Activity Visualising formula for area of a circle

This is a photo story describing an activity to viaualise the formula for area of a circle by paper cutting and pasting . This activity is based on transforming one figure into another and then calculating the area.

General point on x-axis/y-axis

This video is created for visualising the concept of a general point on x -axis/y-axis.

To multiply a number by 11

This video explains a short cut method to multiply a number by 11.

Squaring a number ending with 5

Learning Vedic Mathematics short cut methods is a useful way for improving  mental mathematics ability of children.

By watching the given video you can learn a short cut method to find the square of a number ending with 5 using the sutra

This means "By one more than the previous one".

I am sharing one example how this sutra is applied?
65^2= [6 X (6+1)] 25 = 4225
For this number , the last digit is 5 and the 'previous' digit is 6. Hence, 'one more than the previous one', that is, 6+1=7.
The Sutra, in this context, gives the procedure 'to multiply the previous digit 6 by one more than itself, that is, by 7'. It becomes the L.H.S of the result, that is, 6 X 7 = 42.
The R.H.S of the result 25..

To multiply two numbers nearing 100

This is a video which has been prepared using an open source screen capturing software Cam Studio.
Aim: To learn how to multiply two numbers nearing 100 by a shortcut method.
Utility: These kinds of tricks develop a skill of oral calculations and helps in saving students time in various competetive examinations.It instill confidence in students that they can do mathematics thus helps in removing a fear for learning mathematics.

square root spiral

Aim Making a square root spiral.
Hint: Begin with an isosceles right triangle.

comparing volumes

Aim
To compare volumes of two cylinders made out of two rectangular sheets having same dimensions.

Material Required
Coloured Paper, Cello tape, A pair of scissors, rice(some material )

Procedure
step 1 Take two rectangular sheets of paper of same dimension.


Step 2 Gently curve the first one along its length and put a cello tape.


Step 3 Find the radius of the base circle using 2*Pi*r = breadth. Cut the circle and paste it on the base of the cylinder.

Step 4 Repeat the process, by taking the 2nd rectangular sheet and curving it along its breadth.
Step 5. Fill the two cylinders with grains and pour it in the same container one by one.

Step 6 What do you observe?

Step 7 Calculate the volume of two such cylinders which are made out of rectangular sheets each of dimension 22cm X 10 cm.

Write the result.

Extended activity

What can you say about their curved surface areas and total surface areas?

Are they same or different?

angles in the same segment

Aim By paper cutting and pasting verify that angles in the same segment of a circle are equal.

Material required
coloured paper, a pair of scissors, geometry box, fevistick, carbon paper.

Procedure
step 1 Draw a circle of any radius with centre O on a coloured paper and cut it.
step 2 Take a rectangular sheet of paper and paste the circle cut out on it.
step 3 Fold the circle in anyway to get a chord. Name the chord as AB.
step 4 Take two points P and Q in the same segment.
step 5 Form a crease joining AP and draw AP.
step 6 Form a crease joining BP and draw BP.
step 7 Form a crease joining AQ and draw AQ.
step 8 Form a crease joining BQ and draw BQ.
step 9 Make replicas of angle AQB and angle APB using carbon paper.
step 10 Place the two replicas on each other.

Observations
1. angle APB and angle AQB are angles in the same segment of the circle.
2. angle APB = angle AQB.

Result
angle APB = angle AQB
ANGLES IN THE SAME SEGMENT OF A CIRCLE ARE EQUAL.

angle subtended by an arc

Aim By paper cutting and pasting verify that angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any other point on the remaining part of the circle.



Material required
coloured paper, a pair of scissors, geometry box, fevistick, carbon paper.



Procedure
step 1 Draw a circle of any radius with centre O on a coloured paper and cut it.
step 2 Take a rectangular sheet of paper and paste the circle cut out on it.

step 3 Mark two points A and B on the circle to get arc AB.

step 4 Form a crease joining OA and draw OA.

step 5 Form a crease joining OB and draw OB.

step 6 Take a point C on the remaining part of the circle.

step 7 Form a crease joining AC and draw AC.

step 8 Form a crease joining BC and draw BC.

step 9 Make two replicas of angle ACB using carbon paper.

step 10 Place the two replicas of angle ACB adjacent to each other on angle AOB.


Observations

1. Arc AB subtends angle AOB at the centre and angle ACB at the point C on the remaining part of the circle.

2. Two replicas of angle ACB completely cover angle AOB.

Result

angle AOB = 2 (angle ACB)

Thus its is verified that "angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any other point on the remaining part of the circle."

area of a circle

Dear students ,
Watch this video and do the activity.



Aim
To find the area of a circle of given radius by paper folding,cutting and pasting.

Material Required
Coloured Paper
Pair of scissors
Fevistick/glue
Geometry Box

Method
Step 1 Cut a circle of given radius from the coloured paper.
Step 2 Divide the circle into 16 equal parts by paper folding.
Step 3 Cut 16 parts and arrange them to form a parallelogram.
Step 4 Take the last cutout and again divide it into 2 equal parts.
Step 5 Arrange the 2 parts and the shape in step 3 so that a rectangle is formed.
Step 6 Measure the length & breadth of the rectangle & calculate its area.

Observation
We observe that the cutouts of the circle are arranged to form a rectangle.
The length of the rectangle is equal to half of the circumference of the circle and breadth of the rectangle is equal to the radius of the circle.
The area of the circle is calculated using the formula of area of the rectangle.

Result
Length of Rectangle =____________________
Breadth of Rectangle=___________________
Area of Rectangle = ___________________

So, the Area of Circle = _________________