CLE and digit sums

[Teek]

I'm having trouble seeing the point of learning digit sums. I was never taught to use them for anything, and did very well in AP maths, both high school and college. CLE seems to talk about them all.the.time. Besides using them for some factors, is it ok to skip it altogether? I'm not convinced they're helpful for things like checking multiplication work, but if your child does learn them for that, or anything else that you feel is helpful, I'd love to hear from you. 

In short, I feel that it's not important overall, but I admittedly am biased as I never used them, andalso don't want to be missing something for my kiddos that has merit without realizing it. :)

[Kiara.I]

Rightstart uses check numbers, is that similar? They're the remainder when dividing by nine, and can be used to check addition, subtraction, multiplication and division. We find them quite useful for that.

 

But a quick Google of digit sums didn't really make it clear whether they're the same thing.

 

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[Teek]

I had never heard the term either, that's why I was taken aback by seeing it so much!  :lol:

 

For CLE a digit sum is the sum of all the digits in a number, and you keep going until you get a single digit. For example:

 

358: 3 + 5 + 8 = 16. Then 1 + 6 = 7.  So the digit sum of 358 is 7.

 

Useful for finding some factors, but they also use it to check multiplication problems by finding the digit sums of different rows of the problem and comparing it to the digit sum of the product. It just confuses my dd, trying to remember which lines to find the sum of, adding all the numbers in her head, making sure the digit sums are correct, etc. Math is a struggle for her in general, and adding all the steps just makes it take 3 times longer than it should. I don't mind doing it if there's a useful application, I'm just not seeing it so far. 

[Kiara.I]

I had never heard the term either, that's why I was taken aback by seeing it so much! [emoji38]

 

For CLE a digit sum is the sum of all the digits in a number, and you keep going until you get a single digit. For example:

 

358: 3 + 5 + 8 = 16. Then 1 + 6 = 7. So the digit sum of 358 is 7.

 

Useful for finding some factors, but they also use it to check multiplication problems by finding the digit sums of different rows of the problem and comparing it to the digit sum of the product. It just confuses my dd, trying to remember which lines to find the sum of, adding all the numbers in her head, making sure the digit sums are correct, etc. Math is a struggle for her in general, and adding all the steps just makes it take 3 times longer than it should. I don't mind doing it if there's a useful application, I'm just not seeing it so far.

Yup, sounds like check numbers.

But CLE has you write the addition of them out? Ugh. RS does them mentally, and you just write the final one digit version.

And then they're used for checking all four basic arithmetic functions, not just multiplication.

 

Using then in a problem looks like this:

https://www.google.ca/search?q=Rightstart+check+numbers&client=ms-unknown&biw=412&bih=652&tbm=isch&prmd=sniv&source=lnms&sa=X&ved=0ahUKEwiG98fe7L3ZAhUW1GMKHXBXBSMQ_AUIESgD#imgrc=MBk-jYDrscg-tM:

(It's a still from a video so I hope the picture works. I'll edit if it doesn't.)

 

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[Teek]

Yup, sounds like check numbers.

But CLE has you write the addition of them out? Ugh. RS does them mentally, and you just write the final one digit version.

And then they're used for checking all four basic arithmetic functions, not just multiplication.

 

Using then in a problem looks like this:

https://www.google.ca/search?q=Rightstart+check+numbers&client=ms-unknown&biw=412&bih=652&tbm=isch&prmd=sniv&source=lnms&sa=X&ved=0ahUKEwiG98fe7L3ZAhUW1GMKHXBXBSMQ_AUIESgD#imgrc=MBk-jYDrscg-tM:

(It's a still from a video so I hope the picture works. I'll edit if it doesn't.)

 

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Thank you! I'll watch the video on check numbers and see if they explain it in a way that makes more sense. CLE doesn't make you write the sums all out, I just wasn't sure if we were talking about the same thing so I wanted to explain what it is in CLE terms. I'd like to find the value in it instead of just teaching it because it's in the books lol. 

