# Welcome to Planet Infinity KHMS

## 06 December, 2007

### Activity Formula for area of a parallelogram

Aim By paper cutting and pasting derive the formula for area of a paralleogram.

Material required
Coloured paper, pair of scissors, glue, geometry box, dotted paper.

Procedure
Watch this slide show and do the activity.

### Diagonal of a parallelogram

Aim :
By paper cutting/pasting verify "diagonal of a paralleogram divides it into two triangles of equal areas.
Material Required:
Dotted paper, ruler,sketch pen, pair of scissors
Procedure:
Step 1 Draw a parallelogram ABCD on a dotted paper.

Step 2 Join diagonal AC.

Step 3 Cut the parallelogram.
Step 4 Cut along the diagonal AC.
Step 5 Place triangle ABC on triangle ADB such that AD coincides with BC, AB coincides with CD
Step 6 Repeat the activity for the other diagonal

Observations:
1.Triangle ABC completely covers triangle CDA.
Result:Diagonal of a parallelogram divides it into two triangles of equal areas.

### Group activity -percentage/graph

Aim :
To find the percentage of the students in a group of students who write faster with their left/right hand.

Material Required:
paper, pen,graph paper,geometry box

Procedure:
Step 1 :Take a paper and a pen.
Step 2 :Write a letter (say a) or a digit (say 2) for 30 seconds with your right hand.
Step 3 :Repeat the activity for same duration with left hand.
Step 4 :Record the data as follows:

Sr. No. Roll No. No. Of letters written with right hand (x) No. Of letters written with left hand (y)
.
.
.
.
.
.
.
.
.

Step 5: Take the number of digits/letters written with right hand as x and the number of digits/letters written with left hand as y.
Step 6 :Plot the co-ordinates (x, y) for every student.
Step 7:Draw the line x = y on the graph paper.
Step 8 :From the graph, count the number of points which are below the line x = y and the number of points which are above the line x = y.

Observation
When x>y, students write faster with right hand.
When x

### Activity Sum of first n natural numbers

Aim : To verify that the sum of first n natural numbers is n (n + 1) / 2, i.e. Σ n = n (n + 1) / 2, by graphical method. Material Required : Coloured paper,squared paper, sketch pen ,ruler Procedure: Let us consider the sum of natural numbers say from 1 to 10, i.e. 1 + 2 + 3 + … + 9 + 10. Here n = 10 and n + 1 = 11. 1. Take a squared paper of size 10 × 11 squares and paste it on a chart paper. 2. On the left side vertical line, mark the squares by 1, 2, 3, … 10 and on the horizontal line, mark the squares by 1, 2, 3 …. 11. 3. With the help of sketch pen, shade rectangles of length equal to 1 cm, 2 cm, …, 10cm and of 1 cm width each.

Observations: The shaded area is one half of the whole area of the squared paper taken. To see this, cut the shaded portion and place it on the remaining part of the grid. It is observed that it completely covers the grid. Area of the whole squared paper is 10 × 11 cm2

Area of the shaded portion is (10 × 11) / 2 cm2

This verifies that, for n = 10, Σ n = n × (n + 1) / 2 The same verification can be done for any other value of n.

Answer the following after doing this activity:

1. What is the sum of first 50 natural numbers?

2. What is the sum of natural numbers between 60 and 80?

3. What is the sum of first 100 multiples of 4?

4. What is the sum of first 60 multiples of 9?

### Sum of areas of 3 sectors of same radii

Aim:
By paper cutting and pasting, verify that the sum of areas of three sectors of same radius “r” formed at the vertices (as center) of any triangle is (Pi x r ^2)/2.

Material Required
Coloured paper, pair of scissors, glue, geometry box.

Procedure
Step 1 Draw an equilateral triangle ABC on a coloured paper and cut it.
Step 2 With suitable radius, draw three sectors on the three vertices.
Step 3 Cut the three sectors.
Step 4 Draw a straight line and place the three sector cut outs adjacent to each other on it.
Step 5 Write the observations.
Step 6 Repeat the activity for two more triangles other than equilateral triangle.
Step 7 Write the observations

Observations
1. When sector cut outs are placed on a straight line, they completely cover the straight angle. So their sum is 180 degrees.
2. The three sectors cut outs placed on a straight-line form a semicircle.
3. The area of semicircle is Pi x r^2 /2.

## 04 December, 2007

### parallelogram by paper folding

Aim
To make a parallelogram by paper folding

Material Required
Coloured paper, Pencil

Procedure
Step 1:Take a rectangular sheet of paper and fold it parallel to the breadth at a convenient distance. Mark the crease obtained as "1".

Step 2: Obtain a crease perpendicular to crease "1" at any point .

Name the crease as crease "2".

Step 3:Obtain a crease perpendicular to crease "2"

and mark the new crease as crease "3".
Step 4:Observe crease "1" and crease "3" (They are parallel).
Step 5:Make a fold cutting the crease "1" and crease "3".
And name this new crease formed as "4".
Step 6:Following the same procedure used for getting a pair of parallel lines , get a fold parallel to crease "4". And name it as crease "5".
Step 7:Mark the parallelogram obtained.

Observations:
(1)-Crease "1"is parallel to crease "3".
(2)Crease "4" is parallel to crease "5".