Changes

5,990 bytes removed , 16:02, 17 May 2017

m

Text replacement - "</mm>" to ""

Line 1: Line 1: −

~~<mm>~~[[Measurements in circles.mm|flash]]~~</mm>~~

+

[[File:Measurements in circles.mm|flash]]

−

= ~~Textbook~~ =

+

==Concept # Measurements in circles: 1. Radius and Diameter ==

−

~~==ncert books==~~

−

~~[http://ncert.nic.in/NCERTS/textbook/textbook.htm?iemh1=10-15 Class 9 Mathematics] contain simple description and theorems on circles.~~

−

~~[http://ncert.nic.in/NCERTS/textbook/textbook.htm?jemh1=10-14Class 9 Mathematics] contain higher level description and theorems on circles.~~

−

~~=Additional Information=~~

−

~~==Useful websites==~~

−

#~~[http://www.mathsisfun.com/geometry/circle.html maths is fun] A GOOD WEBSITE ON DEFINITIONS FOR CIRCLES~~

−

~~#[http://www.coolmath.com/reference/circles-geometry.html COOL MATH] GIVES CLEAR AND EASY DEFINITIONS~~

−

~~#[http://www.mathopenref.com/circle.html OPEN REFERENCE] CONTAINS FEW SIMULATIONS~~

−

~~#[http://en.wikipedia.org/wiki/Math_circle#History WIKIPEDIA] CONTAINS EXPLANATIONS FOR CIRCLES~~

−

~~#[http://www.khanacademy.org KHAN ACADEMY] CONTAIN GOOD VIDEOS~~

−

~~#[http://www.arvindguptatoys.com ARVIND GUPTA TOYS] CONTAIN VERY GOOD BOOKS ON MATHEMATICS AND SCIENCE~~

−

~~#[http://nrich.maths.org/2490 nrich.maths.org] Contain very good description of Pie~~

−

~~==Reference Books==~~

−

~~#[http://archive.org/stream/schoolgeometry00hall#page/n11/mode/2up School Geometry] By Hall and Stevens. Part3 pageno 143. Contains basic definitions and proofs given by Euclid.~~

−

~~=Notes for teachers =~~

−

~~Introduction:~~

−

~~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.<br>

−

~~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.~~

−

~~===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.~~

−

~~[[File~~:~~circle.gif]]~~

−

~~===Activity No #~~ 1. ~~A discussion on “Life without wheels / circular shaped figures.”===~~

−

~~{| 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: 45 minutes

−

*Materials/ Resources needed: Paper, pen

−

*Prerequisites/Instructions, if any:

−

~~Previous day homework :~~

−

~~# Ask the children to make a list of all circular objects that they can think of :~~

−

~~# List as many devices as you can think of that depend on the wheel.(Consider objects in your home, at school, games and toys, machines, vehicles and engines as you make your list.)~~

−

# Now imagine living in a world without any kind of wheels or rolling devices. How would life be different? Would it be harder? How and why? Describe what it would be like to live without any wheels.

−

*Multimedia resources

−

*Website interactives/ links/ / Geogebra Applets

−

*Process:(How to do the activity)

−

~~Have an open discussion with children. Initially let the children share their ideas~~ and do most of the talking. Ensure that the intended discussion remains within the context. Make a mind map on blackboard of all relavant points discussed . Let them appreciate the significance of circular shape thus setting the stage for further study of this fantastic shape called “circles”.

−

*Developmental Questions :(What discussion questions)

−

~~# What all shapes do we see around us ?~~

−

~~# Can you imagine bicycles and your other vehicles without circular wheels ?~~

−

~~# How different life would have been if wheel was not disovered ?~~

−

~~# How could we explain centrifugal force ?~~

−

~~# What about potter's wheel and stone mill?~~

−

~~# Do you think that it is necessary for us to study and understand the parameters of circle in depth and detail ?~~

−

*Evaluation:

−

~~# Do you all now agree that wheel is one of the greatest inventions of mankind? Justify~~

−

*Question Corner:

−

~~# Are shapes important ? How?~~

−

~~# Is bangle a circle ?~~

−

~~# Would it be possible to understand pi without understanding circles ?~~

−

~~==Concept # Measurements in circles~~ ==

===Learning objectives===

−

# ~~The students should learn~~ to measure radius, diameter, circumference, chord length and angles subtended at the centre and on the circumference of the circle.

+

# Ability to measure radius, diameter, circumference, chord length and angles subtended at the centre and on the circumference of the circle.

