I have the feeling that these posts don’t need any introduction anymore. Hopefully you got used to them so far, but if you are new to the blog take a look at part 1, part 2, part 3 and part 4. For today I thought I will share one of those good lessons I had in my first weeks of teaching.
I was doing the chapter on factors and multiples with S1 (11 years) and the lesson was about introducing the prime numbers, they already had a lesson on factors so I could use this concept freely. I started the lesson explaining to them we a doing a couple of activities (puzzles) to find out different properties about numbers. With this introduction I went straight to a small activity about finding numbers with a specific number of factors. I didn’t do anything especially fancy, I just had this slide on the board, but the questions can be asked freely if you want:
We went through as many examples as possible in around 5 – 10 minutes as explaining what a factors was and proving the numbers actually have that specific number of factors. With this we went to the next puzzles which was the Sieve of Eratosthenes. For those of you that don’t know the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the multiples of 2. The worksheet explained the algorithm and also had a couple of questions at the end.
So after they completed the sieve as above, they had to answer the following questions: what did the algorithm help us found? what is the connection with the examples we have done previously? They got quite excited at this moment and I told them that all of these are the prime numbers. Together, we made a definition for them and discussed the problem with 1. Then I had a discussion on how hard they thought it is to find prime numbers and how many prime numbers they think are there. You can imagine I didn’t get into extreme things like infinity and methods to find these numbers, but I thought it is interesting to let them know that people are still trying to find out these numbers and that they use complicated algorithms and things like that. I had the idea to tell them that the biggest prime we know has 17425170 digits (now the biggest prime we know has 22338618 – Prime number with 22 billion digits is the biggest ever found ~2016) and they got quite excited about this because it seemed to them like something impossible.
I thought I have made the lesson fascinating for them and by telling them from the begging that we are doing puzzles to solve something extremely fascinating made them quite excited. If there is anything you would add to my lesson let me know, I am sure it is not the perfect one.
Let me know if you like this types of posts in the comment box bellow. Have a great day. You can find me on Facebook, Tumblr, Google+, Twitter, Instagram and WeHeartIt. I will try to post there as often as possible.
Don’t forget that maths is everywhere! Enjoy! ~LThMath~