Mathematics

Class 8     Paper folding activity:- Exponential relationship between the number of folds We can generate the sequence of numbers 1, 2, 4, 8, 16, 32 and so on, just by folding the paper in half again each time. This means that there is an exponential relationship between the number of folds you have made and the number of areas created on the paper. Notice that if I instead fold the paper into thirds each time, the sequence changes into 1, 3, 9, 27, etc… which suggests that folding a piece of paper is a little bit like multiplication.  

                             EARTH DAY Ever wondered how Earth Day started? The first Earth Day was April 22, 1970. The idea was to raise awareness about our role in protecting our natural world. It’s hard to believe today but many people were not aware of some serious environmental issues—from air pollution to toxic dumps to pesticides to loss of wilderness.  It started out as more of a political movement, though today it was become a popular day for many communities to clean up litter, plant trees, or simply reflect on nature. Nature’s gifts to our planet are the millions of species that we know and love, and many more that remain to be discovered. Unfortunately, human beings have irrevocably upset the balance of nature and, as a result, the world is facing the greatest rate of extinction since we lost the dinosaurs more than 60 million years ago. But unlike the fate of the dinosaurs, the rapid extinction of species in our world today is the result of human activity.

Sieve of Eratosthenes                             Class VI A  prime number  is a  natural number  that has exactly two distinct natural number  divisors :  1  and itself. The sieve of Eratosthenes is one of the most efficient ways to find all primes smaller than n when n is smaller than 10 million. https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif

Sieve of Eratosthenes                             Class VII A  prime number  is a  natural number  that has exactly two distinct natural number  divisors :  1  and itself. The sieve of Eratosthenes is one of the most efficient ways to find all primes smaller than n when n is smaller than 10 million. https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif Following is the algorithm to find all the prime numbers less than or equal to a given integer  n  by Eratosthenes’ method: 1.     Create a list of consecutive integers from 2 to  n : (2, 3, 4, …,  n ). 2.     Initially, let  p  equal 2, the first prime number. 3.     Starting from  p 2 , count up in increments of  p  and mark each of these numbers greater than or equal to  p 2  itself in the list. These numbers will be  p(p+1) ,  p(p+2) ,  p(p+3) , etc.. 4.     Find the first number greater than  p  in the list that is not marked. If there was no such number, stop. Otherwise