Why '5+5+5=15' is wrong under Common Core

[mark_j]

Interesting:

Here's a "repeated addition" Common Core problem that's taught in third grade in US schools:

Use the repeated-addition strategy to solve: 5x3

If you answer the question with "5+5+5=15,” you would be wrong.

The correct answer is "3+3+3+3+3.”

Mathematically, both are correct. But under Common Core, you're supposed to read "5x3" as "five groups of three." So "three groups of five" is wrong.

According to Common Core defenders, this method will be useful when students do more advanced math. This way of reading things, for instance, can be used when students learn matrices in multivariable calculus in high school.

But parents aren't happy about it.

Linky

 

[Aella_]

wtf
Can someone explain all this to me in my own -aka stupid- language?

 

[RoryN]

http://www.lolzhumor.com/wp-content/uploads/2013/05/48023-e1368038153844.jpg

 

[Que]

Interesting:



Linky

The entire concept of repeated addition versus simply memorizing multiplication tables is an idiotic crutch that will harm students far more than it could ever help then in dealing with actual instances of such a technique should they ever encounter it in the advanced mathematics that they will never study if they do not know at a glance that 3x5 and 5x3 are both 15.

It also locks them into a myopic mindset that ignores the very important (multiplicative identity ?) property. It is important to know that 5x3 is exactly the same number as 3x5, in case you for example run into (x)(5) and need to express that (5)(x) for ease of collecting terms.

 

[BotanyBoy]

wtf
Can someone explain all this to me in my own -aka stupid- language?

Common core wants to teach kids how to read math problems correctly and it makes conservatives mad because common core is liburhul evil.

Seriously, it's that fucking stupid.

The entire concept of repeated addition versus simply memorizing multiplication tables is an idiotic crutch that will harm students far more than it could ever help then in dealing with actual instances of such a technique should they ever encounter it in the advanced mathematics that they will never study if they do not know at a glance that 3x5 and 5x3 are both 15.

It also locks them into a myopic mindset that ignores the very important (multiplicative identity ?) property. It is important to know that 5x3 is exactly the same number as 3x5, in case you for example run into (x)(5) and need to express that (5)(x) for ease of collecting terms.

If you don't teach kids how to read and understand that 5x3 (five groups of 3) is conceptually different than 3x5 (three groups of five) they will be lost when memorization just isn't an option. What happens when they can't just memorize and solve an equation that is describing something far more complex than three groups of five is fifteen? Suddenly they realize they don't have the most basic of equation reading skills.

It's not myopic to be teaching the basic concepts of math in 3rd grade....it's myopic to think that rote memorization without any sort of context to it is superior because common core is liburhul evil.

 

[Que]

wtf
Can someone explain all this to me in my own -aka stupid- language?

Sure. They are teaching kids to add groups of numbers together instead of actually multiplying which would mean you would have to memorize 5x3=15. Keep in mind they had to memorize (I hope) their addition tables to know that 1+1=2 2+1=3 3+1=4 4+1=5.

What they are asking kids to do is to visualize this problem as five bundles of three sticks each.

First reason this is dumb, is because when multiplying, sometimes it is easier, more intuitive to look up the answer in the "5"s table than in the "3"s table. It is important to know that the answer is on both tables, of course, but humans are better at counting by 5 than by 3. We have 5 fingers per hand, and 5 toes per foot. It is easier to picture the fingers on three hands than it is to picture five bundles of severed fingers. 5-10-15-20-25-30-35-40. Any child can do that. 3-6-9-12-15-18-21 is harder, marginally.

This problem solved as 5-10-15 requires three sums in your head as opposed to 3-6-9-12-15 that requires you to correctly add (and keep track of) or 5 individual sums.

The "correct" answer is:scrunching eyes shut: 1-2-3 (3) 1-2-3 (6) 1-2-3 (9) 1-2-3 (12) 1-2-3 (15!!)

And you KNOW with this method kids are counting on their fingers, What happens when they get past 20? (well 21 for the fellas)

 

[RobDownSouth]

Interesting:



Linky

There's a better explanation here about reasoning out a matrice properly, but I suspect the logic will be lost on the "hurr...durr...just memorize!" demographic.

Rote memorization will not help you when you get to algebra and beyond. That's when the "hurr...durr...just memorize!" folks start whining "I was doin' fine in maths until they added the entire alphabet!"

 

[Lord Pmann]

Common core wants to teach kids how to read math problems correctly and it makes conservatives mad because common core is liburhul evil.

Seriously, it's that fucking stupid.

No. I'm pretty math friendly and I can't think of a way that this has anything to do with conservatives and liberals.

There are patterns in the time tables. You never see those with this ridiculous form of mathematics. It's not a liberal or conservative thing.

 

[Que]

Common core wants to teach kids how to read math problems correctly and it makes conservatives mad because common core is liburhul evil.

Seriously, it's that fucking stupid.



If you don't teach kids hot to read and understand that 5x3 (five groups of 3) is conceptually different than 3x5 (three groups of five) they will be lost when memorization just isn't an option.

It's not myopic to be teaching the basic concepts of math in 3rd grade....it's myopic to think that rote memorization without any conceptual background to it is superior because common core is liburhul evil.

That notation does not mean what you say it means. That notation means multiply 5 and 3 . Any two items you put in this notation (X)(Y) are to be multiplied together and all items you put in that notation would be equally accurately expressed as (Y)(X) because they express the same result for all numbers from integers to real numbers to imaginary numbers. All of them.

Whats next? Teaching kids that 1+2 is somehow different than 2+1? It isn't.

The only time that the order you place the numbers in is when the operands are different, such as 2+1x5 =/= 1+2x5. On the other hand, 1x2+5 does = 2x1+5. In that case operative order applies.

 

[Aella_]

I wasn't able to focus on all the answers, so maybe I still don't get it.
This all seems like intellectual masturbation to me.

When I was in school, half of my class (average kids in all respects) were passionate about and did very well in math. But perhaps that's because we had an extremely gifted/renown mathematician as a teacher, who made everything easy to understand and fascinating.

As far as rote memorization is concerned: if I like something, I remember it. But if I have to memorize or learn a topic that I hate, it takes me three times the time and effort.

 

[BotanyBoy]

No. I'm pretty math friendly and I can't think of a way that this has anything to do with conservatives and liberals.

There are patterns in the time tables. You never see those with this ridiculous form of mathematics. It's not a liberal or conservative thing.

It's to do with liberals and conservatives because of the funding involved in common core. Liberals are getting paid, it pisses conservatives off.

So conservatives look at this math problem and try to turn it into outrage with all the people math illiterate enough to not realize that despite the fact that both equations equal fifteen they conceptually do not represent the same thing.

 

[Aella_]

EDIT.
And it makes sense that 5*3 is easier to vizualize and remember than the others, so that seems like a good suggestion.
But what I don't get is: why are either parties making such a big fuss about it? And where do politics come into this

EDIT,.
But maybe people are alluding to something else and I missed the entire point, so I'll shut up and read what people are saying.

 

[Que]

No. I'm pretty math friendly and I can't think of a way that this has anything to do with conservatives and liberals.

There are patterns in the time tables. You never see those with this ridiculous form of mathematics. It's not a liberal or conservative thing.

I also can think of no useful application of this in higher mathematics . If any such thing (if it exists) would be no stumbling block to those studying higher mathematics.

Kids need to be able to look at three $5 dollar items on the shelf and decide that they could also afford five $3 items for the same $15. In their head. If you cannot do basic multiplication in your head from at 1x1 to at least 10x10 you cannot function well enough to make change with any degree of speed and accuracy.

This is not even properly, mathematics. This is basic arithmetic.

Just because there is an additive property within multiplication does not mean that you arrive at the answer that way. All this does is encourage kids counting on their fingers which fucks up development of spatial reasoning.

If this is a good idea and they REALLY are trying to make the kids get down in the weeds, because it somehow helps in advanced differential calculus, the "correct" answer is thus:

(1+1+1) + (1+1+1) + (1+1+1) + (1+1+1) + (1+1+1) + (1+1+1) = 15, then put your left boot back on.

 

[BotanyBoy]

That notation does not mean what you say it means.

Maybe not to you because you can do organic chemistry and particle physics via rote memorization

 

[BotanyBoy]

All this does is encourage kids counting on their fingers which fucks up development of spatial reasoning.

I'm guessing the closest thing to "I didn't totally just make this bullshit up" is some uber whackadoodle RW rag opinion piece from the likes of britbart or AmericanThinker.

If this is a good idea and they REALLY are trying to make the kids get down in the weeds, because it somehow helps in advanced differential calculus, the "correct" answer is thus:

(1+1+1) + (1+1+1) + (1+1+1) + (1+1+1) + (1+1+1) + (1+1+1) = 15, then put your left boot back on.

But 5x3 (five groups of three) is so much easier, and this is why we multiply.....

See......it's context.....not a socialist plot to destroy your freedoms, brain wash jr into communism and a death warrant for grandma by Kenyan commie death panels all rolled into one DNC super scandal.

 

[Lord Pmann]

It's to do with liberals and conservatives because of the funding involved in common core. Liberals are getting paid, it pisses conservatives off.

So conservatives look at this math problem and try to turn it into outrage with all the people math illiterate enough to not realize that despite the fact that both equations equal fifteen they conceptually do not represent the same thing.

They should, conceptually represent the same thing. This is a short sighted way to teach math. It ignores the commutative (I believe that's the one) property.

It doesn't teach kids to multiply. It only teaches kids to add. And this is such a small portion of math. If you try to conceptually represent multiplication with addition, what happens once you get into numbers bigger than 30? Bigger than 100?

I think it's blindingly stupid to attribute something as foolish as this to politics. It's bad math.

