Is this a "common core" problem?

[Gravekeeper]

From the context, it could just as easily be read as "group of 5, taken 3 times". After all, a flat of 710ml (24 ounce) soda bottles has 6x4 bottles. Would you say that means it has 6 4-packs? I wouldn't - the plastic banding (Pepsi) or shrinkwrap (Coke) groups the bottles into 4 6-packs.

No, again, in this lesson 5 x 3 is specifically to be read as five groups of three. That's literally what the Common Core denotes about this particular method of problem solving. It is suppose to be read as five groups of three. That is the lesson.

Making "common sense" arguments about how you read it is irrelevant to the lesson. That's not what the lesson is trying to teach. But it's the trap that the parents in question are falling into. Thinking that out of context the question says the standard method is wrong.

Yes, we all read 5 x 3 as 5 times 3 or 3 fives. That method is a given. But that's not the method being taught with this particular lesson. Nor is the method being taught suppose to supplant what we see as the common sense method. Its suppose to foster problem solving methods that can be used in more advanced mathematics courses in later grades.

[mjr]

No, again, in this lesson 5 x 3 is specifically to be read as five groups of three.

That seems like an awfully confusing way to teach it, given the 5 x 3 aspect of the question.

That's literally what the Common Core denotes about this particular method of problem solving. It is suppose to be read as five groups of three. That is the lesson.

Then to me, that seems like the lesson is over-complicated. Even within the "context" of the question, it's backward.

Making "common sense" arguments about how you read it is irrelevant to the lesson.

I disagree. Look at the question. The question says:

"Use the repeated addition strategy to solve 5 x 3".

The teacher obviously wanted 3 + 3 + 3 + 3 + 3.

Most people, myself included, would write 5 + 5 + 5, which is the correct answer, based on the question. Tell me you wouldn't, based on the wording and structure of the question. It's rather straightforward and non-nuanced.

That's not what the lesson is trying to teach. But it's the trap that the parents in question are falling into. Thinking that out of context the question says the standard method is wrong.

It's possible that the lesson is wrong -- or at least flawed in some way.

And here's another "example" (anecdotal, I will grant) of a Common Core "method" that is, again, over complicated. Sure, it may not be the only method taught, but don't you think it's a little over-complicated?

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

Or how about this lady, who gives an example of a class of 18 that counts by a number and ends up with 90. The simplest thing to do is "simple" division.

But no...they want the kids to draw EIGHTEEN circles, and NINETY marks (five per circle). To quote "The Doctor", that's like "going home...the long way around."

Yes, both result in FIVE, but one is VASTLY more complicated than another.

https://www.youtube.com/watch?v=wZEGijN_8R0

And also, I saw someone bring this up. "Showing your work" means that you are able to follow a process to get a correct result. So in the question above, 5 + 5 + 5 = 15 is a correct result of 5 x 3.

Put also as I've seen it, A x B is B instances of A.

But how about one more vid, just for good measure?

https://www.youtube.com/watch?v=d1Ubjg_o8vg

[NecCat]

That seems like an awfully confusing way to teach it, given the 5 x 3 aspect of the question.


"Use the repeated addition strategy to solve 5 x 3".

The teacher obviously wanted 3 + 3 + 3 + 3 + 3.

Most people, myself included, would write 5 + 5 + 5, which is the correct answer, based on the question. Tell me you wouldn't, based on the wording and structure of the question. It's rather straightforward and non-nuanced.



It's possible that the lesson is wrong -- or at least flawed in some way.

First : I don't think this shows a problem in 'common core' either way you look at
Second: I realize multiplication works in any direction, and doing it either way won't hurt anything
Third: You are exactly wrong

In math the symbol x means 'multiples of', 'times of', or just 'of'
5 times of 3 is 3,3,3,3,3
5 multiples of 3 is 3,3,3,3,3
5 of 3 is 3, only five of them - 3,3,3,3,3

If you buy a bulk flat of water the case says 24x575ml not the other way around, there is 24 instances of or multiples of the 575ml. Same with anything else labelled in bulk.


3+3+3+3+3 is exactly the correct answer to the question the way it is written.

[mjr]

Again, most people (at least most in my generation) take 5 x 3 to mean 5, 3 times.

A 5 x 3 grid is this:

XXXXX
XXXXX
XXXXX

Not this:

XXX
XXX
XXX
XXX
XXX

[Kheldarson]

The point is that they're both the same but you sometimes need to consider other breakdowns of the problem. Because if you get locked in to one way of thinking you can miss the solution. Higher level math requires being able to break problems into parts and understanding the manipulation. And when you get a student who can't, or won't, grasp other forms of a problem, it's an issue.

[mjr]

The point is that they're both the same but you sometimes need to consider other breakdowns of the problem. Because if you get locked in to one way of thinking you can miss the solution. Higher level math requires being able to break problems into parts and understanding the manipulation. And when you get a student who can't, or won't, grasp other forms of a problem, it's an issue.

I understand that, but taking off a point because the student wrote 5 + 5 + 5 instead of 3 + 3 + 3 + 3 + 3 kinda defeats the purpose, doesn't it? 5 + 5 + 5 arrived at the same answer as 3 + 3 + 3 + 3 + 3, but is more in line with the problem as it is stated. Neither answer is wrong, but if the student thinks to themselves, "even when the answer is right, the answer is wrong", then how does that help them?

Manipulatives may be a far better way to do these things. The way the question is on paper is clunky and unclear.

