Never in my life would I write “2 x 8 - 5 x 3” and expect people to know what I meant. Parentheses exist for a reason! (See also: every dumb “most people can’t solve this problem” meme)
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Isn't this just a case of "sometimes in the real world there is ambiguity. But that's okay we have a standard approach for it. Here it is, please show you can utilize it."?
PEMDAS has rarely been used in advanced mathematics. Neither is the symbol × for multiplication (because it looks too similar to x). Actually, "the basics" are rarely used in some branches of math (like in Group Theory)
Even then, parantheses are always better for clarification
Order of Precedence helps when one has to read code written by crappy coders 😂
Some of which include computers that don’t care if humans can read what they understand implicitly 🤖
I'm in the UK and that would be a perfectly normal sum for a primary school child to ensure they learn order of operators. I learned the same way 50 years ago.
Going from 2×8 to 2a, it is easier if they only have to get their heads around
1) there is a letter where they have only seen numbers before and
2) we don't write the multiplication sign.
To throw on
3) we don't write brackets.
Just makes things much harder.
This type of problem as written is designed to help kids "see" the need for order of operations...the problem today is teachers want you to "show and explain" your work (step by step). If you understand Order of Operations you can see it and answer 1. Right answer is most important, period.
And to be clear here, this is not “I don’t understand how to do it” or any of the usual “I can’t do my kid’s HW” complaints. I see what they want, and it’s usually clear. The issue is that the problems are sometimes examples of things that nobody with any knowledge of math would pose
This was a thing that I had to keep explaining - there were definitely assignments (into early algebra) where it's like yes, this is validly written, but you'd never write them like that if you were doing the math for real because you're just ASKING for mistakes to happen
(The other unrelated thing that I did that helped was, as I do a fair amount of algebra for my job, sometimes I make dumb transcription errors or other silly mistakes, and I'd show her like "look, I literally get paid to do this and I make the same types of mistakes you do, don't feel bad about it")
I think this specific problem is one that’s a step behind pre algebra. It’s obviously about order of operation, and the only place it might be used is in inventory versus sales situation. Replace one of those numbers with a variable set equal to 0, then you have the next discipline
I learned how derivatives work by replacing numbers with variables. Our teacher was having us do it the slow way with numbers in the hundreds and thousands. Wayyyy too much so I replaced all the numbers with letters.
Oh dear lord. To be fair: I went to school for Economics, but in lack of practice, I sometimes need to refresh on derivatives. I first learned them properly in 11th grade and even then it was a functional education and not knowledge.
Great distillation of the failed teaching process.
I trained people to operate multi-axis computer controlled machining centers and often had to teach them how to frame the equation. Each problem is unique. There is no cookie cutter or template approach to real life math.
This mostly reminds me of those viral memes like "80% of people get this math problem wrong" and it's because the math problem is written in some weird way math people don't actually use. Often using a ÷ like a complete psychopath
Oh, ÷ is a telltale sign. Then you must figure out what country of origin is.That's a hint they got used to a calculator. But, these had different order of operation based on region\brand, it never correct PEMDAS though :P
I thought parenthesis were like...required, for reasons exactly like that one. But I haven't done "math" since school fifteen years ago, and even then I wasn't the best at it, so I could be very wrong.
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I don't see the issue
Even then, parantheses are always better for clarification
Some of which include computers that don’t care if humans can read what they understand implicitly 🤖
Parentheses exist so that we can write 2×(8–5)×3, (2×8–5)×3 etc.
When students come to algebra, and they learn 2×a‐5×a they won't have brackets.
If they rely on brackets, they often struggle to make the switch to pronumerals.
1) there is a letter where they have only seen numbers before and
2) we don't write the multiplication sign.
To throw on
3) we don't write brackets.
Just makes things much harder.
If students struggle and need the brackets, I would draw them in a different colour and say that we don't normally draw them.
I trained people to operate multi-axis computer controlled machining centers and often had to teach them how to frame the equation. Each problem is unique. There is no cookie cutter or template approach to real life math.
chill