Common Core math problem: what is a "Mentally Visualized 5-Group"?

Somehow I have become a walking cliche: a parent who is unable to understand his kid’s math homework. Damn you, [del]New Math[/del] Common Core! Damn you to 7734!

So here it is. My kid has to sort “number sentences” (simple equations like 3+4=7) into different groups. Doubles, doubles +1, etc. One of the groups is identified solely as “Mentally Visualized 5-Groups.” I have a notion of what this means but I can’t figure out which “number sentences” would go into this group. Equations with a 5 in them? Equations with 5 as the answer? Help! Any elementary school teachers please chime in.

If I’m reading this and this right, Mentally Visualized 5 groups would be equations with a 5 in them. Perhaps it makes more sense bundled with classroom instruction.

Also, strike the strikes and use [del].


Paging Tom Lehrer… and there are so many rhymes with “common core”…

There is so much wrong with public education these days, and the standardizing of curriculum is just one piece of it. Where are the “get the government off our backs” people when there’s an actual need for them? Answer: they’re behind all this federal testing/common core crap. Agh - don’t get me started.

Moderator Note

CC, political opinions don’t belong in GQ. No warning issued, but since you have started, let’s not continue.

General Questions Moderator

Yes, it appears Eureka Math defines a “5 group” as an equation with a 5 in it.

I’d be more interested in where this term “5 groups” even shows up in the Common Core - I looked through grades K and 1 and couldn’t find it. The closest I could find is K.OA.A.5, “Fluently add and subtract within 5,” or K.OA.A.3, “Decompose numbers less than or equal to 10 into pairs in more than one way.”

I doubt the term “5 groups” is in the actual Common Core documents.

I see a lot of this term in Google searches from Eureka Math, which is at, but it isn’t clear if they’re just a non-profit making materials based on Common Core or whether they’re actually affiliated with Common Core - their URL makes it appear that it’s the latter and yet I suspect it’s the former.

Sorry for the slightly off-topic ramble, but since the OP mentioned – er, damned – the Common Core, I thought I’d post.

Common Core is a cooperative effort by a group of state governments, not the feds.

So a “mentally visualized 5-Group” would be an imaginary equation with a 5 in it. :rolleyes:

Gotta love the fancy terminology. When I was a child, one of the vogue math terms was “facts”. A “fact” was a completed, basic math problem. So, 1+1=2 was a “fact”. 5*3 = 15 was a “fact”. Quizzes were actually testing you on your “math facts” knowledge.

Another math pedagogy idea that was in vogue was the idea of teaching little children that subtraction didn’t actually exist, and that what you were actually doing was adding a negative number. I think we got that in like 7th grade or something. We showed up, and they told us to stop doing subtraction and start adding negative numbers. So instead of 567-43, it was 567 + -43. Of course, the hands-on mechanics were the same as what subtraction was, but it wasn’t subtraction, y’know? Because subtraction doesn’t exist.

Has your kid considered leaving an anally excreted long product on the teacher’s desk?

In most cases the teacher is rolling her eyes as she teaches this, so you’d have to go higher to find someone with the power to change the curriculum.

You want eye roll material?

“Rubrics.” :rolleyes: :rolleyes: :rolleyes:

I am retired, and if I never hear that word again I will be happy. One of my principals thought rubrics were the best thing since sliced bread. She didn’t realize rubrics could be just as big of a pain in the neck as any other type of grading.

I retired two years ago, just when Common Core was being introduced to the district. I was able to work in my room during all of the inservices, and so all of these Common Core math questions perplex me just as they do the average person.

The kid can barely add. I think it’s a bit early for natural logs.

Judging by the info on it, my best guess is equations whose solutions are multiples of five.

In general, five-groups seem really cool and how a lot of people with number sense do math.

The general practice is decomposing numbers into groups of 5 or 10, for instance:

15 + 7 = 15 + (5 + 2) = 20 + 2 = 20


123 + 17 = (120 + 3) + (7 + 10) = 120 + 10 + 10 = 140

Of course, as you get more comfortable with the material, you can do this more quickly and skip steps. Personally (keep in mind I didn’t learn this formally), I just do “123 + 17 = 130 + 10 = 140”.

I’m really not sure the visualizations they use are helpful, but the basic idea is sound. It seems to me that a five group is, well, a group of five dots *****, so by “mentally visualizing it”, they’re imagining the number 5 is *****. So 20 is:

Which is a “five group”, 12, on the other hand, is


Which isn’t part of a five-group because one of the rows is incomplete. This is what I gather at least.

Umm, no.

5-groups are a way of teaching numbers to Kindergarteners and First Graders. They look at their own hands and see 5 fingers on the left hand and 5 fingers on the right hand. They can take out a piece of paper and draw 8 dots in a row but honestly can you tell just by glancing whether … is 8 or is is 7 or is it 9? But if you put them into 5-groups, you have something like this:

ooooo ooo

which is clearly 8. not 7, not 9.

Then when they eventually get to questions like “what’s 8 plus 6?” they can do this:

ooooo ooo plus ooooo o equals ooooo ooooo oooo which is 14.

The point is they can SEE it, rather than just memorizing the “fact” that 8+6=14.

Visualize the 8 as 5+3, visualize the 6 as 5+1, and clearly you have two 5s and a 3 and a 1, so that’s ten plus 4, which is 14.

Try watching this video:

Ah yes it is a 5 group card… A 5 group card is a card that shows value in dots … in groups of 5 just like that… whatever value it shows.

Alternate way of looking at it: numbers whose representation in tally marks only contains sets with a diagonal slash.


The point is to know what you’re doing, not get the right answer :stuck_out_tongue: