Reply
Thread Tools Display Modes
#1
Old 11-04-2014, 02:59 PM
BANNED
Join Date: Oct 2008
Location: Stars Hollow
Posts: 3,358
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, New Math 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.

Last edited by Erdosain; 11-04-2014 at 03:00 PM.
#2
Old 11-04-2014, 03:13 PM
Guest
Join Date: Jul 2005
Location: Minnesota
Posts: 14,294
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].
#3
Old 11-04-2014, 03:21 PM
Charter Member
Join Date: Sep 2003
Location: Southeast Florida USA
Posts: 20,672
nm

Last edited by LSLGuy; 11-04-2014 at 03:22 PM.
#4
Old 11-04-2014, 03:46 PM
Guest
Join Date: Apr 1999
Location: F.O.S.O.N.E.
Posts: 19,903
Paging Tom Lehrer... and there are so many rhymes with "common core"...
#5
Old 11-04-2014, 04:12 PM
CC CC is offline
Charter Member
Join Date: Apr 2000
Location: not elsewhere
Posts: 4,291
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.
#6
Old 11-04-2014, 04:36 PM
SD Curator of Critters
Moderator
Join Date: Oct 2000
Location: Panama
Posts: 37,514
Quote:
Originally Posted by CC View Post
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.

Colibri
General Questions Moderator
#7
Old 11-04-2014, 05:32 PM
Guest
Join Date: Jun 2004
Posts: 334
Quote:
Originally Posted by Erdosain View Post
Somehow I have become a walking cliche: a parent who is unable to understand his kid's math homework. Damn you, New Math 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.
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 commoncore.org, 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.
#8
Old 11-04-2014, 06:27 PM
Guest
Join Date: May 2003
Location: Florida
Posts: 67,142
Quote:
Originally Posted by CC View Post
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.
Common Core is a cooperative effort by a group of state governments, not the feds.
#9
Old 11-04-2014, 06:30 PM
Guest
Join Date: Jul 2004
Location: U.K.
Posts: 12,068
Quote:
Originally Posted by yearofglad View Post
Yes, it appears Eureka Math defines a "5 group" as an equation with a 5 in it.
So a "mentally visualized 5-Group" would be an imaginary equation with a 5 in it.
#10
Old 11-04-2014, 08:12 PM
Guest
Join Date: Oct 2009
Posts: 8,791
Quote:
Originally Posted by njtt View Post
So a "mentally visualized 5-Group" would be an imaginary equation with a 5 in it.
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.
#11
Old 11-04-2014, 08:16 PM
Guest
Join Date: Oct 2009
Posts: 8,791
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.
#12
Old 11-04-2014, 09:37 PM
Guest
Join Date: Oct 2009
Posts: 8,791
Has your kid considered leaving an anally excreted long product on the teacher's desk?
#13
Old 11-04-2014, 10:23 PM
Guest
Join Date: Jul 2010
Posts: 3,644
Quote:
Originally Posted by robert_columbia View Post
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.
#14
Old 11-04-2014, 10:42 PM
Guest
Join Date: Apr 1999
Location: F.O.S.O.N.E.
Posts: 19,903
You want eye roll material?

"Rubrics."
#15
Old 11-04-2014, 10:49 PM
Guest
Join Date: Jul 2010
Posts: 3,644
Quote:
Originally Posted by Amateur Barbarian View Post
You want eye roll material?

"Rubrics."
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.
#16
Old 11-04-2014, 10:55 PM
Guest
Join Date: Apr 2007
Posts: 6,556
Quote:
Originally Posted by robert_columbia View Post
Has your kid considered leaving an anally excreted long product on the teacher's desk?
The kid can barely add. I think it's a bit early for natural logs.
#17
Old 11-04-2014, 11:14 PM
Guest
Join Date: Mar 2007
Location: Miskatonic University
Posts: 10,269
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

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 five-group because one of the rows is incomplete. This is what I gather at least.

Last edited by Jragon; 11-04-2014 at 11:18 PM.
#18
Old 11-05-2014, 12:07 AM
Guest
Join Date: Nov 2009
Location: Eugene, Oregon
Posts: 1,030
Quote:
Originally Posted by Inner Stickler View Post
Mentally Visualized 5 groups would be equations with a 5 in them.
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: http://commoncore.org/maps/math/vide...ups-ten-frames
#19
Old 11-05-2014, 12:15 AM
Guest
Join Date: Mar 2013
Posts: 4,194
Quote:
*****
*****
**

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

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; 11-05-2014 at 12:20 AM. Reason: bad quote tag
#20
Old 11-05-2014, 12:25 AM
Guest
Join Date: Mar 2007
Location: Miskatonic University
Posts: 10,269
Alternate way of looking at it: numbers whose representation in tally marks only contains sets with a diagonal slash.

