Maths with my teenager

[Alberto]

Last night my teenager was in crisis mode because next day was maths test and she knew that she knew nothing.
At least she did care, already an improvement from the previous year.
So at 6pm when I returned home I offered to study together. I love maths since I was born, and it also belongs to my training and my profession.

"I would have to learn tonight everything we did in the last 3 months, and this is not going to happen, so there's no point"

I made it clear I was only offering, it was not a must, she was free to take it or leave it.

Nothing at dinner.

At 9:30 she comes downstairs with a face like "Papi, let's give it a try".
After 10 min she went back upstairs saying "Oh my God, I learnt more in 5 min with you than in the last 3 months at school". I could tell that yes, she did indeed learn.

That made me sooooooo happy . I expect I will soon return enemy #1 but hey, for now I'm very happy.

[Franklan]

If you want to make your daughter happy, teach her this:

"Commutative" means that a multiplication can be "swapped", as in "5 times 3" is the same as "3 times 5".

Now, what is "19% of 50€"?

It is the same as "50% of 19€"!

Just sayin'...

[Alberto]

Sounds catchy, thanks.

[Robinson100]

Well done Alberto!!!
The maths teacher at the Gymnasium that Shorty attended was pretty useless at explaining things, and this, coupled with Shorty having a ( at the time not diagnosed) learning problem, meant that the best thing the maths teacher could do was suggest she attend a different level of school!
Yeh, well, as things turned out, Shorty is currently studying to be a maths and English teacher, and is particularly quick to notice kids in a similar situation to the one she was once in!
Anyway, what I actually meant to say was that the German way of teaching maths is not for everybody, so don´t wonder if your child finds it damned-near impossible to grasp!

[LeonG]

"Commutative" means that a multiplication can be "swapped", as in "5 times 3" is the same as "3 times 5".

I had a teacher who didn't know that. He wanted me to multiply 3 by 3 by 3 by 3 and I went 9 by 9 equals 81. He started off with "Wait, you can't do that?" To "Oh, it works too".

[Alberto]

"Commutative" means that a multiplication can be "swapped", as in "5 times 3" is the same as "3 times 5".

I had a teacher who didn't know that. He wanted me to multiply 3 by 3 by 3 by 3 and I went 9 by 9 equals 81. He started off with "Wait, you can't do that?" To "Oh, it works too".

Made me think about this story about Gauss.
He was unruly at school, especially at maths, because the subject for him was too easy and therefore boring.
So the teacher, unhappy with his bad behaviour, decided to "punish" him, and instructed him to calculate the sum of the first 100 integer numbers. How long would this take you? The teacher thought it was going to take him many days. All good.

Problem is, he was done after few minutes.
How would you calculate the sum of the first 100 numbers? I think most people would do 1+2+3+..., like 1+2=3, 3+3=6, 6+4=10, 10+5=15, 15+6=21, etcetera. But not Gauss, he was one of the greatest genius ever.

in a sum, you can reshuffle the numbers as you wish. Result always the same. So instead of adding the first to the second, then adding the third, the the fourth, and so on, you could also:
add the first and the last: 1+100 = 101
add the 2nd smallest and the 2nd biggest: 2+99 = 101
add the 3rd smallest and the 3rd biggest: 3+98 = 101
this way you have 50 different pairs, all summing up to 101.
In other words:
1+2+ ... + 100 = 50*101 = 5050
1+2+ ... + N = N*(N+1)/2

And before you conclude: "come on, that's easy, not so genius after all....". Do you really think many people find this easy BEFORE it is ever explained to them?

The crazy and cool thing is that the teacher who gave him this task, to force him quiet, was probably unaware of this cool thing. After all this is one of many equations that still carries Gauss name. Poor teacher. Love Gauss.