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Sample problem for K-1 [1]: "Jane fills a bag with three types of chips. There are 3-point, 4-point and 7- point chips. Jane picks 3 chips worth 15 points. W

Sample problem for K-1 [1]: "Jane fills a bag with three types of chips. There are 3-point, 4-point and 7- point chips. Jane picks 3 chips worth 15 points. Which chips did she pick?" Sample problem for grades 5-6 [2]: "Pinocchio drank half a cup of black coffee. He then filled the cup back up with milk and drank one third of the mixture. Again he filled the cup to the top with milk, drank one sixth of the mixture and filled it back to the top with milk one final time before he drank the whole cup. Did he drink more coffee or milk?" [1]https://f.hubspotusercontent30.net/hubfs/981338/Blog/Elementary_School_Problems.pdf https://f.hubspotusercontent30.net/hubfs/981338/Blog/Element... [2]https://f.hubspotusercontent30.net/hubfs/981338/Blog/Middle_School_Problems.pdf https://f.hubspotusercontent30.net/hubfs/981338/Blog/Middle_...

xmprt 5y ago
Those are pretty challenging problems and they also require a bit of working out. How many of these problems are students expected to solve in, say, and hour long test?
- eps 5y ago
  These represent classes of problems and the test checks which classes students have covered in their studies and which they slacked on. These two are straight-forward problems, both will be allocated some basic nominal time. You either know how to solve them or you don't. Sometimes there'd be problems that are more puzzling, because they'd combine several problem classes and will take time to unfold (this is typical in math olympics). These will be allocated more time as they require thinking and searching for a solution.
  - dkn775 5y ago
    From the examples I guess it is the ability to intuitively manipulate fractions? Like “oh that’s kind of like .8 of this other thing so it’s close to X” ?
  - xmprt 5y ago
    I see what you mean by classes of problems. Some of the problems from the above links I know how to do (although working out might take some time and a pen and paper) and then there are some problems where I don't know where to start. I was just never taught how to think about numbers that way even though the link says those problems are for middle school children.
andi999 5y ago
I don't like the second question. Probably the kid is supposed to see the 'trick' :he drank a full cup of coffee since he didn't refill coffee and drank all. He added 1/2, 1/3 and 1/6 of a cup of milk and drank it all, so (3+2+1)/6=1. He drank the same amount of coffee and milk. I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever. But I don't think it teaches you anything (maybe it does, didn't study pedagogy, and while I was good at such fun questions I preferred the more structured approach in university mathematics) Edit: this might make the kids think you need some 'magical' insights to do math and if they don't see it they are not apt for it, while the opposite might be true. For the other questions: 2 also seems to rely on a trick, 3 looks ok, 4 is ok, 5a looks dodgy (probably just trying out numbers), 6 looks ok About the K1 question:these are for 3 year olds? I only met one 3 year old in my life who could read, probably I am missing something here.
- zozbot234 5y ago
  > I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever. But I don't think it teaches you anything These word problems are intended quite precisely as introduction to algebra. They show you the kinds of questions that algebra can solve in a "structural" way, which makes it way easier to grok algebra later on since motivation for the subject has been provided in such depth. A good review article on the subject: Persson, Ulf and Toom, André: Word Problems in Russian Mathematical Education, available at http://toomandre.com/my-articles/swedish/ULFENG.PDF http://toomandre.com/my-articles/swedish/ULFENG.PDF
  - andi999 5y ago
    Why do you think this is the starting point of a structured introduction?
- carlmr 5y ago
  >I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever. If you see the trick, you save some time on the calculation. If you don't you have to add some more numbers. It's not that difficult.

xmprt 5y ago

Those are pretty challenging problems and they also require a bit of working out. How many of these problems are students expected to solve in, say, and hour long test?

eps 5y ago
These represent classes of problems and the test checks which classes students have covered in their studies and which they slacked on. These two are straight-forward problems, both will be allocated some basic nominal time. You either know how to solve them or you don't. Sometimes there'd be problems that are more puzzling, because they'd combine several problem classes and will take time to unfold (this is typical in math olympics). These will be allocated more time as they require thinking and searching for a solution.
- dkn775 5y ago
  From the examples I guess it is the ability to intuitively manipulate fractions? Like “oh that’s kind of like .8 of this other thing so it’s close to X” ?
- xmprt 5y ago
  I see what you mean by classes of problems. Some of the problems from the above links I know how to do (although working out might take some time and a pen and paper) and then there are some problems where I don't know where to start. I was just never taught how to think about numbers that way even though the link says those problems are for middle school children.

andi999 5y ago

I don't like the second question. Probably the kid is supposed to see the 'trick' :he drank a full cup of coffee since he didn't refill coffee and drank all. He added 1/2, 1/3 and 1/6 of a cup of milk and drank it all, so (3+2+1)/6=1. He drank the same amount of coffee and milk. I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever. But I don't think it teaches you anything (maybe it does, didn't study pedagogy, and while I was good at such fun questions I preferred the more structured approach in university mathematics) Edit: this might make the kids think you need some 'magical' insights to do math and if they don't see it they are not apt for it, while the opposite might be true. For the other questions: 2 also seems to rely on a trick, 3 looks ok, 4 is ok, 5a looks dodgy (probably just trying out numbers), 6 looks ok About the K1 question:these are for 3 year olds? I only met one 3 year old in my life who could read, probably I am missing something here.

zozbot234 5y ago
> I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever. But I don't think it teaches you anything These word problems are intended quite precisely as introduction to algebra. They show you the kinds of questions that algebra can solve in a "structural" way, which makes it way easier to grok algebra later on since motivation for the subject has been provided in such depth. A good review article on the subject: Persson, Ulf and Toom, André: Word Problems in Russian Mathematical Education, available at http://toomandre.com/my-articles/swedish/ULFENG.PDF http://toomandre.com/my-articles/swedish/ULFENG.PDF
- andi999 5y ago
  Why do you think this is the starting point of a structured introduction?
carlmr 5y ago
>I think it is ok as a brain teaser, but there will probably be one kid in the class to see it and all the other kids feel dumb or whatever. If you see the trick, you save some time on the calculation. If you don't you have to add some more numbers. It's not that difficult.