6th Grade Math Problem

[Eric DeSilva]

I'm going to go further than saying "this isn't a math problem" to saying "the solution presented is incorrect." The problem could be phrased as a symbol logic problem--can you arrange these symbols in a way that creates a mathematically valid equation. But, the problem is currently stated as a mathematics problem--it was on a "math" test and relies exclusively on the language of mathematics. What people seem to forget here is that mathematics is a different language--if you are going to state a problem in that language, you are implying a solution in that language.

I previously noted, in the language of math, we imply multiplication all the time when two symbols are placed adjacent with no operator--"ab" is "a times b." Therefore, in the language of mathematics, two discrete numbers adjacent to one another should be multiplied together. The "solution" presented relies on concatenation. The operator used to denote concatenation in mathematics is a double bar, since concatenation is useful in some work with prime numbers and other number theory--in other words, "5 || 4 = 54" is a correct mathematical expression. However, the problem implicitly restricts you to combining certain numbers using addition--denoted by "+"--and multiplication--denoted through parentheses. The problem does not allow you to use concatenation through parentheses, and therefore a solution relying on parentheses is wrong.

This math teacher should be de-certified.

[Rick Potter]

Well,

Did she get it correct?

[Phil Thien]

I applaud the effort of the teacher(s), but I think this actual "puzzle" falls a little short. I think the instructions need to be more clear, maybe some examples demonstrating that space elimination is acceptable.

I'd encourage the teachers to do more of it, they will improve.

[Bruce Boone]

(5+4)2/3 =(3)(2) That's as close as I come if other operators are allowed. I agree. The spaces argument is pretty weak. It belongs on a logic test, not a math test.

[Jason Roehl]

Wait a minute!!!! I call fowl. No where did it say you could remove spaces. In only allowed inserting parentheses and addition signs. Plus, if parentheses indicates multiplication of the numbers inside then 5 + 4 + (2 3) would equal 15 correct?

(2 3) is not used to represent 6 when speaking of parentheses and multiplication. When numbers are used some sort of operator is needed between them, such as the 'x' (better is the Greek letter chi--I think that's the one that looks sort of like a cursive x), asterisk, a raised dot, or even two sets of parentheses--(2)(3) or even just 2(3) = 6. However "2a" implies "2 times a".

Okay, now I'm going to throw all this back in the mental attic where it can resume its dust-collecting experiments.

[Rick Christopherson]

A buddy of mine posted this on his Facebook page and no one could solve it.

And there is your answer right there. I am betting that your buddy didn't post anything, but instead "Shared" a posting or picture seeking the answer. It is just a scam to get other people to like or share the posting in order to increase ranking.

[Charlie Velasquez]

(2 3) is not used to represent 6 when speaking of parentheses and multiplication. When numbers are used some sort of operator is needed between them, such as the 'x' (better is the Greek letter chi--I think that's the one that looks sort of like a cursive x), asterisk, a raised dot, or even two sets of parentheses--(2)(3) or even just 2(3) = 6. However "2a" implies "2 times a".

Okay, now I'm going to throw all this back in the mental attic where it can resume its dust-collecting experiments.

Have to go with this. In the 80's the National Council of Teachers of Mathematics recommended that numbers be written without commas, and a space was to be used between the periods. So 34,265,117 would be written 34 265 117. I think the rationale was that when programming computers commas delineated separate values, while spaces added nothing to the place value. So maybe the NCTM felt this would help negate confusion for those that would later turn to computers. Not many teachers followed suit- many teachers were notoriously stubborn and taught the way and stuff that they were taught (see, we are still using and teaching the imperial units of measurement...). Or, the rationale may have been just to better align ourselves with the rest of the world as most non-English speaking countries did not use commas to identify periods...

[Frank Trinkle]

The Europeans confuse issues even more. They don't use a decimal point for monetary tenths (cents). They use a comma.
Therefore 120Euros and 25 cents is expressed as €120,25 rather than €120.25. Takes a while to get used to!

[John Coloccia]

I could just write:

32 = 32

Because it didn't say I can change the numbers to be whatever I want, but it also didn't say I CAN'T.

That's the problem with this sort of smarty pants puzzle. Where do you draw the line at how far out of the box is too far? In this case, it's entirely unclear that putting parentheses around two numbers magically turns them them into one number. All I did was reverse two numbers and get rid of two. If I can magically get rid of spaces, why can't I get rid of numbers too? I don't even have to move any around. I can simply say:

3=3

having gotten rid of all the superfluous characters (numbers and spaces).