[Tanaqui]

Checksums are a good sanity check. When used alongside pre-estimation, they can be faster than checking your answers the other way - laboriously reversing the procedure and working backwards, I mean.

 

And they have some interesting applications in the real world, as well! For example, specialized checksums are used to ensure you've punched in a valid credit card number instead of a not-valid one (they even catch transposition errors), which is an enormous benefit to those of us who purchase things online.

 

Edited February 24, 2018 by Tanaqui

[Joyofsixreboot]

They are a cool trick. I explained to the kids they were leftover from days before easy access to calculators. I gave a quick explanation and moved on. I had kids who liked them and kids who didn't. I didn't grade that.

 

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[Garga]

Yup, sounds like check numbers.

But CLE has you write the addition of them out? Ugh. RS does them mentally, and you just write the final one digit version.

And then they're used for checking all four basic arithmetic functions, not just multiplication.

Using then in a problem looks like this:https://www.google.ca/search?q=Rightstart+check+numbers&client=ms-unknown&biw=412&bih=652&tbm=isch&prmd=sniv&source=lnms&sa=X&ved=0ahUKEwiG98fe7L3ZAhUW1GMKHXBXBSMQ_AUIESgD#imgrc=MBk-jYDrscg-tM:

(It's a still from a video so I hope the picture works. I'll edit if it doesn't.)

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CLE’s digit sums work for all 4 basic functions as well.

 

OP: We did them as part of our CLE lessons, but my son doesn’t ever use them on his own. I think somewhere in the CLE book it said that some people will use them a lot to check themselves, but other people won’t, and using them is optional (other than the lessons where they’re trying to teach it to you.). It seems to me that they teach the concept and then let you decide whether to use it or not.

[scoutingmom]

RightStart calls them check sums. CLE calls them digit sums. They are the same except RightStart says that a checknum of 9 is reduced to 0. CLE allows digit sums of 9 (when crossing out 9's it says to leave one.... so CLE says if the digit sum is 0, it would be 9.) The method is also called casting out nines.

 

Mostly used to check arithmetic. Variations of the idea are used in computers.... checking if the digital memory is working. Checking that a file has not been corrupted etc. Other variations are used to verify that a number is valid... credit card numbers, Social Insurance Numbers, presumably U.S. Social Security Numbers, etc. I think they are used (variations) with codes and cyphers and security systems.

 

Most people never NEED to use them. They are a shortcut except for those specialized applications mentioned.

 

Just a note of interest.... My Mom had a job years ago in England (Pounds and Shillings timeframe, not decimal money) where she had to accurately add columns of money. Check numbers were vital to her job.

 

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[boscopup]

They're more useful for divisibility (like seeing if a number is divisible by 3,6,9).

[KrissiK]

I love CLE math, but the digit sum emphasis drives me insane. I was taught to use the reverse operation to check an answer, so that is what I teach my kids.

 

They're more useful for divisibility (like seeing if a number is divisible by 3,6,9).

I do agree that this is a good use for it, though we don’t even use it for this.

[Teek]

They're more useful for divisibility (like seeing if a number is divisible by 3,6,9).

 

Yeah that's the only use I really see for them to be honest. 

[Teek]

I love CLE math, but the digit sum emphasis drives me insane. I was taught to use the reverse operation to check an answer, so that is what I teach my kids.

 

I do agree that this is a good use for it, though we don’t even use it for this.

 

They do seem to find a way to talk about it as much as possible!  :lol:

[kiana]

It's commonly called casting out nines. But really, it's not that necessary.

 

CLE is designed for people who aren't using technology. Without technology, it makes 100% sense to heavily emphasize them. 

[Teek]

It's commonly called casting out nines. But really, it's not that necessary.

 

CLE is designed for people who aren't using technology. Without technology, it makes 100% sense to heavily emphasize them. 

 

That totally makes sense. Thank you!