Even within this thread there's disagreement as to whether or not the answer should be 5 + 5 + 5, or 3 + 3 + 3 + 3 + 3.

[Kheldarson]

I understand that, but taking off a point because the student wrote 5 + 5 + 5 instead of 3 + 3 + 3 + 3 + 3 kinda defeats the purpose, doesn't it? 5 + 5 + 5 arrived at the same answer as 3 + 3 + 3 + 3 + 3, but is more in line with the problem as it is stated. Neither answer is wrong, but if the student thinks to themselves, "even when the answer is right, the answer is wrong", then how does that help them?

Because if they were told to read it a certain way for the assignments, then expressing it a different way is wrong. If they were told to give all possible answers, then answering with only one answer is wrong.

Not following directions is always a reason to mark off points. Common Core doesn't change that.

And there's no real disagreement on which way is right in here. Given that multiplication is communicative. The only question is how the lesson was taught, which a snapshot of a single problem doesn't tell us.

Here's a couple of truths about education: it's constantly changing. But it is usually very slow to do so because new teachers have to fight against the status quo to get the new implemented and accepted. A good portion fail because they either leave or fold to the status quo. But new ideas and methods of teaching are always being explored. The only reason why Common Core is getting such a bad rap is because it's coming from the top which makes the fight visible.

[s_stabeler]

there's also the fact that, from my read of it, it is a 6-mark paper, and they were marked down as if they got the answer completely wrong. THAT is a problem, since the student would almost certainly think "my teacher's stupid/deliberately marking me down- I got the right answer, why has she marked it as if I got it wrong?" NOT "I made a mistake in solving the question"

To be honest, this should probably be a two-or-three mark question, and IF the lesson requires you to solve the problem in a particular way, then you give them however many marks are given for the right answer, and a reasonable, though incorrect method.

However, it's worth noting that this is an assignment fthird-graders- they are 8 or 9 years old. They are in Elemantary School at that level, that they are able to use the basic method to solve a multiplication is good enough,

[mjr]

Because if they were told to read it a certain way for the assignments, then expressing it a different way is wrong. If they were told to give all possible answers, then answering with only one answer is wrong.

Then shouldn't the way they were told to read it actually reflect the way it is?

They should teach the way the question says. They can't just say, "I know the question reads like this, but that's not really what it means..."

What does "Use the repeated addition strategy to solve 5 x 3." mean to you?

I know what it means to me. It means 5 + 5 + 5 = 15.

[Kheldarson]

Then shouldn't the way they were told to read it actually reflect the way it is?

They should teach the way the question says. They can't just say, "I know the question reads like this, but that's not really what it means..."

What does "Use the repeated addition strategy to solve 5 x 3." mean to you?

I know what it means to me. It means 5 + 5 + 5 = 15.

But is that the way the students were taught? That's the question.

Here. When I was in fourth grade, I started learning algebra thanks to my parents. Being an elementary student, I ended up using some of the methods they taught me. Got the answers right, but my teacher had a talk with me about using the methods taught while taking tests on those methods.

Then she helped me and some others test for skipping up a grade in math.

But I still had to show that I knew the basic steps as taught.

So how you or I read it doesn’t matter. What matters is how it was taught in the class.

[mjr]

So how you or I read it doesn’t matter.

Indeed it does matter.

"Use the repeated addition strategy to solve 5 x 3."

reads differently, and has a different "result" than

"Use the repeated addition strategy to solve 3 x 5."

The "answer" to both is ultimately 15. But the first is a result of 5 + 5 + 5. The other is a result of 3 + 3 + 3 + 3 + 3.

I write software. How I read a spec or requirement matters. It doesn't really matter much what the person who wrote the spec meant.

[Rageaholic]

Not necessarily. If it's homework, how do you know they didn't just punch it into a calculator? You have them show the work to show that they understand the concept and theories.

Can't believe I didn't think of that.

Well, no. Again, context. In the context of the lesson 5 x 3 is read as five groups of three. The correct answer is the one the lesson is trying to teach. The reasoning behind teaching this method actually turns out because it works as a basis into more advanced math later on in high school. Such as the dreaded calculus.

Don't get me started on calculus...

[Greenday]

Not necessarily. If it's homework, how do you know they didn't just punch it into a calculator? You have them show the work to show that they understand the concept and theories.

You'll figure it out when they get the test and fail. That's why homework is optional in a lot of college courses. It's your job to do the homework correctly and if you choose not to do it, you'll be the one to suffer when you fail a test that's worth 20% of your overall grade.

[Kheldarson]

You'll figure it out when they get the test and fail. That's why homework is optional in a lot of college courses. It's your job to do the homework correctly and if you choose not to do it, you'll be the one to suffer when you fail a test that's worth 20% of your overall grade.

Yeah, that works at college. Why do you think I stopped teaching after a year? Middle school and below the teacher has to make sure there's opportunity to learn and prove learning and make it upand... etc.

So yeah. Have to show your work to show that you've learned the material so when the student fails the teacher can show where there didn't seem to be a problem.

[Kheldarson]

Indeed it does matter.

No, it doesn't because we're not being graded. We're not in the class, we're not the teacher. Saying that it matters how we read it matters is like saying how we view an ant matters to an ant. We're not even in the same world as each other.

But the problem more is this: even beyond whether it makes sense or not, this is a matter of following directions. It would be like saying a teacher should accept, without penalty, a paper done in MLA when the directions said to put it in APA. Just because they're both citation methods doesn't mean you get to ignore the directions.