[Chris Kennedy]

Easy:

5 4 2 3 becomes (5)(4)(2)(3) and I multiply them together, mod 88, and I get 32.

As someone who does math research, these kind of "cute" puzzles annoy me. They aren't math, and I wouldn't even say they are logical.

Chris

[Prashun Patel]

Jeez, why are you guys so worked up about it? The problem made us all think. It made my 9 year old son shout "hey, that's not fair" when he heard the solution, but he was smiling and thought it clever.

What's wrong with a little cheek? Why are these problems 'annoying'? The thought exercise is way more valuable that way than if it were written so that we could all solve it easily:

"5_4_23 = 32. Fill in the blanks - and only the blanks - with plus signs to make this equation true."

[Phil Thien]

And there is your answer right there. I am betting that your buddy didn't post anything, but instead "Shared" a posting or picture seeking the answer. It is just a scam to get other people to like or share the posting in order to increase ranking.

I guess I'm pretty naïve about facebook, do people actually increase rankings there by getting others to share postings? How does that work?

[Dan Hintz]

Jeez, why are you guys so worked up about it? The problem made us all think. It made my 9 year old son shout "hey, that's not fair" when he heard the solution, but he was smiling and thought it clever.

What's wrong with a little cheek? Why are these problems 'annoying'? The thought exercise is way more valuable that way than if it were written so that we could all solve it easily:

I think that's the issue right there... it's a "clever" solution. Occasionally my daughter will bring home one of these and I just roll my eyes. The intent is to teach the kids the subject of mathematics, not to show how cutesy the problem creator can be. Offer those problems as "extra credit", and make the rules of solving the problem crystal clear (or specify they've been left intentionally vague), but don't parade them as real problems and make the child suffer looking for a solution. It sends the wrong message and has the child questioning if they understand the core subject.

[John Coloccia]

I think that's the issue right there... it's a "clever" solution. Occasionally my daughter will bring home one of these and I just roll my eyes. The intent is to teach the kids the subject of mathematics, not to show how cutesy the problem creator can be. Offer those problems as "extra credit", and make the rules of solving the problem crystal clear (or specify they've been left intentionally vague), but don't parade them as real problems and make the child suffer looking for a solution. It sends the wrong message and has the child questioning if they understand the core subject.

Exactly. If you lay out rules that say "Add + signs and Parentheses" then you expect to be able to solve it with + signs and (). Make the rules clear:

5423 = 32
Make the above statement true. You may insert + signs and parentheses, but you may not change the order of the numerals.

And then you can simply say

5+4+23=32

That actually makes a lot of sense and you don't even need the parentheses.

(2 3) doesn't equal 23, so the whole thing is just stupid, incorrect and doesn't belong in a classroom. What a stupid thing to teach a child. "When you have two numbers that have spaces between them, when you put parentheses around them they become one number". There's no other reason for the parentheses, and in this case their use is so completely wrong that this doesn't belong anywhere near any classroom. There are so many ways to "think out of the box" that actually results in correct answers without all of this nonsense, why would anyone use this particular example?

[Eric DeSilva]

One key about mathematics and the language of mathematics is that any value should be able to be replaced by a variable without ambiguity. When you have symbols separated by spaces--"3 2"--you should be able to replace that with "x y, where x = 3 and y =2," because abstraction is one of the fundamentals of mathematics. Honestly, we never used actual numerical values when I studied higher math because everything was a symbol--actual values generally were reduced to constant generically labeled "K" or something. In my math studies, I don't think I did anything with an actual Arabic numbers from 8th grade on. So when you use spaces in formulation of a problem--NCTM be damned(*)--the indication is that each symbol is a unique value. Unique values placed next to each other without a space denotes multiplication--"xy" where x=3 and y=2 is "x times y" or 6.

(*) if the NCTM had succeeded, what they would have done is to create ambiguity as to whether certain strings of symbols were one value or not. But, if that was commonly adopted, people writing in the language of math would therefore be unable to use numerical values and spaces without resolving the ambiguity. For example, a 2 dimensional matrix is typically denoted with curly braces and values separated by rows of numbers separated by spaces (the only place I can recall where standard math notation involves Arabic numerals separated by spaces). I'll separate rows with a comma, so something like {1 0, 0 1}. If NCTM got their way, it might be "valid" to write a matrix like {100 101 102, 0 1}, but it is ambiguous, because that it could mean either {100,101 102, 0 1} or {100 101,102, 0 1}. So, I'll call the proposal silly on that basis. Like Texas trying to say pi should be 3.