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I'm not quite sure why everyone seems to be having so much difficulty doing this, but then again this is one of the tricks I sort of taught myself/worked out over time to speed up mental arithmetic, so I'm used to what they're talking about.

Basically, you first work out what value is required to increase one of the numbers in the sum to the nearest ten.

so to bring 26 up to 30 you need 4.

this 4 has to come from somewhere, so it's taken from the other number: 17-4=13, and so the sum becomes 30+13 rather than 26+17; a far simpler looking sum.

It's a method to turn scary looking sums into easier looking sums, and the fact that you're all lining up to mock common core (whatever the hell that is) based on a single excerpt from an exercise book (not exactly known for being amazing) is kind of amusing.

Maybe, but I think that whole way of explaining it is incredibly confusing.

Its probably easier for people to come up with their own way of quick addition that makes sense to them. Maybe teach a few easy shortcut methods but nothing complex like what this abomination is.

 Frazzled wrote:
How would you do this with 27+18?

I might be late to the party, your example would work to the tune of:

18 is 15+3
So 27+3 = 30
30 + 15 =45
so 27+ 18 = 45.

It's a very roundabout way of just not having kids memorize anything bigger than 10s. I think. I get it, but it's just lazy.

 Grey Templar wrote:
Maybe, but I think that whole way of explaining it is incredibly confusing.

Its probably easier for people to come up with their own way of quick addition that makes sense to them. Maybe teach a few easy shortcut methods but nothing complex like what this abomination is.

It's not complex though! It's an incredibly simple method, it's just that the explanation in that book is completely ridiculous and presumably relies on knowledge of what some of the terms mean.

It might not actually be hard for kids to learn though. Keep in mind that we are looking at it as people that already know how to do it and who have our own way of doing this in our heads.

So maybe for somebody that has never done any math this is actually an easier way to learn the concepts if you have nothing else to build on.

I'm no educator, so this is just speculation.

The way Nevelon explained it makes sense and seems pretty intuitive, but the way they laid it out in the image in the first post is horrible.

How would you do this with 27+18?

I *kind* of get the theory.

But....why wouldn't you just break it down in your head into two problems: 20+10, and then 7+8, and then quick add 30+15 to get 45?

Based on the method presented by the OP, shouldn't it be like this?

= 27 + 18
= 27 + (3 + 15)
= 30 + 15
= 45 QED

I have never done this with addition though, I was taught to just 'know' it by doing 1000 questions back in grade school.

I do use a varation of this method for power multiplication though, for example

= 27^2
= (25 +2)^2
= (625 + 100 + 4)
= 729

Through this method you can do power (2) or even (3) on your head.

I actually do this in my head all the time.

 SlaveToDorkness wrote:
I actually do this in my head all the time.

sorta in the same boat, that initial explanation was kinda crap though

I just think of it as trying to simplify algebra... I'm weird and lazy, and kinda do that method naturally on top of the stacking method...

37+45...
I don't want to do those numbers so:

37+45= x = (37-1) + (45+1)

30
+ 40
+ (6+6) = 82.

Yay. Math complete.

I could figure out what the original example was saying, and I see why they're framing it in that way, and I even think for some kids it can be a good alternate method to double digit addition if they're struggling (though it should be set out a little more clearly).

But for most people I think it's just a really roundabout way of handling the issue and it surprises me that it's presented as a first approach. I mean, what's wrong with;
27 + 18
27 + 10 + 8
37 + 8
45

 Frazzled wrote:
How would you do this with 27+18?

Since 7 + 3 = 10, you add 3 to 27 (giving 30) and subtract 3 from 18 (giving 15).
30 + 15 = 45.

The smart way to teach this would be with pictures.
27 + 18: ooooooo oooooooo oooooooooo + oooooooooo oooooooooo To fill that top row and make a nice block of tens, you take three from the right block and give them to the left block: (27+3) + (18-3) oooooooooo ooooo oooooooooo + oooooooooo oooooooooo Then you've got four lots of ten and one lot of five: 45

 chromedog wrote:
But I don't use it for arithmetic in general. I was taught to determine the result doing the "working" in my head. Then they brought in "show working on paper" which I never learned.

I used to get flak for not showing my working, and they always told me that I couldn't get marks for a half-right answer that way. On the other hand, not showing my working meant I could work fast enough to get more marks by doing more questions.

If it ain't broke...

