Difference between revisions of "Circles"
| Line 45: | Line 45: | ||
==== Non-OER[edit | edit source] ==== | ==== Non-OER[edit | edit source] ==== | ||
# Web resources | # Web resources | ||
| − | # | + | #*[http://www.mathsisfun.com/geometry/circle.html maths is fun]Here you get description of terms of circles |
| − | # | + | #*[http://www.scribd.com/doc/11489830/Circles-Intresting-Facts Intersting facts] this web link is full of circle facts. |
| − | # | + | #*[http://www.sparknotes.com/math/geometry1/circles/section4.rhtml sparknotes] Gives some more details about properties of circles |
| + | #*[http://www.regentsprep.org/Regents/math/geometry/GP14/PracCircleSegments.htm www.regentsprep.com] conatins good objective problems on chords and secants | ||
| + | #*[http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php www.mathwarehouse.com] contains good content on circles for different classes | ||
| + | #*[http://staff.argyll.epsb.ca/jreed/math20p/circles/tangent.htm staff.argyll] contains good simulations | ||
| + | #*This is a video showing construction of tangent at any point on a circle | ||
| + | |||
| + | {{#widget:YouTube|id=LLKFqv71i0s|left}} : This is a resource file created by Suchetha, Mathematics teacher, GJC Thyamangondlu | ||
| + | #*This is a video showing construction of tangent from external point and theorem | ||
| + | {{#widget:YouTube|id=xvXaxx1u-iA|left}} : This is a resource file created by Suchetha, Mathematics teacher, GJC Thyamangondlu | ||
| + | *** you want see the kannada videos on theorems and construction of circle [http://karnatakaeducation.org.in/KOER/index.php/%E0%B3%A7%E0%B3%A6%E0%B2%A8%E0%B3%87_%E0%B2%A4%E0%B2%B0%E0%B2%97%E0%B2%A4%E0%B2%BF%E0%B2%AF_%E0%B2%B5%E0%B3%83%E0%B2%A4%E0%B3%8D%E0%B2%A4_-_%E0%B2%B8%E0%B3%8D%E0%B2%AA%E0%B2%B0%E0%B3%8D%E0%B2%B6%E0%B2%95%E0%B2%A6_%E0%B2%97%E0%B3%81%E0%B2%A3%E0%B2%B2%E0%B2%95%E0%B3%8D%E0%B2%B7%E0%B2%A3%E0%B2%97%E0%B2%B3%E0%B3%81 click here] this is shared by Yakub koyyur GHS Nada. | ||
# Books and journals | # Books and journals | ||
# Textbooks | # Textbooks | ||
| + | ##[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter14.pdf Karnataka text book for Class 10, Chapter 14 - Chord properties] | ||
| + | ##[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter15.pdf Karnataka text book for Class 10, Chapter 15 - Tangent Properties] | ||
# Syllabus documents (CBSE, ICSE, IGCSE etc) | # Syllabus documents (CBSE, ICSE, IGCSE etc) | ||
# | # | ||
| Line 81: | Line 92: | ||
===== Activities ===== | ===== Activities ===== | ||
| − | ====== [[Centre of a circle| | + | ====== [[Centre of a circle|Centre of a circle]] ====== |
[[Radius and diameter of a circle|'''Radius and diameter of a circle''']] | [[Radius and diameter of a circle|'''Radius and diameter of a circle''']] | ||
| Line 100: | Line 111: | ||
[[Congruent circles|'''Congruent circles''']] | [[Congruent circles|'''Congruent circles''']] | ||
| − | ==== Concept #3: Theorems and properties ==== | + | ==== Concept #3: Circles and Lines ==== |
| + | |||
| + | ===== Activities ===== | ||
| + | |||
| + | ==== Concept #4: Theorems and properties ==== | ||
===== Activities ===== | ===== Activities ===== | ||
====== The longest chord passes through the centre of the circle ====== | ====== The longest chord passes through the centre of the circle ====== | ||
| + | |||
| + | ==== Concept #5: Cyclic Quadrilateral ==== | ||
| + | A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle | ||
| + | |||
| + | =====Activities===== | ||
| + | |||
| + | ====== [[Circles and lines activity 6|Cyclic quadrilateral]] ====== | ||
| + | |||
| + | ====== [[Circles and lines activity 7|Properties of cyclic quadrilateral]] ====== | ||
| + | Concept #5 Constructions in circles | ||
| + | |||
| + | The students should know that tangent is a straight line touching the circle at one and only point.They should understand that a tangent is perpendicular to the radius of the circle.The construction protocol of a tangent.Constructing a tangent to a point on the circle.Constructing tangents to a circle from external point at a given distance.A tangent that is common to two circles is called a common tangent.A common tangent with both centres on the same side of the tangent is called a direct common tangent.A common tangent with both centres on either side of the tangent is called a transverse common tangent. | ||
| + | |||
| + | ===== Activities ===== | ||
| + | |||
| + | ====== [[Circles and lines activity 4|Construction of Direct common tangent]] ====== | ||
| + | |||
| + | ====== [[Circles and lines activity 5|Construction of Transverse common tangent]] ====== | ||
=====[[Class10 circles tangents problems|Solved problems/ key questions (earlier was hints for problems).]]===== | =====[[Class10 circles tangents problems|Solved problems/ key questions (earlier was hints for problems).]]===== | ||
Revision as of 12:58, 7 May 2019
| Philosophy of Mathematics |
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Concept Map
Additional Resources[edit | edit source]
OER[edit | edit source]
- Web resources :
- maths is fun A good website on definitions for circles.
