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Common Core math problem: what is a "Mentally Visualized 5Group"?
Somehow I have become a walking cliche: a parent who is unable to understand his kid's math homework. Damn you,
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 5Groups." 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. Last edited by Erdosain; 11042014 at 03:00 PM. 




Paging Tom Lehrer... and there are so many rhymes with "common core"...







opinion hijack
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.





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CC, political opinions don't belong in GQ. No warning issued, but since you have started, let's not continue. Colibri General Questions Moderator 




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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 commoncore.org, but it isn't clear if they're just a nonprofit 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 offtopic ramble, but since the OP mentioned  er, damned  the Common Core, I thought I'd post. 




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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 56743, it was 567 + 43. Of course, the handson mechanics were the same as what subtraction was, but it wasn't subtraction, y'know? Because subtraction doesn't exist.





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.







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. 




Judging by the info on it, my best guess is equations whose solutions are multiples of five.
In general, fivegroups 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 or 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 fivegroup because one of the rows is incomplete. This is what I gather at least. Last edited by Jragon; 11042014 at 11:18 PM. 




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5groups 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 5groups, 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: http://commoncore.org/maps/math/vide...upstenframes 




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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. Last edited by Isilder; 11052014 at 12:20 AM. Reason: bad quote tag 






Alternate way of looking at it: numbers whose representation in tally marks only contains sets with a diagonal slash.
22 The point is to know what you're doing, not get the right answer Last edited by Jragon; 11052014 at 12:27 AM. 




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...00000043 becomes: ...99999956 which becomes: ...99999957 Now we just add normally: ...00000567 ...99999957 ...00000524 Of course, once we get to the nines, we end up carrying a ones digit forever, so we have to recognize this and stop early. Easy, and a nice prep for two'scomplement representation, which is how basically every computer stores integers. 




Well, that's certainly dumb terminology for a sound concept.





I never heard this term before and illustrates the tendency to focus on obscure words rather than concepts. In the new math, first iteration, they spent a lot of time teaching words like commutative and associative. The words themselves are obscure and come into focus only when you find natural examples of noncommutative or nonassociative systems.
To me, the 5group is subgroup of symmetries of a regular pentagon consisting of the rotations, of which there are 5 (including the one by 0 degrees). 




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TEACHER: What's eight plus seven? STUDENT: twelve! twenty! fifteen! TEACHER: Yes you got it right; the answer is fifteen. Okay, moving on.... Of course, accuracy should count too. And, to a certain degree, over analyzing the problem can become counterproductive. But there's a balance to be struck there. Current consensus is that we should expect the students to understand that eight plus seven is the same as five plus three plus five plus two, which is the same as five plus five plus three plus two, which is the same as ten plus five. But we won't ask them to do it that way all through the other grades. It's a stepping stone. 




Here's some 5 group cards, aka dot cards.
http://teacherspayteachers.com/P...ivities766067 You can see cards for 6,7, 9 and 15, without having to log in . Last edited by Isilder; 11052014 at 05:51 PM. 