# Common Core math problem: what is a "Mentally Visualized 5-Group"? **URL:** \ **Category:** Factual Questions\ **Created:** [November 4, 2014, 7:59pm UTC](https://boards.straightdope.com/t/common-core-math-problem-what-is-a-mentally-visualized-5-group/703663 "2014-11-04T19:59:25Z")\ **Posts on this page:** 7\ **Page:** 2
**Author:** ![Inner\_Stickler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/inner_stickler/32/318_2.png) [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)\ **Post date:** [November 5, 2014, 6:24am UTC](https://boards.straightdope.com/t/common-core-math-problem-what-is-a-mentally-visualized-5-group/703663/21 "2014-11-05T06:24:48Z")
> [@sbunny8](#): > > 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. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 5, 2014, 7:11am UTC](https://boards.straightdope.com/t/common-core-math-problem-what-is-a-mentally-visualized-5-group/703663/22 "2014-11-05T07:11:09Z")
> [@robert\_columbia](#): > > 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. ---
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [November 5, 2014, 8:44am UTC](https://boards.straightdope.com/t/common-core-math-problem-what-is-a-mentally-visualized-5-group/703663/23 "2014-11-05T08:44:57Z")
> [@Inner\_Stickler](#): > > 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. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [November 5, 2014, 2:00pm UTC](https://boards.straightdope.com/t/common-core-math-problem-what-is-a-mentally-visualized-5-group/703663/24 "2014-11-05T14:00:58Z")
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). ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 5, 2014, 4:16pm UTC](https://boards.straightdope.com/t/common-core-math-problem-what-is-a-mentally-visualized-5-group/703663/25 "2014-11-05T16:16:19Z")
I prefer to think of that group as the integers mod 5. ---
**Author:** ![sbunny8](https://avatars.discourse-cdn.com/v4/letter/s/c77e96/32.png) [@sbunny8](https://boards.straightdope.com/u/sbunny8)\ **Post date:** [November 5, 2014, 7:39pm UTC](https://boards.straightdope.com/t/common-core-math-problem-what-is-a-mentally-visualized-5-group/703663/26 "2014-11-05T19:39:23Z")
> [@Jragon](#): > > 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. > [@Jragon](#): > > 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. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [November 5, 2014, 10:50pm UTC](https://boards.straightdope.com/t/common-core-math-problem-what-is-a-mentally-visualized-5-group/703663/27 "2014-11-05T22:50:35Z")
Here’s some 5 group cards, aka dot cards. > **[Large 5-Group Cards for Fluency Activities](https://www.teacherspayteachers.com/Product/Large-5-Group-Cards-for-Fluency-Activities-766067)** > > Large 5-group cards for fluency flashes. If you are interested in more fun, engaging versions of these cards (with seasonal clipart instead of the dots), you may wish to purchase my seasonal 5-Group Cards.Enjoy! You can see cards for 6,7, 9 and 15, without having to log in . [Previous page](https://boards.straightdope.com/t/common-core-math-problem-what-is-a-mentally-visualized-5-group/703663.md?page=1)