 Piston Honda wrote:
If it ain't broke...

Not broken, but a different way of doing math.

I'd fall asleep in statistics, then get 100s on all the tests and quizzes, while blacking out through half the test.

Calculus made me cry though.

If the practical application is there, it should make it easier. Give examples and make it work for the kids.

 Piston Honda wrote:
If it ain't broke...

I think the problem is that the old way was broken. The old way of teaching maths didn't work in your head. Short addition only works for small numbers. Long addition works fine, but only if you do it on paper. And doing stuff on paper only works if you have some idea of what the outcome should be. My understanding of this is it gives kids a way of understanding the basics when they are not very strong.


Automatically Appended Next Post:

 chromedog wrote:
I was taught to determine the result doing the "working" in my head. Then they brought in "show working on paper" which I never learned.

Not.. showing... working... Who ever taught that needs shooting!

 AlexHolker wrote:

 Frazzled wrote:
How would you do this with 27+18?

Since 7 + 3 = 10, you add 3 to 27 (giving 30) and subtract 3 from 18 (giving 15).
30 + 15 = 45.

The smart way to teach this would be with pictures.
27 + 18: ooooooo oooooooo oooooooooo + oooooooooo oooooooooo To fill that top row and make a nice block of tens, you take three from the right block and give them to the left block: (27+3) + (18-3) oooooooooo ooooo oooooooooo + oooooooooo oooooooooo Then you've got four lots of ten and one lot of five: 45

 chromedog wrote:
But I don't use it for arithmetic in general. I was taught to determine the result doing the "working" in my head. Then they brought in "show working on paper" which I never learned.

I used to get flak for not showing my working, and they always told me that I couldn't get marks for a half-right answer that way. On the other hand, not showing my working meant I could work fast enough to get more marks by doing more questions.

When they are teaching this, they do use a lot of pictures. And stacking blocks. The concept is stack 10 blocks to get a tower, each tower is ten, count by tens.

When they are teaching this, they do use a lot of pictures. And stacking blocks. The concept is stack 10 blocks to get a tower, each tower is ten, count by tens.

I nearly dropped out in high school because it was so childish. I think if someone pulled out BLOCKS I would have just started throwing desks through windows.

Seriously? Considering everyone has a cellphone with a calculator we're flying butt first into Kafka land. Just at my desk I have two calculators, two phones with calculators and excel with with some serious programs written in it. More importantly I can shout out and have an associate figure it for me.

 Steve steveson wrote:
[
I think the problem is that the old way was broken. The old way of teaching maths didn't work in your head. Short addition only works for small numbers. Long addition works fine, but only if you do it on paper. And doing stuff on paper only works if you have some idea of what the outcome should be. My understanding of this is it gives kids a way of understanding the basics when they are not very strong.

I respectfully disagree. In order to do this, you have to remember three operators and, what, five operands? subtraction, addition, and then addition, and 26, 17, 4, 30, and 13.

Using the old (sane) way, you'd only need to do 26 + 7, and then 33 + 10. Two operators, and four operands, but one of them is a ten you didn't have to do sketchy math to get, and none of them are subtraction, so you can teach it to kids in a way that they don't need to know basic subtraction to get.

EDIT: Added the 30 to the top example. It's intermediary, but I included the 33 so to be fair I need to add it there too.

I... My mind....

I may have been working hard today, but even if i hadnt that would still have slagged my braincells.
Why is that gak being taught, and who is mad enough to teach it?

Also, what wrong with the good old way of doing sums.

The old way often involved not actually learning how to do sums, or any math for that matter, It's just memorizing tables. Kids know the answers because they have repeated them often enough, but they might not know why that is the answer.

Coming up with ways to teach stuff that actually lets kids understand and do the steps in their heads is always a positive. That's the best way to learn: don't teach them the answers, teach them how to find the answers. And base 10 is a good way of doing that, i play Warmahordes and when I roll 5 D6 I basically do exactly this.

 d-usa wrote:
The old way often involved not actually learning how to do sums, or any math for that matter, It's just memorizing tables. Kids know the answers because they have repeated them often enough, but they might not know why that is the answer.

Coming up with ways to teach stuff that actually lets kids understand and do the steps in their heads is always a positive. That's the best way to learn: don't teach them the answers, teach them how to find the answers. And base 10 is a good way of doing that, i play Warmahordes and when I roll 5 D6 I basically do exactly this.