Quote:
Originally Posted by Jragon View Post
15 + 7 = 15 + (5 + 2) = 20 + 2 = 20
22

The point is to know what you're doing, not get the right answer

Last edited by Jragon; 11-05-2014 at 12:27 AM.
#21
Old 11-05-2014, 01:24 AM
Guest
Join Date: Jul 2005
Location: Minnesota
Posts: 14,294
Quote:
Originally Posted by sbunny8 View Post
Umm, no.
Then umm take it up with Eureka math because their answer key was putting only equations adding a number to a 5 in the mentally visualized 5 group.
#22
Old 11-05-2014, 02:11 AM
Guest
Join Date: Dec 2010
Posts: 6,077
Quote:
Originally Posted by robert_columbia View Post
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.
They could have taken the opportunity to teach p-adic numbers. To negate a p-adic number, you don't just stick a minus sign in front. You take the complement of each digit (with respect to the base-1) and then add 1. So:
...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's-complement representation, which is how basically every computer stores integers.
#23
Old 11-05-2014, 03:44 AM
Guest
Join Date: Mar 2007
Location: Miskatonic University
Posts: 10,269
Quote:
Originally Posted by Inner Stickler View Post
Then umm take it up with Eureka math because their answer key was putting only equations adding a number to a 5 in the mentally visualized 5 group.
Well, that's certainly dumb terminology for a sound concept.
#24
Old 11-05-2014, 09:00 AM
Member
Join Date: Mar 2002
Location: Trantor
Posts: 11,219
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 non-commutative or non-associative systems.

To me, the 5-group is subgroup of symmetries of a regular pentagon consisting of the rotations, of which there are 5 (including the one by 0 degrees).
#25
Old 11-05-2014, 11:16 AM
Charter Member
Moderator
Join Date: Jan 2000
Location: The Land of Cleves
Posts: 73,064
I prefer to think of that group as the integers mod 5.
#26
Old 11-05-2014, 02:39 PM
Guest
Join Date: Nov 2009
Location: Eugene, Oregon
Posts: 1,030
Quote:
Originally Posted by Jragon View Post
Alternate way of looking at it: numbers whose representation in tally marks only contains sets with a diagonal slash.
Yes, tally marks occurred to me too. Look at it this way: If you're an adult who already understands tally marks, then five-groups are pretty much the same thing but shown in a different way.

Quote:
Originally Posted by Jragon View Post
The point is to know what you're doing, not get the right answer.
That's true. You can guess the right answer without having a clue about how to do the problem and that doesn't mean you should get points for learning math.

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.
#27
Old 11-05-2014, 05:50 PM
Guest
Join Date: Mar 2013
Posts: 4,194
Here's some 5 group cards, aka dot cards.

http://teacherspayteachers.com/P...ivities-766067

You can see cards for 6,7, 9 and 15, without having to log in .

Last edited by Isilder; 11-05-2014 at 05:51 PM.
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -5. The time now is 05:00 PM.

Copyright © 2017
Best Topics: pure price scion certified letter gouda rind safelite windshield quality retroactive cobra buy liquid nitrogen keurig symbols first alarm fire ms or ma does alcohol sterilize raccoons trash cans too many mushrooms unshelled pumpkin seeds peanut coke bread heel old library card jatech door tammy haynes is co flammable ass dimple boeing 747 mpg beard waxing horse gallop speed sideways outlet crispy apples frankenstein's head british salute bald hipsters hobbits ears kiss bicep what does the iron cross represent moving to ashland oregon how do loaded dice work how to kill yourself with a shotgun internet explorer has closed this webpage to help protect your computer pt cruiser consumer reports bachelor of science in engineering technology salary smelly eyes in humans how long does it take for your stomach to empty cite dsm 5 mla we are all living in america what time does the mail come in my area what happens if you get the wrong blood how to kill pigeon compound w white buildup how much was a guinea worth difference between 215 and 225 tires cork stuck in bottle can you buy chloroform brokeback mountain ending meaning what is the first monotheistic religion get high off pseudoephedrine drywall sanding sponge home depot why do you mount a horse from the left is it weird to like pain how to pronounce the last name ng does an s video cable carry sound usps insurance restricted delivery vomiting after drinking water on empty stomach barry bonds arm guard snatch all bets are off