The new math

[BoyNextDoor]

"Write a repeated addition sentence for 6x3"

 

[lemonbread]

"Write a repeated addition sentence for 6x3"

Um.. . 6+6+6? That looks like repeated addition.

3+3+3+3+3+3 is too, but that would be 3x6? Just guessing.

 

[Mike_Yates]

Because of common core, kids today are literally being taught that 2+2 = 5.

 

[BoyNextDoor]

"repeated addition" is definitely not the same as multiplication. If so, then...

3+3+3+3+3+3=6+6+6

Right?

 

[lemonbread]

"repeated addition" is definitely not the same as multiplication. If so, then...

3+3+3+3+3+3=6+6+6

Right?

Well... It kind of is multiplication. 6x3 is just another way to say 6, 3 times. That's 6+6+6. I don't know, my only school age child is in first grade, we haven gotten to common core yet.

 

[Que]

Mathematics is a language. It is read left to right just as English is.

The literal English translation of 6 x 3 is "Six times three" or to put it less awkwardly, "Count to three, six times."

Mathmatics has some rules and acrobatics that are allowed while retainign the same meaning.

Using commutative property of multiplication, 6x3 is also 3x6.

So answer one and two are both correct.

It is also "Three times six" or "Count to six, three times."

Since usually these things are taught in an order from more simpler concept, but more difficult solves to more advanced concepts but ultimately simpler solves, the correct answer is probably the first, but if I am thinking in groups of things in my head I would solve it as Lemonbread did.

The only notation that would clearly delineate if you had 6 groups of three or tree groups of 6 would be" 6(3) or 3(6). It is a distinction without a difference because whether you had 3 packs of 6 wolves, or 6 packs of 3 wolves you still have 18 wolves so not understanding the intent of the person posing the problem makes no difference.

I always hated that about mathematics instruction. The instructor would say, "This is he way you are going to solve for the area under a curve for now, but eventually you will be doing it a simpler way."

I object to teaching additive method for multiplication because it is inefficient, and unnecessary. Generations of mathematics students successfully learned their multiplication tables.

If the objection is the difficulty of rote memorization, anyone with an IQ over about 80 can do it. To do the additive method you already had to memorize equally long additive tables.

Please tell me they are not teaching kids to add on their fingers?

 

[lemonbread]

But I think for this particular problem, 6x3 is counting to six three times, = 6+6+6
And 3x6 is counting to three six times = 3+3+3+3+3+3. Even though the answer is the same and they're essentially the same problem, the method of getting the answer is different. They specifically want 6, 3 times. Not 3, 6 times. Maybe I'm thinking too hard though.

 

[Que]

But I think for this particular problem, 6x3 is counting to six three times, = 6+6+6
And 3x6 is counting to three six times = 3+3+3+3+3+3. Even though the answer is the same and they're essentially the same problem, the method of getting the answer is different. They specifically want 6, 3 times. Not 3, 6 times. Maybe I'm thinking too hard though.

I turned that version over in my head as well, but that requires knowledge of mutiplication.

Your translation including a comma is exactly right if you are mutiplying.

You start with "6" and then you multiply that by 3. "6, 3 times."

It is a stupid question. If you want someone to solve a problem in retarded fashion, write it that way: 6+6+6=?

A smart person seeing 6+6+3+3+3+4+2+3+6 will collect terms... 3 6's + 4 3's which is 2 6's really and the 4 and the 2 is a 6. So you really have 6 6's or 36.

Most people do that when there are a lot of 5s and 10's. It is routine to do it when counting money where you can easily make stacks.

18x3 would be retarded to do additively. But it is also (2x9)3 or better (2x3)9

 

[subdued_passion]

... I object to teaching additive method for multiplication because it is inefficient, and unnecessary. Generations of mathematics students successfully learned their multiplication tables.

If the objection is the difficulty of rote memorization, anyone with an IQ over about 80 can do it. To do the additive method you already had to memorize equally long additive tables.

Please tell me they are not teaching kids to add on their fingers?

Your post qualifies you for the title of 'ganit guru'.

Anyway, while repeated addition may seem silly it is done so that people can understand the concept of multiplication. If they understand the concept the practical applications come more naturally.

Learning the tables by heart is also important but that's step 2.

 

[PeteHulbert37]

I'm not a fan. The way it was always taught worked for me. I'm not even very smrt.

 

[removed121614]

Maths is just for the logical minds.

> Mastered calculus at the age of 14.

 

[Que]

Looking at sample questions for this nonsense around the web it looks like Lemonbread's take is correct.

It is 6, 3 times or 6+6+6.

