1,122
edits
Changes
From Karnataka Open Educational Resources
no edit summary
[[File:circle.mm|flash]]
[[File:circle.mm|flash]]
=== Additional Resources[edit | edit source] ===
== Introduction ==
The following is a background literature for teachers. It summarises the things to be known to a teacher to teach this topic more effectively . This literature is meant to be a ready reference for the teacher to develop the concepts, inculcate necessary skills, and impart knowledge in Geometry - Circles from Class 6 to Class 10.
==== OER[edit | edit source] ====
The first step is to understand how to define circles and related terms using geometric vocabulary. The next step is to understand what is Pi. That it is a constant and that for any circle the ratio of the circumference by the diameter is always a constant value Pi. The interesting properties of Pi – an irrational number can also be discussed here in the basic form. Ability for the child to do simple area and perimeter calculations. Next the learner should understand that the circle is a 2 dimensional plane figure and how to visualise solid 3-dimensional figures. What are the solid shapes that have a circle as a part of them. Mensuration – more complex area measurements which include circular shapes. Surface Area and Volume measurement of sold shapes such as cylinder, sphere and cone. Understand the properties of the circles by proving theorems deductively. Also acquire the skills of deductive proofs, understand that all the properties can be deduced from the axioms. Understand the relationship between lines and circles – secant and tangent
== Additional Resources[edit | edit source] ==
=== OER[edit | edit source] ===
# Web resources :
# Web resources :
##[http://www.coolmath.com/reference/circles-geometry.html Cool math] For clear and easy definitions.
##[http://www.coolmath.com/reference/circles-geometry.html Cool math] For clear and easy definitions.
# Syllabus documents
# Syllabus documents
=== 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.mathsisfun.com/geometry/circle.html maths is fun]Here you get description of terms of circles
# Syllabus documents (CBSE, ICSE, IGCSE etc)
# 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.
* 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.
* To make students know that circle is a 2-dimensional plane circular figure.
* To elicit the difference between a bangle or a circular ring and circle as such.
* To elicit the difference between a bangle or a circular ring and circle as such.
== Teaching Outlines ==
==== Concept #1 Introduction to Circle ====
==== Concept #1 Introduction to Circle ====
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.
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.”|A discussion on “Life without circular shaped figures.”]]====
Discussion based activity to relate and assimilate circular shapes seen in our surroundings.
Discussion based activity to relate and assimilate circular shapes seen in our surroundings.
A circle is the set of all points in the plane that are a fixed distance from a fixed point.
A circle is the set of all points in the plane that are a fixed distance from a fixed point.
==== [[Is circle a Polygon ? - A debate|Is circle a Polygon ? - A debate]] ====
A polygon when increased in number of sides tends to form a circle is shown with this interesting activity.
A polygon when increased in number of sides tends to form a circle is shown with this interesting activity.
====== [[Pi the mathematical constant|Pi the mathematical constant]] ======
====== [[Pi the mathematical constant|Pi the mathematical constant]] ======
=== Concept #2 Terms associated with circles ===
===== Activities =====
===== Activities =====
Slice of a circle enclosed between any two radii is called a sector.Semicircle and quadrant are special types of sectors.
Slice of a circle enclosed between any two radii is called a sector.Semicircle and quadrant are special types of sectors.
=== Concept #3: Circles and Lines ===
===== Activities =====
===== Activities =====
A tangent is a line touching a circle in one point. A secant is the line through two distinct points on a circle.
A tangent is a line touching a circle in one point. A secant is the line through two distinct points on a circle.
=== Concept #4: Theorems and properties ===
A chord is a straight line joining 2 points on the circumference of a circle.Chords within a circle can be related in many ways.
A chord is a straight line joining 2 points on the circumference of a circle.Chords within a circle can be related in many ways.
The angle made at the centre of a circle by the radii at the end points of a chord is called the central angle or angle subtended by a chord at the centre.
The angle made at the centre of a circle by the radii at the end points of a chord is called the central angle or angle subtended by a chord at the centre.
=== Concept #5: Cyclic Quadrilateral ===
In Euclidean geometry, a '''cyclic quadrilateral''' or inscribed '''quadrilateral''' is a '''quadrilateral''' whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.
In Euclidean geometry, a '''cyclic quadrilateral''' or inscribed '''quadrilateral''' is a '''quadrilateral''' whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.
Relation between the angles of a cyclic quadrilateral are explored with this hand on activity.
Relation between the angles of a cyclic quadrilateral are explored with this hand on activity.
=== Concept #6 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.
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.
