math question for 12 year olds

May 08, 2022,12:53 PM

this is a question in my son's math homework. poor boy... and of course, poor father too πŸ˜…

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Darn...Im rusty

 By: guycord : May 8th, 2022-13:41
The area of a quarter is Pi / 4 x r^2 >>>>. The White square is a height of triangle base thing so r^2 /2 as we know the hypotenuse=r >>>>> Hence the area of the curved areas is [(Pi / 4 x r^2) - (r^2 /2)] x 2 = A1 >>>> The small shaded square (A2) is kno... 

Scribed methodology….

 By: guycord : May 8th, 2022-18:43

thanks! πŸ‘

 By: terbaboom : May 8th, 2022-22:37
as he hasn't learnt pythagoras' theorem, I've used the "area of biggest square in a circle" (2Γ—r^2) to explain to him

Solution (just including for your son the details of what our friend Guycord wrote, which was both clear and correct): The shaded area is $32 \pi - 48$. If you approximate $\pi $ by 3.14, then this area is roughly 52.48.

 By: FabR : May 8th, 2022-14:04
We just use that the area of a circle of radius $R$ is $\pi R^2$, hence the area of each quadrant is $\pi 8^2 / 4=16 \pi$. Also, by Pythagoras' theorem, the diagonal of a square is $\sqrt{2}$ times its side (where \sqrt indicates the square root function)... 

thanks Fab! πŸ™ now I'll just need to explain to him without using pythagoras' theorem as he hasn't learnt it yet πŸ˜‰

 By: terbaboom : May 8th, 2022-15:00
and I'll be very happy if he does become a Patek collector, since this will mean he has some accomplishments in his life πŸ˜‚


 By: InHavenPro : May 8th, 2022-15:54
I know now whom to turn to if I ever end up having children in need of math tutoring! xD Somehow, despite having two parents who were both either excellent or brilliant at math, I utterly 'suck' at it LoL ........

I see you're in Singapore...

 By: mdg : May 8th, 2022-14:24 that age in the US would never get that question until late in high school if ever : )

frankly, it can be very stressful for kids and their parents over here, so i can't say if this is ideal

 By: terbaboom : May 8th, 2022-15:08
all 12 year olds here will take one of the most important national exams in their lives after which they'll find themselves being "categorized" according to their results

That sort of exam is something...

 By: mdg : May 8th, 2022-15:14
...we do not have here. Rather students can take SAT tests that can affect their college choices...

From what I read recently....

 By: InHavenPro : May 8th, 2022-15:55
They were debating removing the SAT testing requirements altogether........


 By: mdg : May 8th, 2022-16:38
...but I won't say why because it will veer into politics.

Sounds tough, much more than the US and certainly Italy! :-) On the flipside, one thing he can do in high school, if he turns out to be good at (and in love with) Math, are the Math Olympics, which are incredibly fun (and entirely optional)...

 By: FabR : May 9th, 2022-00:37
In the US and Canada, later on the (undergrad) college students can also take the Putnam Exam, an equally optional and fun but *horrendously* challenging competition for talented students, which essentially ranks them at the country level before they can ... 

MIT is impressive...

 By: mdg : May 9th, 2022-02:04
...a whole other level of smart than most people realize.

thanks again Fab! it's definitely not easy and parents here are contributing to the high level of competitiveness by enrolling their children in various enrichment classes πŸ˜“

 By: terbaboom : May 10th, 2022-00:41
and yes, his school makes their students take part in math olympiad every year and offers extra classes for that. my son has never made it to the next round though πŸ˜… i prefer to let him enjoy his childhood as much as possible with the right balance. it's ... 

+1, in full agreement --- sounds like a very competitive environment, which is a great thing but indeed only if it's within the natural bounds of a child's overall development (emotional, social, cultural, etc.)!

 By: FabR : May 10th, 2022-07:57
That's also a critical age for children to develop self-confidence, a correct way to relate to the other kids of both genders, etc...success in my view should always be pleasant and never toxic! As a future HUGE Patek collector, your son should first and ... 

Singapore's 12 year olds might be more prepared than average country's 12 year olds!

 By: patrick_y : May 8th, 2022-18:16
Where's that Patek Philippe advertisement of a dad and son doing the son's homework together? ...  

Maybe! But that's because this kid probably isn't 12 yet!

 By: patrick_y : May 9th, 2022-04:49
Or his math homework (it looks like math) in this photo isn't as difficult as your child's homework!


 By: FabR : May 9th, 2022-07:20

In my day job I was MD of Excel Math elementary mathematic curriculum

 By: cazalea : May 11th, 2022-15:49
for a decade, and I oversaw the production of K-6 lessons in English and Spanish, print and electronic formats, books for students, teachers and parents. I retired 10 years ago and couldn't solve that problem now without thinking hard and doing some diagr...  

I am a reclusive sort of watch person, more handy with tweezers and screwdrivers than with children

 By: cazalea : May 20th, 2022-18:57
My expertise lies in getting the books out on time without errors, not with coaching students on how to do math. Anyway I am retired now... but thank you for the offer.