Ok to all my math teachers I just want to say how much I feel let down by you – especially to the 11th grade trig teacher who really did write the book.
Now that that is off my chest let me explain how I reduced things. Does it end in a 0? – Ok not a 10. Does it end in a 5? – Ok not a 5. Does it end in an even number? – Ok it does. I can divide by 2. Keep dividing by two for as long as I can. If it doesn’t meet any of these qualifications give up and go to the next problem. To say I don’t see patterns in numbers is an understatement.
If I had known these rules, I would have been quite a bit less frustrated – and probably made fewer mistakes in my formative math years.
Today I taught divisibility to the boys. I had no idea there were laws governing number divisibility. I learned thanks to my Montessori training about the patterns numbers make multiplying and ergo there must be patterns in division. But who knew how to find them.
So we worked together using decimal work (I don’t own the golden beads.) because it differentiates by units, tens, hundreds in the various families. The boys quickly began to make a rule for 2.
A number is divisible by 2 if the number ends with an even digit (2,4,6,8,0).
We worked through 4 – harder.
A number is divisible by 4 if the last 2 digits of the number are divisible by 4.
Five and 10 were easy.
A number is divisible by 5 if the number ends with a 5 or a 0.
A number is divisible by 10 if the number ends with a 0.
We then put logic and golden beads on the mat and began to puzzle through 8. Much more difficult.
A number is divisible by 8 if the last three digits are divisible by 8.
AV brought up that it must be difficult if not impossible for 7 as it doesn’t have a pattern until in the thousands. Yes. There is one but it requires an algorithm.
We then veered down a different logical path for the 3’s and 9’s.
A number is divisible by 3 if the sum of the individual digits in the number adds up to 3, 6, 9.
A number is divisible by 9 if the sum of the individual digits in the number adds up to 9.
Last was 6. This took the most time to puzzle out.
A number is divisible by 6 if it is both divisible by 3 and 2.
Go ahead. You know you want to try it. 4,579,106.