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Measurements in circles (view source)
Revision as of 11:05, 6 December 2013
, 11:05, 6 December 2013→Activity No # 2. Angles in a circle.
*Question Corner:
*Question Corner:
# Recall the theorems related to angles in a circle.
# Recall the theorems related to angles in a circle.
*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.
==Concept # 4. Finding the Circumference of a circle==
===Learning objectives===
# The children understand that the distance around the edge of a circle is known as circumference.
# The children learn to measure the circumference of the circle.
# Derivation of formula for circumference.
# They understand what is pi.
===Notes for teachers===
The circumference of a circle relates to one of the most important mathematical constants in all of mathematics. This constant pi, is represented by the Greek letter П. The numerical value of π is 3.14159 26535 89793 , and is defined by the ratio of a circle's circumference to its diameter.
C = п. D or C = 2пr.
===Activity No # 1 Derivation of formula for circumference and the value for pi.===
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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
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*Estimated Time : 45 mins
*Materials/ Resources needed:
Note books, compass, pencil, mender, scale.
*Prerequisites/Instructions, if any:
# The children should have prior knowledge of circle, radius, diameter and circumference.
# They should have measuring and computational skills.
*Multimedia resources:
*Website interactives/ links/ / Geogebra Applets
*Process:
#Ask the children to draw five circles with different radii.
# Let them carefully measure their circumferences using wool.
# Mark the distance around the circle on the wool with a sketch pen.
# Measure the length of the measured wool using a scale.
# Make a table with columns radius, diameter and circumference
# For every circle find Circumference / diameter.
# Round C/d to two decimal places.
# Observe the answers in each case. It would be aprroximately 3.14 .
# The value 3.14 is the value of pi which is constant.
C/d = п or C = п d or C = 2п r.
*Developmental Questions:
# Have you noted down radius, diameter and their respective circumferences.
# Check if your calculations are correct.
# What do you infer from the observed results ?
*Evaluation:
# Are the children taking correct measurements.
# Are they comparing the results of C/d with all circles.
# Are they noticing that it is constant .
# Are they questioning why it is constant?
*Question Corner:
# How do you derive the formula for circumference of a circle ?
# What is the name of that constant ?
# Try to collect more information on Pi.
= Hints for difficult problems =
= Hints for difficult problems =