Not the way I was taught to interpret the language by wither reading the formula as a sentence or converting English into a formula, left to right.

Maths is just for the logical minds.

> Mastered calculus at the age of 14.

Linguistically, we now know Canky is not in the US.

 

[removed121614]

Linguistically, we now know Canky is not in the US.

I don't follow any syllabus, I'm self-taught.

 

[Que]

I don't follow any syllabus, I'm self-taught.

Be that as it may, Americans go to "the" hospital, attend "the" university and study Mathematics (plural) or abbreviate the subject as Math (singular.)

I don't know why we do that.

Most Americans when mentioning the "subject" of Math mean arithmetic computation, possibly complaining that they hate algebra, where the objection is adding letters.

They usually know that Mathematics involves mysterious things beyond the above.

 

[RobDownSouth]

Logically, the answer is 6+6+6.

 

[subdued_passion]

Logically, the answer is 6+6+6.

Six times three would read as six groups of threes. So, 3+3+3+3+3+3.



Query, I tried looking but in my searches I got the same explanation and not the 6, 3 times version.

 

[JAMESBJOHNSON]

I learned standard math applications in school, and again when I was in college. Once or twice the educrats tried to impose new standards but all went away as they made learning math tougher to do. My kids got hit with NEW MATH in school and I caught hell for teaching them what I knew. I failed geometry in high school tho I have a 100th percentile aptitude for geometry and aced a 4 year course in sheet metal pattern making...its entirely descriptive geometry applications.

https://www.youtube.com/watch?v=oCRpVqle_ck

 

[Que]

Logically, the answer is 6+6+6.

That is the logical answer to the sentence "3 times (6") or "thrice six" not "6 times (3)", although as discussed both are the same thing.

It comes down to whether you would say "A lady times three" or "Three times a lady" when either locution make equal sense.

 

[RobDownSouth]

I decoded it as "write six, three times", ergo, 6+6+6.

I think you may be overcomplicating things.

 

[Que]

I decoded it as "write six, three times", ergo, 6+6+6.

I think you may be overcomplicating things.

Your reading has merit. 6 is what we are inputing into a formula and (x3) is the function that we are plugging the 6 into.

Fair enough. But look at 3 x 10. Would you also not instantly see that as 10+10+10?

I think what you did was consider (briefly) in your mind what makes more sense... adding up 3 sixes, or adding up 6 threes and just chose the addition problem that is easier to visualize.

I would never teach it this way, so the point is moot, but I would tell a kid to add up groups of the larger number. So whether it was written 365x3 or 3x365, I would expect them to add 365+365+366.

 

[tactful]

"Write a repeated addition sentence for 6x3"

There is no period or question mark, for the question, if it is in fact, a question, therefore, the answer is open to interpretation.

 

[Bad_Doggie]

I was taught it reads 6 lots of 3.

Although at the same time being bludgeoned to rote memorize it.

It's probably the most boring, dreary and frustrating period a student can go through.

Woof!

 

[RobDownSouth]

Your reading has merit. 6 is what we are inputing into a formula and (x3) is the function that we are plugging the 6 into.

Fair enough. But look at 3 x 10. Would you also not instantly see that as 10+10+10?

I think what you did was consider (briefly) in your mind what makes more sense... adding up 3 sixes, or adding up 6 threes and just chose the addition problem that is easier to visualize.

Well yes, after I learned the commutative property of multiplication back in third grade, I began to routinely and reflexively group largest to smallest.

...I would tell a kid to add up groups of the larger number. So whether it was written 365x3 or 3x365, I would expect them to add 365+365+366.

America is very fortunate that you don't teach math.

 

[Que]

Well yes, after I learned the commutative property of multiplication back in third grade, I began to routinely and reflexively group largest to smallest.



America is very fortunate that you don't teach math.

It is reflexive, but you have to know how to multiply, before you can know that that it is communicative. That's why this intermediate step of teaching they are doing is silly.

The thing that made me obsess over how it could be seen both ways is my assumption that a and b were given as multiple choice answers and since there was no c (all of the above) choice that means that when they teach this one of those two is "wrong" and I was trying to figure out how either version (both of which will yield the correct answer of course) is "wrong."

I think I am stuck in a logic loop of my own making.

 

[BoyNextDoor]

There is no period or question mark, for the question, if it is in fact, a question, therefore, the answer is open to interpretation.

That was exactly the way it appeared on the math test for a 6th grader

I should add, that the answer "6+6+6=18" was marked as incorrect, and that "3+3+3+3+3+3=18" was written in by the teacher as the correct answer.