−

# ~~The students should understand that radius~~, diameter and chord lengths are linear measurements.

+

# Radius, diameter and chord lengths are linear measurements.

−

# ~~They should learn to relate~~ the size of the circle with radius.

+

# Relate the size of the circle with radius.

# They realise that to draw a circle knowing the measure of radius or diameter is essential.

# There can be infinite radii in a circle.

Line 78: Line 11:

# Chords of different lengths can be drawn in a circle.

# Chord length can be measured using a scale and its units is cm.

−

# ~~They should know that the~~ length of the chord increases as it moves closer to the diameter.

+

# The length of the chord increases as it moves closer to the diameter.

# The longest chord in the circle is its diameter.

# Distance of chord from the centre is its perpendicular distance from the centre.

Line 90: Line 23:

{| 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>

+

''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>

|}

*Estimated Time: 15 mins

Line 97: Line 30:

#students' geometry box

*Prerequisites/Instructions, if any:

−

# ~~Children should have the knowledge of circle, centre, radius, diameter~~ and ~~circumference.~~

+

# Circle and its basic parts should have been done.

−

~~# The teacher~~ should have ~~the necessary skill of using geogebra tool~~.

*Multimedia resources: Laptop

−

*Website interactives/ links/ / Geogebra Applets

+

*Website interactives/ links/ / Geogebra Applets : This file was done by ITfC-Edu-Team.

<ggb_applet width="1280" height="572" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="false" />

*Process:

Line 109: Line 41:

# Given diameter, radius = D/2.

# Also the other way i.e. If a circle is given, then its radius can be measured by using scale which is the linear distance between centre of the circle and any point on the circumference.

−

#To ~~measur~~ diameter, measure the length of that chord which passes through the centre of the circle.

+

# To measure diameter, measure the length of that chord which passes through the centre of the circle.

Then she can project the digital tool 'geogebra.' and further clarify concepts.

−

*Developmental Questions:

# Name the centre of the circle.

Line 132: Line 63:

{| 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>

+

''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>

|}

*Estimated Time : 10 minutes

Line 138: Line 69:

Laptop, geogebra file, projector and a pointer.

*Prerequisites/Instructions, if any:

−

~~# The students should have prior knowledge of circle, radius , diameter and circumference..~~

−

~~# The teacher should have knowledge of using geogebra.~~

*Multimedia resources:

Laptop, geogebra file, projector and a pointer.

Line 145: Line 74:

<ggb_applet width="1278" height="571" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />

*Process:

−

# ~~The teacher can review the concept of a circle , radius , diameter and circumference .~~

+

# Show the geogebra file and ask the following questions.

−

~~# Any two points on the circumference can be joined.~~

−

~~# The joining line segment is called the chord.~~

−

~~# Let the students name the chord .~~

−

~~# Move the chord on~~ the geogebra and ~~let them observe its changing size.~~

−

~~# Let them observe the chord becoming a diameter while passing through the centre of the circle.~~

−

~~# The length of~~ the ~~chord is measued using a scale with its unit being cm~~.

*Developmental Questions:

# The teacher can point to centre of circle and ask the students as to what it is.

Line 161: Line 84:

# How do you measure a chord and in what units ?

*Evaluation:

−

Were the students able to distinguish between radius, diameter and chord ?

+

# Were the students able to distinguish between radius, diameter and chord ?

*Question Corner:

−

After drawing a chord,what are the two segregated parts of the circle called ?

+

3 After drawing a chord,what are the two segregated parts of the circle called ?

−

==Concept # 3 Angles in circles==

+

==Concept # 2. Angles in circles==

===Learning objectives===

# students should understand that the angle at the centre of the circle is 360 degrees.

Line 172: Line 95:

{| 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>

+

''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>

|}

−

*Estimated Time :40 minutes

+

*Estimated Time : 40 minutes

−

*Materials/ Resources needed :Laptop, geogebra file, projector and a pointer.

+

*Materials/ Resources needed : Laptop, geogebra file, projector and a pointer.

*Prerequisites/Instructions, if any

−

# ~~The students~~ should have ~~prior knowledge of a circle and circumference.~~

+

# Circles and its parts should have been done.

−

~~# They should know that an arc is a curved line along the circumference of a circle.~~

−

~~# If the end points of an arc are joined to a third point on the circumference of a circle, then an angle on the circumference is formed.~~

−

~~# If the end points of an arc are joined to the centre of a circle, then an angle at the centre of the circle is formed.~~

−

~~# They should know to measure the angles~~.

