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− | === Concept Map === | + | <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;"> |
| + | ''[https://karnatakaeducation.org.in/KOER/index.php/%E0%B2%B0%E0%B3%87%E0%B2%96%E0%B3%86%E0%B2%97%E0%B2%B3%E0%B3%81_%E0%B2%AE%E0%B2%A4%E0%B3%8D%E0%B2%A4%E0%B3%81_%E0%B2%95%E0%B3%8B%E0%B2%A8%E0%B2%97%E0%B2%B3%E0%B3%81 ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div> |
| + | <!-- This portal was created using subst:box portal skeleton --> |
| + | <!-- BANNER ACROSS TOP OF PAGE --> |
| + | {| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;" |
| + | |- |
| + | | 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=== |
| + | [[File:Lines_and_Angles.mm|flash]] |
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| === Additional Resources === | | === Additional Resources === |
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| * Web resources: | | * Web resources: |
| ** [https://www.ck12.org/geometry/parallel-and-skew-lines/lesson/Parallel-and-Skew-Lines-BSC-GEOM/ CK12] - This website gives basic facts about parallel lines with examples and review questions. | | ** [https://www.ck12.org/geometry/parallel-and-skew-lines/lesson/Parallel-and-Skew-Lines-BSC-GEOM/ CK12] - This website gives basic facts about parallel lines with examples and review questions. |
| + | ** [https://www.education.com/lesson-plan/angles-and-lines/ Education.com] - An exemplar for a lesson plan for lines and angles is on the web site. |
| + | ** [https://www.projectmaths.ie/documents/T&L/IntroductionToAngles.pdf Project Maths] - A detailed lesson plan for the topic is available in pdf format. |
| + | ** [https://teachers.net/lessons/posts/3404.html Teachers.net] - An exemplar for discussion based approach for to introduce lines and angles is shown. |
| + | ** [http://www.cpalms.org/Public/PreviewResourceLesson/Preview/73308 CLAMS] - This is an interactive lesson exploring Parallel and Perpendicular lines. |
| + | ** [https://www.ck12.org/geometry/parallel-and-skew-lines/lesson/Parallel-and-Skew-Lines-BSC-GEOM/ CK – 12] - Basic facts of parallel lines are discussed and introduced. |
| + | ** [http://jsuniltutorial.weebly.com/uploads/7/8/7/0/7870542/9th_geometry_mock_test_paper.pdf JsunilTutorial] - Worksheet for the chapter can be downloaded. |
| *Books and journals | | *Books and journals |
| *Textbooks | | *Textbooks |
− | ** NCERT Textbooks – [http://ncert.nic.in/textbook/textbook.htm?iemh1=7-15][http://ncert.nic.in/textbook/textbook.htm?iemh1=6-15 Class] 9 | + | **Karnataka Govt Text book – Class 8 : [http://ktbs.kar.nic.in/New/website%20textbooks/class8/8th-english-maths-1.pdf Part 1] , [http://ktbs.kar.nic.in/New/website%20textbooks/class8/8th-kannada-maths-2.pdf Part 2] |
| *Syllabus documents | | *Syllabus documents |
| + | *YouTube Videos |
| + | Watch Video on Vertical Opposite angles and Pair of Linear Equations |
| + | |
| + | {{#widget:YouTube|id=BRtNvXpZW6Y}} {{#widget:YouTube|id=cUvL-tdRRDo}} |
| + | |
| + | Watch video on parallel lines and transversal |
| + | |
| + | {{#widget:YouTube|id=fo7EF2NNaak}} |
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| === Learning Objectives === | | === Learning Objectives === |
− | What are the students expected to understand/ learn from this topic. These can drive from the large concept map and should be listed at the concept level.