Exalted. Understanding is the true goal of education after all.

 sebster wrote:
I could figure out what the original example was saying, and I see why they're framing it in that way, and I even think for some kids it can be a good alternate method to double digit addition if they're struggling (though it should be set out a little more clearly).

But for most people I think it's just a really roundabout way of handling the issue and it surprises me that it's presented as a first approach. I mean, what's wrong with;
27 + 18
27 + 10 + 8
37 + 8
45

It appears that they are trying to stay away from having to carry any 1's over. 8+7 = 5 carry the 1 for 15. 30+15 is just 3+1 in the tens column and 0+5 in the ones column, so much easier to do in your head I suspect.

 daedalus wrote:

 Steve steveson wrote:
[
I think the problem is that the old way was broken. The old way of teaching maths didn't work in your head. Short addition only works for small numbers. Long addition works fine, but only if you do it on paper. And doing stuff on paper only works if you have some idea of what the outcome should be. My understanding of this is it gives kids a way of understanding the basics when they are not very strong.

I respectfully disagree. In order to do this, you have to remember three operators and, what, five operands? subtraction, addition, and then addition, and 26, 17, 4, 30, and 13.

Using the old (sane) way, you'd only need to do 26 + 7, and then 33 + 10. Two operators, and four operands, but one of them is a ten you didn't have to do sketchy math to get, and none of them are subtraction, so you can teach it to kids in a way that they don't need to know basic subtraction to get.

EDIT: Added the 30 to the top example. It's intermediary, but I included the 33 so to be fair I need to add it there too.

Without knowing the full details of the concept I can only assume that it makes more complex maths easier to understand later on. It's the same with "chunking" which is how they teach division in the UK now.

The way they used to teach maths was stupid. Multiplication tables and lots of "Its this way because it is". Most of the "old ways" are from the days when the world relied on rooms full of clerks doing maths on paper using slide rules and long working.


Automatically Appended Next Post:

 Frazzled wrote:

When they are teaching this, they do use a lot of pictures. And stacking blocks. The concept is stack 10 blocks to get a tower, each tower is ten, count by tens.

I nearly dropped out in high school because it was so childish. I think if someone pulled out BLOCKS I would have just started throwing desks through windows.

Seriously? Considering everyone has a cellphone with a calculator we're flying butt first into Kafka land. Just at my desk I have two calculators, two phones with calculators and excel with with some serious programs written in it. More importantly I can shout out and have an associate figure it for me.

Far to many people struggle with maths even at university level because they use a calculator and rely on it without being able to sense check with ballpark figures. You've still got to be able to do metal arithmetic.

 Frazzled wrote:

When they are teaching this, they do use a lot of pictures. And stacking blocks. The concept is stack 10 blocks to get a tower, each tower is ten, count by tens.

I nearly dropped out in high school because it was so childish. I think if someone pulled out BLOCKS I would have just started throwing desks through windows.

Seriously? Considering everyone has a cellphone with a calculator we're flying butt first into Kafka land. Just at my desk I have two calculators, two phones with calculators and excel with with some serious programs written in it. More importantly I can shout out and have an associate figure it for me.

When you are teaching math to Kindergartners through second graders blocks are a valid teaching tool. Which is the level of math we are talking about here. I have no idea how they are teaching high school math these day, I presume it is not with blocks.

I remember an old rule of thumb: You only need to be able to do the last two years worth of math, you can use tools for anything beyond that. At some point you no longer need to be able to do basic math on a daily basis. As you point out, there are calculators for that. But you need to have mastered it before you hand off the work to machines.

 Steve steveson wrote:

 daedalus wrote:

 Steve steveson wrote:
[
I think the problem is that the old way was broken. The old way of teaching maths didn't work in your head. Short addition only works for small numbers. Long addition works fine, but only if you do it on paper. And doing stuff on paper only works if you have some idea of what the outcome should be. My understanding of this is it gives kids a way of understanding the basics when they are not very strong.

I respectfully disagree. In order to do this, you have to remember three operators and, what, five operands? subtraction, addition, and then addition, and 26, 17, 4, 30, and 13.

Using the old (sane) way, you'd only need to do 26 + 7, and then 33 + 10. Two operators, and four operands, but one of them is a ten you didn't have to do sketchy math to get, and none of them are subtraction, so you can teach it to kids in a way that they don't need to know basic subtraction to get.

