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− | = Concept Plan =
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− | <mm>[[angles.mm|Flash]]</mm>
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− | [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] |
− | |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/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus] | + | [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; "| | + | | 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] |
− | |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/Text_Books#Mathematics_-_Textbooks Textbooks] | + | [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; "| | + | | 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:_Question_Papers Question Bank] | + | [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''']. | | 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]] |
| + | <!-- This portal was created using subst:box portal skeleton --> |
| + | <!-- BANNER ACROSS TOP OF PAGE --> |
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| __FORCETOC__ | | __FORCETOC__ |
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| = Teaching Outlines = | | = Teaching Outlines = |
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− | ==Concept #1.What is an angle ? == | + | ====Concept #1.What is an angle ? ==== |
− | ===Learning objectives===
| + | ===Activities=== |
− | ===Notes for teachers===
| + | Foramtion of |
− | ===Activity No # === | |
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− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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− | |}
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− | *Estimated Time
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− | *Materials/ Resources needed
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− | *Prerequisites/Instructions, if any
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− | *Multimedia resources
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− | *Website interactives/ links/ / Geogebra Applets
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− | *Process/ Developmental Questions
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− | *Evaluation
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− | *Question Corner
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− | | |
− | ===Activity No # ===
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− | ''[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 | + | * |
− | *Materials/ Resources needed
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− | *Prerequisites/Instructions, if any
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− | *Multimedia resources
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− | *Website interactives/ links/ / Geogebra Applets
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− | *Process/ Developmental Questions
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− | *Evaluation
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− | *Question Corner
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| | | |
| ==Concept #2. Using a Protractor- Measuring an angle == | | ==Concept #2. Using a Protractor- Measuring an angle == |
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− | ''[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 |
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− | ''[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 |
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| ===Learning objectives=== | | ===Learning objectives=== |
| ===Notes for teachers=== | | ===Notes for teachers=== |
− | ===Activity No # === | + | ===Activity No #1.Crazy Angles using Geogebra === |
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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> |
| |} | | |} |
− | *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 |
− | *Process/ Developmental Questions
| + | <span> </span> |
− | *Evaluation
| + | |
− | *Question Corner
| + | <span></span><div id="ggbContainer4a44ef2dc4b78417b74d34b3b537830b"></div><span></span> |
− | ===Activity No # ===
| + | *Process: |
− | {| style="height:10px; float:right; align:center;"
| + | # The teacher should recaptulate the concept of a point, line segment, ray, vertex and angles. |
− | |<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;">
| + | # The teacher should show how angles are formed. |
− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
| + | # 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. |
− | *Estimated Time
| + | # Define and illustrate the classification of the types of angles—acute, obtuse, right, straight zero and complete angles. |
− | *Materials/ Resources needed
| + | # In the succeeding class give the students protractors and let them have enough practise measuring and classifying angles. |
− | *Prerequisites/Instructions, if any
| + | Developmental Questions: |
− | *Multimedia resources
| + | # What is a point ? |
− | *Website interactives/ links/ / Geogebra Applets
| + | # A minimum of how many points are needed to define a line segment ? |
− | *Process/ Developmental Questions
| + | # A minimum of how many points are needed to form an angle ? |
− | *Evaluation
| + | # Name the line segments from the figure. |
− | *Question Corner
| + | # What is a vertex ? |
− | ===Activity No # ===
| + | # How many rays /line segments are needed to form an angle ? |
− | {| style="height:10px; float:right; align:center;"
| + | # Name the vertex at which the angle is formed |
− | |<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;">
| + | # Name the angle . |
− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
| + | # Name the type of angle formed. |
− | |}
| + | *Evaluation: |
− | *Estimated Time
| + | # Assess the students knowledge of angles by projecting different types of angles and asking them to name |
− | *Materials/ Resources needed
| + | # What are the characteristics of an acute angle ? |
− | *Prerequisites/Instructions, if any
| + | # 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 # === |
− | {| style="height:10px; float:right; align:center;"
| + | ==Concept # 5. Angle bisector-Its construction== |
− | |<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://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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− | |}
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− | *Estimated Time
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− | *Materials/ Resources needed
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− | *Prerequisites/Instructions, if any
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− | *Multimedia resources
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− | *Website interactives/ links/ / Geogebra Applets