*Multimedia resources: Laptop and a projector.

*Website interactives/ links/ / Geogebra Applets

<ggb_applet width="1280" height="600" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />

*Process:

−

# ~~The teacher should initially discuss about~~ the ~~circle , radius, centre and circumference.~~

+

# Project the geogebra file and ask the questions listed below.

−

~~# Projecting~~ geogebra file ~~she can show the major and the minor arcs.~~

−

~~# Name the arc in discussion.~~

−

~~# Let students find out and name the angle subtended by the arc at the centre and angle subtended by the same arc on the circumference.~~

−

~~# Observe that the end points of the arc lie on the angle.~~

−

~~# Each side of the angle contains at least one end -point of the arc.~~

−

~~# Project different angles subtended by the same arc on the circumference. What is the inference ?~~

−

~~# Compare angle formed at the centre~~ and ~~angle formed on the circumference by the same arc.~~

−

~~# Change the angles/arc using slider. Note down~~ the ~~two angles in each case.~~

−

~~# Ask students what they observed ? Let them infer~~.

*Developmental Questions:

# Name the centre of the circle?

Line 220: Line 130:

{| 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>

+

''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>

|}

*Estimated Time: 40 minutes

*Materials/ Resources needed:Laptop, projector, geogebra file and a pointer.

*Prerequisites/Instructions, if any

−

#~~The students should have prior knowledge~~ of a circle, angles, arcs and segments.

+

# Knowledge of a circle, angles, arcs and segments.

−

#~~The students should have a thorough knowledge about~~ the types of angles.

+

# About the types of angles.

−

#~~They should have the skill~~ of drawing a circle , angles and measuring them.

+

# Skill of drawing a circle , angles and measuring them.

*Multimedia resources : Laptop, Projector.

−

*Website interactives/ links/ / Geogebra Applets

+

*Website interactives/ links/ / Geogebra Applets: This file has been done by Mallikarjun Sudi of Yadgir.

<ggb_applet width="1280" height="600" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />

+

*Process:

+

# The teacher can recall the concept of circle, arc segment.

+

# She can then project the geogebra file , change slider and make clear the theorems about angles in a circle.

+

Developmental Questions:

+

# Name the minor and major segments.

+

# Name the angles formed by them.

+

# Where are the two angles subtended ?

+

# What is the relation between the two angles.

+

# Name the major and minor arcs.

+

# What is an acute angle?

+

# What is an obtuse angle?

+

# What type of angles are formed by minor arc ?

+

# What type of angles are formed by major arc ?

+

# What are your conclusions ?

+

*Evaluation:

+

# How many angles can a segment subtend on the circumference ?

+

# What can you say about these angles ?

+

*Question Corner:

+

# Recall the theorems related to angles in a circle.

*Process:

# The teacher can recall the concept of circle, arc segment.

Line 251: Line 180:

# Recall the theorems related to angles in a circle.

−

==Concept # 4. Finding the Circumference of a circle==

+

==Concept # 3. Finding the Circumference of a circle==

===Learning objectives===

# The children understand that the distance around the edge of a circle is known as circumference.

Line 264: Line 193:

{| 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>

+

''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>

|}

*Estimated Time : 45 mins

Line 270: Line 199:

Note books, compass, pencil, mender, scale.

*Prerequisites/Instructions, if any:

−

# ~~The children~~ should have ~~prior knowledge of circle, radius, diameter and circumference.~~

+

# Circles basics should have been done.

−

~~# They should have measuring and computational skills~~.

*Multimedia resources:

*Website interactives/ links/ / Geogebra Applets

Line 299: Line 227:

# Try to collect more information on Pi.

−

==Concept # 5 Finding the area of a circle.==

+

==Concept # 4. Finding the area of a circle.==

===Learning objectives===

# The child should understand that the area of a circle is the entire planar surface.

Line 313: Line 241:

{| 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>

+

''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>

|}

*Estimated Time:90 mins

Line 339: Line 267:

{| 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>

+

''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>

|}

*Estimated Time: 45mins

Line 347: Line 275:

Prior knowledge of circle, radius, square and area of square.

*Multimedia resources: Laptop.

−

*Website interactives/ links/ / Geogebra Applets

+

*Website interactives/ links/ / Geogebra Applets: This file was done by Bindu.

<ggb_applet width="1280" height="600" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />

*Process:

KOER admin

Bureaucrats, oversight, Administrators

1,823

edits

Changes

Measurements in circles (view source)

Revision as of 16:02, 17 May 2017

Navigation menu

Search