EDIT: Added the 30 to the top example. It's intermediary, but I included the 33 so to be fair I need to add it there too.

Without knowing the full details of the concept I can only assume that it makes more complex maths easier to understand later on. It's the same with "chunking" which is how they teach division in the UK now.

The way they used to teach maths was stupid. Multiplication tables and lots of "Its this way because it is". Most of the "old ways" are from the days when the world relied on rooms full of clerks doing maths on paper using slide rules and long working.

I hated the rote memorization of multiplication tables. I never got the "this way because it is" bit though. When I was first taught the concept of multiplication, it was with stacks of boxes in a grid. 1x8 was eight boxes in a column, 2x8 was two sets of eight boxes in a column. It was practical and made sense. Nowadays, I multiply larger numbers in my head because I factor out and multiply the smaller numbers until I get one side to a prime number, and then just worry about multiplying that. 26*16 is much easier as 52*8, and even easier as 104*4, not to mention as 208*2. The problem is that no one teaches things that way, at least, not directly.

I'll give you that their way does look like it could pave the way for algebra later, but I think they should really introduce those concepts earlier. There's no reason, as long as you're going out of your way to offhandedly introduce mathematical properties in a subtle and convoluted way, that you can't just throw in a y on the other side and call it a day. At least then anyone who knows higher math could look at it and more easily figure out what they're trying to do. As it stands now, I can't imagine many parents being able to easily help their kids with their homework if they need it.

Automatically Appended Next Post:

 Frazzled wrote:

When they are teaching this, they do use a lot of pictures. And stacking blocks. The concept is stack 10 blocks to get a tower, each tower is ten, count by tens.

I nearly dropped out in high school because it was so childish. I think if someone pulled out BLOCKS I would have just started throwing desks through windows.

Seriously? Considering everyone has a cellphone with a calculator we're flying butt first into Kafka land. Just at my desk I have two calculators, two phones with calculators and excel with with some serious programs written in it. More importantly I can shout out and have an associate figure it for me.

Far to many people struggle with maths even at university level because they use a calculator and rely on it without being able to sense check with ballpark figures. You've still got to be able to do metal arithmetic.

Maths are so metal.

As someone who teaches maths (sometimes!) and is trained to do it, the "old sane way" works pretty well for a lot of kids. The problem in Maths is that sometimes you hit a kid who just "can't do it" using your explanation. It makes no sense to them, they don't get it, it's a brick wall. A poor educator decides the kid is dumb, and leaves it there. A good educator tries a range of different approaches and explanations. I actually LIKE finding stuff like this in maths books because it gives me another tool for cramming maths into kid's heads. If it works for a kid, I don't care if I find it crazy or overly complex- if it gets them to the next stage, I am generally happy. As their confidence builds they generally do learn how to do things in other ways, but overcoming that initial crunch can be a big problem.

That said, I am against any fixed policy that tells me how I have to teach. I am the professional, trained person in the classroom with the kid in front of me. I'm really motivated to help them understand (nothing so rewarding as a lightbulb moment for an educator). Just give me the tools and let me pick which ones are appropriate- if the ones I'm using don't work, I'll start using others.

The problem with talking about education is that people form their views on it primarily when they are kids and have an even more self orientated view on life than other humans. A lot of common wisdom works for a majority of kids, and the much maligned other techniques are for helping people who think in a different way.

Edit: And as a maths teacher, I prefer it when parents DON'T help the kid with their homework. Notify me of the difficulty (or let the kid do it) but helping is often not helping in those situations. The kid needs to deal with it themselves, because otherwise they will not develop independence.

"Throwing a y" in is a good way to totally paralyse weak students as well. But my main point is that there's no "one best way" to explain anything.

One thing to also keep in mind:

I've seen posts like OPs all over my Facebook lately. And it's always shared by "common core is socialist Obama math" folks getting it from "common core is the antichrist government brainwashing our children" groups and websites.

So I always accept that there is a very real possibility that the stuff posted may just be a common core concept presented in the most difficult backwards way possible to make common core look worse than it actually is.

We don't even have a source of where that picture came from, what grade level it is supposed to be taught to, and where in Common Core it is actually found it.

 Da Boss wrote:
As someone who teaches maths (sometimes!) and is trained to do it, the "old sane way" works pretty well for a lot of kids. The problem in Maths is that sometimes you hit a kid who just "can't do it" using your explanation.

Thats what the taser is for.

If only Fraz, if only.