User:Komaljerawla/sandbox

Pythagorean theorem working model
This model consists of two parts. The first part demonstrates the proof of the concept of Pythagoras theorem that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It also proves the pythagorean equation a2+b2=c2 where c is the length of the hypotenuse and a, b the length of the triangle’s other two sides. The second part shows the application of Pythagoras theorem and verifies the formula.

Part 1
Materials required: mount board, sand, three square boxes of the size of the sides of a right angle triangle, transparent sheets, glue.

Process: on a mount board draw a right angled triangle. Then draw squares on each of the sides of the triangle. Now make square boxes of the size of the sides of the triangle. Paste the square boxes on the appropriate sides of the triangle drawn on the mount board. Make small holes on all the sides of the square boxes and fill the smaller two squares with sand. Now cover this structure with a transparent sheet so that the sand does not come out.

Observation: rotate the model in such a way that the sand filled in the smaller squares gets transferred to the bigger square (hypotenuse). It can be noticed that the sand in the smaller squares fitted in perfectly in the bigger square, which means the bigger square (Hypotenuse) has the exact same area as the other two squares put together. This way the model stands as a proof of the Pythagoras theorem that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Part one of the model can be demonstrated at the introduction stage where the teacher states the Pythagoras theorem followed by its demonstration through the working model.

Part 2
Materials required: cardboard sheets, bending wire, box, string, protractor, glue, marker, scale, sand.

Process: first take a mount board and cover it with a chart paper. Make a rough line in the center of the mount board. past the protractor on the center of the mount board. Then decide on the base length from the protractor to where you want to place the lift building. With the help of a shoe box make the building of the lift. To make a lift inside the building use a small box and suspend it with a string to a pully. To make the pully/machine to help the movement of the lift upward and downward use a bending wire and a small wheel like structure. Insert the wheel in the middle of the wire and place it on the top of the building by cutting a slit. now coil the string on the wheel which is already attached to the lift. This will look and work like a pully. Connect an elastic wire from the protractor to the lift to make it look like a hypotenuse. Finally paste a measuring scale on the building of the lift to measure the height at which the lift is placed.

Observation: in this model there is a D i.e protractor and a lift which is placed at a fixed distance which forms the base length. Now as you increase the height of the lift by rotating the pully, the length of the hypotenuse will also increase. Similarly as you decrease the height of the lift the length of hypotenuse will also decrease. Hence it can be seen that the length of the hypotenuse changes with the change in the height and this change is equal to the sum of the squares of the other two sides.

Teaching plan: The teacher can introduce the concept of Pythagoras theorem by stating the theorem and then can present the part 1 of the model to prove the theorem. In the development stage the teacher can state the formula of the Pythagoras theorem followed by showing the 2nd part of the model to demonstrate the application of the theorem and verification of the formula. The teacher can move the lift at different heights by rotating the pully and ask the students to work out the hypotenuse using the formula.

Learning outcomes:
·      students are able to explain the Pythagoras theorem

·      prove the Pythagoras theorem logically

·      verify the formula

·      find the missing side of the right angle triangle