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− | *Process/ Developmental Questions
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− | *Evaluation
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− | *Question Corner
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− | | |
− | ===Activity No # ===
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− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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− | |}
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− | *Estimated Time
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− | *Materials/ Resources needed
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− | *Prerequisites/Instructions, if any
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− | *Multimedia resources
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− | *Website interactives/ links/ / Geogebra Applets
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− | *Process/ Developmental Questions
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− | *Evaluation
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− | *Question Corner
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− | | |
− | ==Concept # 4. Angle bisector-Its construction== | |
| ===Learning objectives=== | | ===Learning objectives=== |
| ===Notes for teachers=== | | ===Notes for teachers=== |
− | ===Activity No # ===
| + | Activity - [[Activity-construction of angles|Construction of angle with measure 22.5∘]] |
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− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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− | |}
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− | *Estimated Time
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− | *Materials/ Resources needed
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− | *Prerequisites/Instructions, if any
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− | *Multimedia resources
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− | *Website interactives/ links/ / Geogebra Applets
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− | *Process/ Developmental Questions
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− | *Evaluation
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− | *Question Corner
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| | | |
− | ===Activity No # ===
| + | 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∘). |
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− | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | |
− | |}
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− | *Estimated Time
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− | *Materials/ Resources needed
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− | *Prerequisites/Instructions, if any
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− | *Multimedia resources
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− | *Website interactives/ links/ / Geogebra Applets
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− | *Process/ Developmental Questions
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− | *Evaluation
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− | *Question Corner
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| | | |
− | ==Concept # 5. Pairs of angles== | + | ==Concept # 6. Pairs of angles== |
| ===Learning objectives=== | | ===Learning objectives=== |
| ===Notes for teachers=== | | ===Notes for teachers=== |
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− | ''[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 |
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− | ''[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 |
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− | ''[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 |
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| *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=== |
− | ===Activity No # ===
| + | '''Activity No # 1.Angles formed when a transversal intersects parallel lines ''' |
| {| 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 :''' 40 minutes<br> |
− | *Materials/ Resources needed | + | '''*Materials/ Resources needed :'''Laptop, geogebra file, projector and pointer.<br> |
− | *Prerequisites/Instructions, if any | + | '''*Prerequisites/Instructions, if any :''' |
− | *Multimedia resources | + | #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. |
− | *Website interactives/ links/ / Geogebra Applets | + | #They should know what the terms interior, exterior, adjacent, alternate, consecutive, congruent, linear and corresponding mean. |
− | *Process/ Developmental Questions | + | #Students should know the definition of complementary angles, supplementary angles, and congruent angles. |
− | *Evaluation | + | '''*Multimedia resources:''' |
− | *Question Corner | + | Laptop<br> |
− | ===Activity No # === | + | '''*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:''' |
| + | #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. |
| + | #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 relationshipsalong with their characteristics. |
| + | 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 |
| + | '''*Developmental Questions :(What discussion 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. |
| + | |
| + | ==='''Activity No 2 Angles formed when a transversal intersects parallel lines''' === |
| {| 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''' : 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. |
− | *Evaluation
| + | #Students should know the definition of complementary angles, supplementary angles, and congruent angles. |
− | *Question Corner
| + | *'''Multimedia resources''': |
− | ===Activity No # ===
| + | Laptop |
− | {| style="height:10px; float:right; align:center;"
| + | *'''Website interactives/ links/ / Geogebra Applets''' |
− | |<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;">
| + | [[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. |
− | *Estimated Time
| + | #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 . |
− | *Prerequisites/Instructions, if any
| + | #Finally the teacher and students can summarize together the angle relationships.<br> |
− | *Multimedia resources
| + | Linear pair of angles - adjacent and supplementary<br> |
− | *Website interactives/ links/ / Geogebra Applets
| + | Vertical angles - congruent<br> |
− | *Process/ Developmental Questions
| + | Corresponding angles -congruent<br> |
− | *Evaluation
| + | Alternate interior angles - congruent<br> |
− | *Question Corner
| + | 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 = |
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| 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]] |