complete angles.
# In the succeeding class give the students protractors and let them have enough practise measuring and classifying angles.
Developmental Questions:
# What is a point ?
# A minimum of how many points are needed to define a line segment ?
# A minimum of how many points are needed to form an angle ?
# Name the line segments from the figure.
# What is a vertex ?
# How many rays /line segments are needed to form an angle ?
# Name the vertex at which the angle is formed
# Name the angle .
# Name the type of angle formed.
*Evaluation:
# Assess the students knowledge of angles by projecting different types of angles and asking them to name
# What are the characteristics of an acute angle ?
# What are the characteristics of an obtuse angle?
*Multimedia resources
# What are the characteristics of a right angle
*Website interactives/ links/ / Geogebra Applets
# Evaluate if the students have understood that :
*Process/ Developmental Questions
*An angle is formed where 2 lines meet at a point.
*Evaluation
*A right angle looks like a corner of a square or a rectangle.
*Question Corner
*An acute angle is narrower than a right angle.
==Concept #3. Angle constructions==
*An obtuse angle is wider than a right angle.
*Question Corner:
# What is an angle ?
# Where do you name an angle ?
# How do you identify different types of angles in 2-dimensional figures?
# How do angles help to classify 2-dimensional figures?
# Are angles <ABA' and <A'BA the same ? Justify
# Differentiate between the zero angle and a complete angle.
==Concept # 4. Angle constructions==
===Learning objectives===
===Learning objectives===
===Notes for teachers===
===Notes for teachers===
===Activity No # ===
===Activity No # ===
==Concept # 5. Angle bisector-Its construction==
==Concept # 4. Angle bisector-Its construction==
===Learning objectives===
===Learning objectives===
===Notes for teachers===
===Notes for teachers===
Activity - [[Activity-construction of angles|Construction of angle with measure 22.5∘]]
This activity helps to illustrate the 'angle bisector' construction three times since we construct ∡22.5 by constructing ∡90∘ (bisecting a segment / straight angle ∡180∘, then bisect ∡90∘ to get ∡45∘ and finally bisect ∡45∘ to get ∡22.5∘).
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
==Concept # 5. Pairs of angles==
==Concept # 6. Pairs of angles==
===Learning objectives===
===Learning objectives===
===Notes for teachers===
===Notes for teachers===
{| 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
{| 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
{| 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
*Evaluation
*Evaluation
*Question Corner
*Question Corner
==Concept # 6.Angles formed when lines are cut by a transversal==
==Concept # 7.Angles formed when lines are cut by a transversal==
===Learning objectives===
===Learning objectives===
===Notes for teachers===
===Notes for teachers===
{| 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 :''' 40 minutes<br>
'''*Estimated Time :''' 40 minutes<br>
Laptop<br>
Laptop<br>
'''*Website interactives/ links/ / Geogebra Applets'''<br>
'''*Website interactives/ links/ / Geogebra Applets'''<br>
<span> </span>
<span></span><div id="ggbContainer507e2592e2313aaf5f5d11fe1655c6bb"></div><span></span>
* This is a resource file on 'vertically opposite angles'
{{#widget:YouTube|id=m7v2g9_3BdU|left}}<br>
It has been created by Sucheta, Mathematics teacher, GHS Thyamangondlu
'''*Process:'''
'''*Process:'''
#Reiterate that when a transversal intersects parallel lines, several pairs of congruent and supplementary angles are formed.
#Reiterate that when a transversal intersects parallel lines, several pairs of congruent and supplementary angles are formed.
# Compare angle relationships formed by parallel lines vs. angle relationships formed by non-parallel lines.
# Compare angle relationships formed by parallel lines vs. angle relationships formed by non-parallel lines.
===Activity No # ===
==='''Activity No 2 Angles formed when a transversal intersects parallel lines''' ===
{| 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;">
|<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'''
*Prerequisites/Instructions, if any
Laptop, geogebra file, projector and pointer.
*Multimedia resources
*'''Prerequisites/Instructions, if any'''
*Website interactives/ links/ / Geogebra Applets
#The students should have prior knowledge of parallel lines , transversal, angles and types of angles formed when a pair of parallel lines are intersected by a transversal.
*Process/ Developmental Questions
#They should know what the terms interior, exterior, adjacent, alternate, consecutive, congruent, linear and corresponding mean.
#Students should know the definition of complementary angles, supplementary angles, and congruent angles.
*'''Multimedia resources''':
Laptop
*'''Website interactives/ links/ / Geogebra Applets'''
[[File:111.png|400px]]
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
*'''Process'''
#Reiterate that when a transversal intersects parallel lines, several pairs of congruent and supplementary angles are formed.
#Have students draw two parallel lines and a third line(transversal) intersecting those two lines on their own paper. Direct them to think about any angle relationships they see. Have them discuss their conjectures with a partner.
*Materials/ Resources needed
#The teacher can next project the GeoGebra worksheet and discuss about types of angles and their relationships with the class .
#Finally the teacher and students can summarize together the angle relationships.<br>
Linear pair of angles - adjacent and supplementary<br>
Vertical angles - congruent<br>
Corresponding angles -congruent<br>
Alternate interior angles - congruent<br>
Same side interior angles - supplementary<br>
Alternate exterior angles - congruent<br>
Same side exterior angles - supplementary<br>
*'''Developmental Questions'''
#How many pairs of corresponding angles are there ?
#What is true about corresponding angles formed when parallel lines are cut by a transversal?
#Compare different pairs of alternate interior angles. What do you notice?
#<EGD and <AHF are alternate exterior angles. What is another pair of alternate exterior angles?
#Compare different pairs of same-side interior angles. What do you notice?
#Compare different pairs of same-side exterior angles. What do you notice?
'''Evaluation'''
#What are the characteristics of linear angles (adjacent and supplementary) ?
#What do you observe about the angle measures of the linear angles?
*'''Question Corner'''
#What do adjacent , alternate, linear , corresponding and consecutive mean individually
#What are complementary angles?
#What are supplementary angles ?
#What does it mean if two angles are congruent?
#What is the complement of 65 degrees
#What is the supplement of 70 degrees?
#Compare angle relationships formed by parallel lines vs. angle relationships formed by non-parallel lines.
= Hints for difficult problems =
= Hints for difficult problems =
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:Lines and Angles]]