- Cool math For clear and easy definitions.
- Open reference Contains good simulations.
- Wikipedia Has good explanations on circles.
- Khan academy Has good educative videos.
- Arvind gupta toys Contains good information.
- nrich.maths.org Refer for understanding Pi.
- Books and journals
- School Geometry By Hall and Stevens. Part3 pageno 143. Contains basic definitions and proofs given by Euclid.
- Textbooks:
- Class 9 Mathematics contain simple description and theorems on circle
- CLASS 10
- Syllabus documents
Non-OER[edit | edit source]
- Web resources
- maths is funHere you get description of terms of circles
- Intersting facts this web link is full of circle facts.
- sparknotes Gives some more details about properties of circles
- www.regentsprep.com conatins good objective problems on chords and secants
- www.mathwarehouse.com contains good content on circles for different classes
- staff.argyll contains good simulations
- This is a video showing construction of tangent at any point on a circle
: This is a resource file created by Suchetha, Mathematics teacher, GJC Thyamangondlu
- This is a video showing construction of tangent from external point and theorem
: This is a resource file created by Suchetha, Mathematics teacher, GJC Thyamangondlu
- you want see the kannada videos on theorems and construction of circle click here this is shared by Yakub koyyur GHS Nada.
- Books and journals
- Textbooks
- Syllabus documents (CBSE, ICSE, IGCSE etc)
Learning Objectives
- Appreciation of circle as an important shape as it is an intrical component in the invention of almost everything that we see around us.
- To make students know that circle is a 2-dimensional plane circular figure.
- All points on its edge are equidistant from the center.
- The method of drawing a circle
- The size of the circle is defined by its radius.
- To elicit the difference between a bangle or a circular ring and circle as such.
Teaching Outlines
Concept #1 Introduction to Circle
Source: http://circlesonly.wordpress.com/tag/inventions/
Summary :
The circle is the most primitive and rudimentary of all human inventions, and at the same time, the most dynamic. It is the cornerstone in the foundation of science and technology. It is the basic tool of all engineers and designers. It is used by the greatest artists and architects in the history of mankind. Without a circular shape the wheel, pulleys, gears, ball bearings and a thousand other items we take for granted wouldn’t exist. And of course we would never have the pleasure of driving a car, riding a giant wheel, or watching the moon landing on our television set.
If you look through any old patent claim, you will most likely find the repeated use of circles, spheres, curves, arches, etc. circles are everything and they are nothing. They don’t exist in reality and yet they are the basis of all that mankind has brought into existence. That is why a circle is so fantastic.
Activities
A discussion on “Life without circular shaped figures.”
Circle as a shape
Is circle a Polygon ? - A debate
Concept #2 Basic terms
Activities
Centre of a circle
Radius and diameter of a circle
Interior and exterior of a circle
Concept #3: Circles and Lines
Activities
Concept #4: Theorems and properties
Activities
The longest chord passes through the centre of the circle
Concept #5: Cyclic Quadrilateral
A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle
Activities
Cyclic quadrilateral
Properties of cyclic quadrilateral
Concept #5 Constructions in circles
The students should know that tangent is a straight line touching the circle at one and only point.They should understand that a tangent is perpendicular to the radius of the circle.The construction protocol of a tangent.Constructing a tangent to a point on the circle.Constructing tangents to a circle from external point at a given distance.A tangent that is common to two circles is called a common tangent.A common tangent with both centres on the same side of the tangent is called a direct common tangent.A common tangent with both centres on either side of the tangent is called a transverse common tangent.
Activities
Construction of Direct common tangent
Construction of Transverse common tangent
Solved problems/ key questions (earlier was hints for problems).
Projects (can include math lab/ science lab/ language lab)
- Collect different types of circular objects
- Collect different Pie Charts.
- Collect different photographs of tools of cutting circles
- Collect different coins of circular shape
- Collect different images of medals