| + | * Introducing lines and line segments |
| + | * Understanding formation of angles and their types |
| + | * Differentiating parallel lines and skew lines |
| + | * Recognizing angles pairs of angles formed in parallel lines |
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| === Teaching Outlines === | | === Teaching Outlines === |
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− | ==== Concept 1: What are angles? ==== | + | ==== Concept 1: Angles ==== |
− | Briefly describe the concept (2-3 sentences)
| + | An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. angles can be classified according to the size of the angle. |
| | | |
| ===== Activities ===== | | ===== Activities ===== |
| + | [[Paper Folding Activity- Lines and Angles|Paper Folding Activity]] |
| | | |
| ====== [[Introducing formation of angle]] ====== | | ====== [[Introducing formation of angle]] ====== |
| + | The standard angle concept based on the relative inclination of two lines meeting at a point irrespective of length of arms is discussed in an exploratory method. |
| | | |
| ====== [[Types of angles]] ====== | | ====== [[Types of angles]] ====== |
| + | We will learn the following types of angles: right angles, acute angles, obtuse angles, straight angles, reflex angles and complete angle. |
| | | |
− | ====== Concept 2: Pairs of angles ======
| + | ==== Concept 2: Pairs of angles ==== |
| + | In geometry, certain pairs of angles can have special relationships. Some examples are complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, corresponding angles and adjacent angles. |
| + | |
| + | ===== Activities ===== |
| + | |
| + | ====== [[Intersection of two lines]] ====== |
| | | |
| ====== [[Adjacent angles]] ====== | | ====== [[Adjacent angles]] ====== |
| + | Adjacent angles are two angles that have a common vertex and a common side. The vertex of an angle is the endpoint of the rays that form the sides of the angle. |
| | | |
| ====== [[Complementary angles]] ====== | | ====== [[Complementary angles]] ====== |
| + | Complementary angles are two angles with a sum of 90°. A common case is when they form a right angle. |
| | | |
| ====== [[Supplementary angles]] ====== | | ====== [[Supplementary angles]] ====== |
| + | Supplementary angles are two angles with a sum of 180°. A common case is when they lie on the same side of a straight line. |
| | | |
| ====== [[Vertically opposite angles]] ====== | | ====== [[Vertically opposite angles]] ====== |
| + | When two straight lines intersect each other four angles are formed.The pair of angles which lie on the opposite sides of the point of intersection are vertically opposite angles. |
| | | |
| ====== [[Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180 degrees|Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180<sup>o</sup>]] ====== | | ====== [[Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180 degrees|Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180<sup>o</sup>]] ====== |
| + | Two adjacent angles are said to be form a linear pair of angles, if their non-common arms are two opposite rays. Linear pair axiom of theorems are if a ray stands on a line , then the sum of two adjacent angles so formed is 180 degree |
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| ====== [[Linear pair axiom : If the sum of two adjacent angles is 180 degrees, then the non-common arms of the angles form a line|Linear pair axiom : If the sum of two adjacent angles is 180<sup>o</sup>, then the non-common arms of the angles form a line]] ====== | | ====== [[Linear pair axiom : If the sum of two adjacent angles is 180 degrees, then the non-common arms of the angles form a line|Linear pair axiom : If the sum of two adjacent angles is 180<sup>o</sup>, then the non-common arms of the angles form a line]] ====== |
| | | |
− | ==== Concept 3: '''Parallel lines''' ==== | + | ==== Concept 3: Parallel lines ==== |
| + | Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. |
| + | |
| + | ===== Activities ===== |
| | | |
| ====== [[Introducing parallel lines|Introducing parallel lines]] ====== | | ====== [[Introducing parallel lines|Introducing parallel lines]] ====== |
| + | Parallel lines are lines that are always the same distance apart. Because they are always the same distance from one another, parallel lines will never intersect. |
| + | |
| + | ====== [[Parallel lines 1|Parallel lines activity1]] ====== |
| | | |
| ====== [[Angles associated with parallel lines]] ====== | | ====== [[Angles associated with parallel lines]] ====== |
| + | Two parallel lines are cut by a transversal the angles formed are alternate angles, corresponding angles co-interior angles and vertically opposite angles. |
| | | |
| ====== [[Parallel lines|Parallel lines and measures of angles formed]] ====== | | ====== [[Parallel lines|Parallel lines and measures of angles formed]] ====== |
| + | Relation between angles that are formed in multiple parallel lines is investigated with geogebra sketch. |
| + | |
| ===== Solved problems/ key questions (earlier was hints for problems). ===== | | ===== Solved problems/ key questions (earlier was hints for problems). ===== |
− | (This will be directly correlated to the textbook so that teacher gets what they may be looking for but we must have additional questions which are sourced from other resources)
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| === Projects (can include math lab/ science lab/ language lab) === | | === Projects (can include math lab/ science lab/ language lab) === |
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| === Assessments - question banks, formative assessment activities and summative assessment activities === | | === Assessments - question banks, formative assessment activities and summative assessment activities === |
| Categories will be: (Subject), (Topic), (Class 8), (Class 9), (Class 9), (Concept Map), (Question banks), (Assessments), Formative, Summative | | Categories will be: (Subject), (Topic), (Class 8), (Class 9), (Class 9), (Concept Map), (Question banks), (Assessments), Formative, Summative |
| + | |
| + | [[Category:Class 9]] |
| + | [[Category:Lines and Angles]] |
| + | [[Category:Class 8]] |
| + | [[Category:Class 10]] |