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Come here to find out what is happening in Division 11.
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About Me
- Miss Owen
- Gibsons, B.C., Canada
- Did you know that I went to Gibsons Elementary School? I'm happy to be teaching in the school I went to. I am also happy to be teaching in a school I can walk to. I live with my mom, Mrs. Owen, who sometimes comes to help in our classroom.
From Wikipedia... "The smallest friendly number is 6, forming for example the friendly pair (6, 28) with abundancy σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14+28) / 28 = 2. The shared value 2 is an integer in this case but not in many other cases. There are several unsolved problems related to the friendly numbers."
ReplyDeleteHowever, I am curious... what are the friendly numbers your students are telling their parents about?
I studied math for many years, but must have missed out on the term. You led me to do some research (i.e. the Wikipedia quote above), but also found some interesting reading, including this reference to Pythagoras:
"Pythagoras regarded two numbers as friendly if each was the sum of the other's divisors. The Greeks were aware of just one such pair, 220 and 284. The divisors of 220 (1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110) add up to 284, while the divisors of 284 (1, 2, 4, 71, 142) add up to 220. Not until 1636 was another pair of friendly numbers -- 17,296 and 18,416 -- discovered by the French mathematician Pierre de Fermat. However, by the middle of the 19th century, the number of known friendly pairs totalled more than 60. Incredibly, the second-lowest pair of all had been missed. In 1867 a 16-year-old Italian, Nicolo Paganini, demonstrated that 1,184 and 1,210 are friendly.
There are questions associated with friendly numbers too. All known examples consist of either two odd or two even numbers. Are pairs consisting of an odd and an even number possible? Why are all the odd friendly numbers multiples of three?"
Great blog... thanks for posting!
Our friendly numbers are much less complicated. Friendly numbers are pairs of numbers whose sum is 10.
ReplyDeleteThe fingers come in first of all because we have ten. If you hold up any number of fingers, the fingers that are down represent the friendly of the number of fingers that are up.
What we really hope, of course, is that the children will find all numbers to be friendly in the sense of being understandable, helpful, and comfortable.
Thanks for the update. I was teaching a grade 5 class the other day... sitting in for the regular teacher, and lo and behold the lesson was on, you guessed it, friendly numbers.
ReplyDeleteYour explanation above fits nicely with the lesson taught at the later grade level. The purpose of the lesson was to use the friendly numbers (in this case, multiples of 10, 100, and 1000) to help students do mental addition and subtraction.
You can let your students know that the math they are are practicing today, will benefit them in the future - and, specially in grade 5!
Cheers...