Hey, it’s Wednesday, so it’s time for a #commoncore red haze across my vision!

14 thoughts on “Hey, it’s Wednesday, so it’s time for a #commoncore red haze across my vision!”

1. Yeah, that’s… a tad above 4th grade. I don’t quite remember at what grade I was taught algebra, but it certainly wasn’t 4th. 6th or 7th, maybe?

2. I’m pretty sure pre-Algebra was 7th, Algebra was 8th. The average 4th grader isn’t going to have the abstraction necessary to do it with algebra, even if they’ve been exposed to the idea. So, how exactly are they supposed to solve it? Iteration? 285+1=286, 284-1 is way off. So, try numbers closer together….

   1. Not to mention, if that’s how it’s supposed to be solved, the set of positive integers for which x+y=286 is much smaller than the set for which x-y=36, so the question would best be asked in the opposite order.

3. If I am not mistaken, this is a classic system of two unknowns question:

   x+y=286
   x-y=36

   add the two equations together and you get:
   2x=322
   x=161

   then you plug that value for x back into the first equation to get
   161+y=286
   y=125

   1. As long as you can see the equations, you know exactly what they want you to do.
      –
      It is not something most people do every day, however.

      1. Wait, 4th grade? That is a bit early.

4. I teach middle school math; maybe I can shed some light on what’s going on [rolls up sleeves]:

   You wouldn’t need algebra at all to work out an answer. JAB is close with his (his?) first idea–try two numbers close together, and then walk them apart until you hit the correct pair.

   I can see the number sense ideas that the problem is attempting to get at:

   • estimating: you need two numbers probably in the vicinity of 150, because 286 is close to 300.
   • mental division: the numbers to start with are 143 and 143, because 286/2 is equal to (200/2)+(80/2)+(6/2), and those are steps you can do in your head. And hey, 143 is indeed close to 150, so we’re so far so good.
   • zero sum: you can’t just add 36 to one of the 143’s, because then your sum would be too large. For every 1 you add to the first 143, you’d have to take away 1 from the other 143.

   At some point, you hope the light would dawn that if you ADD half of 36 to one number, and SUBTRACT half of 36 to the other number, you’ll get the desired difference, while keeping the desired sum intact.

   We used to teach ourselves similar ideas when we were kids following MLB standings. Like how to calculate how many Games Behind your team is behind the division leader, or what’s the Magic Number if your team was in first place. Stuff like that.

   1. Ok, makes sense. But isn’t this a more complicated form of mental algebra?

      1. I suppose you could see it that way, but on the other hand not necessarily. What’s neat about the problem is that so much of it IS mentally do-able by fourth grader–what you need the paper for, actually, is to keep track of your results as you go. I tell my 6th graders that their brains are the CPU processors, and their paper is the RAM memory.

         Actually, there’s one more very important lesson here, which is that “You’re clever enough to find a way to do this problem.” Growth mindset, donchaknow. As adults, we recognize the classic algebra formulation of the problem, so that’s the tool we apply. But the kids wouldn’t know that, so they have to grind out the answer through lots of guess and check, which is totes ok, or else try to find some neat “shortcut” ways of thinking about the problem, like in the bullets in my previous post. Which leads to better understanding of how it All Works.
         The hoped-for pay-off is that when they DO learn algebra, it won’t be such a total mystery.

         1. I can see what you are saying. Thinking about the problem in the way you describe, while not what I instantly go to, I see why it could be better if you can teach the ‘number sense’ to the kids.
            –
            I never developed that. I HAVE to write out the equations on a piece of paper. I do great at using them and adapting them and fitting them into what I am doing, but I have never been able to ‘do the math’ in my head.

            1. Actually, for the last step (adding/subtracting 18 to/from 143), I pulled out a calculator! That was the only time that I had to carry or regroup. The rest was easy to do in my head, so long as I kept track of my progress on paper so that I wouldn’t mix up all the figures.
               Aetius451AD, I’d say if you can adapt the equations to novel situations, then you’ve got your own number sense working just fine!

         2. “At some point, you hope the light would dawn that if you ADD half of 36 to one number, and SUBTRACT half of 36 to the other number, you’ll get the desired difference, while keeping the desired sum intact.” Ok, I get the idea you’re trying to teach. But it still sounds pretty abstract for a 4th grader.

         3. Given that my child will probably be the only one in his class to hand in that assignment tomorrow with the correct answer, I think that whoever created this question failed in their goal. I’m basing this assessment on the fact that his teachers hadn’t even gotten it established for him yet that equations are supposed to balance, which is the single most important thing that I made doubly sure to try make sure that he learned. And I’m not expecting them to teach that in the first half of the fourth grade, at that.

         4. Alternately, rather than plugging in numbers to try and brute force it for an unknown period of time, they give up.
            Which is exactly what kids are doing.
            .
            Common Core has been throwing the transitive property of addition at my kids since kindergarten. They’ve been having to solve for x since first grade.
            But the tools to actually succeed are purposely withheld from them. They either independently derive mechanics that took generations to formalize, are independently taught by their parents for hours every week, or they fail.

Comments are closed.