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Measurements in circles (view source)
Revision as of 16:35, 6 December 2013
, 16:35, 6 December 2013→Activity No # 2. Angles in a circle.
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*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.===
+{| 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 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 =