 

[Que]

It's to do with liberals and conservatives because of the funding involved in common core. Liberals who obviously suffer from innumeracy are getting paid to create formulaic ways for kids to pass tests at the expense of actual learning, and it pisses conservatives off.

So conservatives look at this math problem and are justifiably outraged because they do not suffer from innumeracy and do realize that because of the fact that both equations equal fifteen they are mathematically, exactly the same thing.

FYP. YW.

How you gather up your sticks to count them has no bearing at all on how many sticks you have. If I have 5 cages with 3 cats in each, and 3 cages with 5 rats in each, I have a one-to-one correspondence between the number of cats and the number of rats. Because arithmetic.

There are no shapes of cages and no animals you can put in said cages in these ratios where that problem would not be true. Because arithmetic.

If you chop your fingers and a foot's worth of toes in half and gather the bloodied bits into groups of two and a half digits, you will find you have six, bloody little piles. 5x3 is also 6x2.5 because of arithmetic.

 

[NYC_Man]

Interesting:



Linky

I studied abroad and if i was to use a calculator i would be in trouble
i study in usa lack of calculator would get me in trouble



I don't sew how 5x5x5 would make it harder for them when they get older.

 

[RoryN]

I remember my 8th-grade math class. We had a teacher who had been featured in the newspaper for trying out a supposedly new method of teaching math fundamentals. It involved visualizing multiplication tables differently depending upon the first number in an equation; 8x6 vs. 6x8, for instance. You showed your work with blocks and, although you'd have the same 48 blocks at the end, the two needed to be expressed differently.

The end result was that we did simple multiplication tables for most of the school year. My parents looked at my homework and were absolutely livid.

 

[Aglaopheme]

Interesting:



Linky

This is completely asinine. There are no Common Core problems taught in schools. Common Core is a set of standards. Much like the standards we've always had set for students. Common Core is not a curriculum.

The Common Core Standards were adopted by the National Governors Association in 2009. Then a massive campaign of misinformation started about Common Core as a way to attack the President.

Keep up the good work.

 

[Lord Pmann]

This is completely asinine. There are no Common Core problems taught in schools. Common Core is a set of standards. Much like the standards we've always had set for students. Common Core is not a curriculum.

The Common Core Standards were adopted by the National Governors Association in 2009. Then a massive campaign of misinformation started about Common Core as a way to attack the President.

Keep up the good work.

How about we attack whatever fuckwit who came up with this bullshit math?

I bet they wear TOMS.

 

[Aglaopheme]

How about we attack whatever fuckwit who came up with this bullshit math?

I bet they wear TOMS.

Feel free to find said stylish and comfy fuckwit and attack away.

 

[tactful]

Common Core: Affirmative Action, for kids.

 

[Que]

I'm guessing the closest thing to "I didn't totally just make this bullshit up" is some uber whackadoodle RW rag opinion piece from the likes of britbart or AmericanThinker.



But 5x3 (five groups of three) is so much easier, and this is why we multiply.....

See......it's context.....not a socialist plot to destroy your freedoms, brain wash jr into communism and a death warrant for grandma by Kenyan commie death panels all rolled into one DNC super scandal.

Yes it is. And three groups of five (which is a perfectly acceptable way to read "5x3") is much easier to conceptualize. All students should be taught, if 7x4 is hard for you to remember, is 4x7 and easier memory hook?

When you have:


9563839
x8489

To solve that you need to know at a glance that the last digit of that problem is a 1 and that you are going to need to carry an 8.

Arithmetic notation can be read in English. The problem is "5 multiplied by 3 is what?" Specifically 5 is your starting point and multiplying the five thrice is what is being directed. Except for little half steps with parenthetical notation or paying attention to the operative order, you read a math problem left to right.

These idjits are reading it as "5 TIMES 3" which is not even mathematically correct. There are no "times tables."

Even if that language was acceptable, and it is not, the question is: is it "5, times 3" or "Repeat 5 times: add three" Either are perfectly fine. Because of arithmetic and it is much more important that kids know that those concepts are both ways of counting the same number of sticks.

The solution given as being the exclusive way to solve that problem is mathematically incorrect. Not just "OK, but not my favorite" Mathematically, conceptually incorrect.

 

[doctor_insanus]

FYP. YW.

How you gather up your sticks to count them has no bearing at all on how many sticks you have. If I have 5 cages with 3 cats in each, and 3 cages with 5 rats in each, I have a one-to-one correspondence between the number of cats and the number of rats. Because arithmetic.

There are no shapes of cages and no animals you can put in said cages in these ratios where that problem would not be true. Because arithmetic.

If you chop your fingers and a foot's worth of toes in half and gather the bloodied bits into groups of two and a half digits, you will find you have six, bloody little piles. 5x3 is also 6x2.5 because of arithmetic.

That's like saying x and y are the same thing, simply because 5x=3y. They are not the same thing. Because arithmetic.