I understand why most people do not see the difference in the two answers. I had to read the explanation to be honest. At first glance I thought it was right until I actually processed it. (I am not a math person)

I agree with Amiga. It may not be exactly what the teacher was looking for, but I'd be happy that the child understood how to use repeated addition. I wouldn't count it wrong, and that is the whole problem with standardized testing. This kid understands the relationship between multiplication and addition and should not be penalized.

You know what? I'd have probably counted it wrong too honestly. Not for the repeated addition but for what he was adding. While the answer to 5 times 3 and 3 times 5 both equal 15 (and both would be marked correct on a standardized test), there's a conceptual difference between 5 groups of 3 or 3 groups of 5, right? The use of repeated addition revealed a lack of understanding of the concept.

I lean towards the answer being correct, because I see the question as seeking to demonstrate knowledge and understanding of repeated addition. The student has clearly demonstrated this.

The problem with that question is that it is not in context.

It is also hard not knowing the student. I have 3rd graders who would write 5 + 5 + 5 because they have strong number sense. They know that multiplication is commutative and that adding three 5's is easier than adding five 3's!

This line in the article really bugs me:

Quote:

The question is typical of Common Core

There is nothing "Common Core" about 5 x 3 or using repeated addition.

When I taught this concept I was repeatedly explicit about the difference between 5x3 and 3x5. I probably would have given half credit to acknowledge partial understanding.

My last year of teaching we went around and around about this with a math coach. Yes, I know the difference in the representations of the groups. I also know that this same coach was a big proponent of math/number talks. We encouraged students to show different ways to make the same numbers.

The second example was also marked wrong because the 4 should represent the rows, not the columns. Really?? 4X6 can only be represented as an array of four rows of 6.

The third one does have the context of the equality so the picture should match.

The only reason I understand this question is because I taught 3rd grade for 6 years using Common Core math.

The question: 5 x 3 translates to 5 groups OF 3 which in repeated addition is 3+3+3+3+3. This is important for the explaining of the reasoning and understand of the concept (ie to get maximin points in standardized tests - I feel your pain Luvmycat).

I 100% understand the frustration and why it’s confusing. Later on it doesn’t make a difference because of the commutative property (as Amiga pointed out) but I’d bet money that this concept and therefore the question was specific to the concept taught in that particular chapter of their math curriculum.

Kingbird queen - fantastic examples and real life scenarios. Thank you!

I've seen that before and it always upsets me. Like Amiga said, the commutative property. As others said, the student showed their thinking and the answer is correct so what could be "wrong?" The student went BEYOND the question in demonstrating knowledge IMO.

If the question had different wording and included something like KingbirdQueen's examples, then the question would be marked wrong but as the question was written, I think the child showed repeated addition and the answer is correct. The test is lame and needs to be rewritten.

I can't believe this went viral. I daresay it's another case of teacher bashing and the teacher in question is probably rethinking her career choice.

I forgot to say that this looks like Engage NY /Eureka where students are taught very clearly that the rows represent the groups and the number in the rows are how many per group. Problems are how many rows multiplied by how many in each row equals total. That’s how you read number sentences for multiplication. Number of rows times how many in each row equals the total.

The problem would be 5 rows with three in each, or 3+3+3….

It’s the same or similar to the same program my son uses because it is free and in depth and he is homeschooled for now. Some people don’t like it. Some people do. It’s big on mathematical reasoning and it’s very insistent that while you can use mathematical properties to solve totals, the rows and groups matter. But it is explicitly taught throughout the program over and over what the rows represent and that the number in each row are how many per group. 5 times
3 is 5 groups of three . 3 times 5 is three groups of five. It’s in the program over and over when they draw their arrays. They write two arrays for both number sentences a lot, point out the differences, etc. The teacher does an entire problem set hitting this point with the student before they ever see their homework.

It is a bit out of context because you can’t see how many times the lesson plans actually go over and over this before you see the homework. There are lessons, arrays, problems sets, and exit tickets the covers this for several lessons before you see this on the homework.

It is a bit out of context because you can’t see how many times the lesson plans actually go over and over this before you see the homework. There are lessons, arrays, problems sets, and exit tickets the covers this for several lessons before you see this on the homework.

My school used McGraw-Hill “My Math” but it seems very similar to what you are describing. I completely agree from experience to what you said above.

I also agree with a PP that this seems like “teacher bashing” and it’s a shame that it went viral.

I've learned a lot from reading these responses! I had not taught math for many years. I think the students should have received partial credit for the correct answer of 15. But I now understand the repeated addition part was incorrect.

It’s interesting reading everyone’s thoughts and experiences. I’m learning so much.

Quote:

I think the students should have received partial credit for the correct answer of 15.

I wonder if I was the teacher if I would have given 1/2 credit for the answer of 15. The last several years I taught we moved to such a data driven learning model - even our report card in 3rd was skills based. I admit that with all the craziness going on that I might have had tunnel vision for that specific skill that was being assessed at that particular assignment. I don’t mean that I wouldn’t encourage the student for having the correct answer of the math fact of
5 x 3 = 15 but that at that time if I was specifically looking for that skill I might overlook the rest.

A few years ago when I was subbing, I'd sometimes assist a first grade teacher during her math instruction time. There was one skill (I don't remember exactly what it was) that had to be done in a certain way. While assisting a confused student on a worksheet, I honestly wasn't sure what to do, so I looked at the teacher's book.

After that I asked myself, "Am I really smarter than a first grader?"

That reminds me of when I started subbing when my children were in 1st and 2nd grade. I hadn't taught in 9 years so math was definitely different. Since I subbed at my kid's school and lived close, they'd sometimes call me for last minute situations. I got called in and ran over and the principal seemed so happy to see me and practically ran out of the room. It was a group of third graders learning lattice multiplication! Fortunately it wasn't their first introduction so there were a few students who were able to explain it to the class AND ME! Nothing like walking into a room mid lesson and having to admit you have absolutely no idea how to do what they are doing!