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domestic_engineer

Math: Left to Right, right to left

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While watching James Tanton's Exploding Dots, he repeats the idea that all of life has us going from left to right, but with so much of math it is taught as right to left.

I'm a devoted RightStart user, so I'm familiar (and now comfortable) with left to right subtraction.  But now, I've got a kiddo who wants to do multi-digit addition from left to right, and I have no good reason not to accommodate this.  Is there a neat, compact notation to deal with left to right addition?   Right now, the best I've got it to make a two-line answer similar to Tanton's demonstrations. It works, but it's not too elegant.  Perhaps look ahead and draw "reminder dots" before writing any sums, similar to how RS marks up Left-to-Right subtraction?!?! 

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I think left-to-right addition works better with mental math than written, but I'm following to see if anyone else has ideas.  DS does most of his work left-to-right, but he does it in his head.

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My DS also works primarily left to right but in his head. When I make him write his work down he doesn't notate anything besides partial sums and final answers. Is it necessary for your child to notate? Perhaps show a few ways and let your kiddo figure out whatever makes sense.

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If I were doing it, I think I would just work in pencil and erase or cross out as needed:

     182
   +279
   +  45
-------------
     3

     182
   +279
   +  45
-------------
     49      (tens column sums to 19, so I fill in the 9 and change the 3 in the hundreds to 4)

     182
   +279
   +  45
-------------
     506      (ones column sums to 16, so I fill in the 6 and change the 9 in the tens to...uh-oh...I change the 9 to a 0 and change the 4 in the hundreds to a 5)

In the big picture I am working left to right, but there is still a lot of right to left manipulation going on as well.

I agree with others that true left to right is easier mentally.

Wendy

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2 hours ago, daijobu said:

Do you have a link to the Tanton video?

He said it in earlier videos, but this was the most memorable/recent to me ...  (It's within the first 1.5 minutes of the video):  https://gdaymath.com/lessons/explodingdots/5-6-remainders/

It was the most memorable because Yes! I'm always telling this child to read left to right, left to right, left to right.  At this point, I'm guessing it will just be a passing phase until he gets tired of all the erasing, but I do want to validate that what he's doing (i.e., left to right is perfectly fine too.   Messy, but correct.)

Here's Tanton's video for multi digit addition where he compares his algorithm to the traditional algorithm:  https://gdaymath.com/lessons/explodingdots/3-3-optional-traditional-algorithm/

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5 hours ago, Sarah0000 said:

My DS also works primarily left to right but in his head. When I make him write his work down he doesn't notate anything besides partial sums and final answers. Is it necessary for your child to notate? Perhaps show a few ways and let your kiddo figure out whatever makes sense.

At this point, yes, it's important for the child to notate.  We're just starting multi-digit addition and careless addition mistakes are the norm.

1 hour ago, wendyroo said:

If I were doing it, I think I would just work in pencil and erase or cross out as needed:

     182
   +279
   +  45
-------------
     3

     182
   +279
   +  45
-------------
     49      (tens column sums to 19, so I fill in the 9 and change the 3 in the hundreds to 4)

     182
   +279
   +  45
-------------
     506      (ones column sums to 16, so I fill in the 6 and change the 9 in the tens to...uh-oh...I change the 9 to a 0 and change the 4 in the hundreds to a 5)

In the big picture I am working left to right, but there is still a lot of right to left manipulation going on as well.

I agree with others that true left to right is easier mentally.

Wendy

^This is what we started doing, but all the (incomplete)  erasing was driving me a bit batty.  I mean, he was getting the concept (yay!) but the paper was a mess!

We've tried Tanton's technique of noting the sum as 3 | 19 | 16 =4 | 9 | 16 = 5 | 0 | 6 = 506  with pretty decent results.

This afternoon, I tried "previewing" where the explosions/trading will occur and making "reminder tallies" in the appropriate column, but it got a lukewarm reception and still a bit of confusion as to where the reminder tally goes.  Maybe it's really tricky, maybe it's just the initial confusion (like the notation for left-to-right subtraction).  Shrug.  I'm still holding out hope for a glorious, elegant notation to solve all the confusion.  😄

 

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6 hours ago, domestic_engineer said:

At this point, yes, it's important for the child to notate.  We're just starting multi-digit addition and careless addition mistakes are the norm.

^This is what we started doing, but all the (incomplete)  erasing was driving me a bit batty.  I mean, he was getting the concept (yay!) but the paper was a mess!

Does he need to actually write the numbers, or would a different form of "notation" work.  What about if the problem was written fairly large (perhaps on a small white board) and then he used magnetic numbers as the answers.  Then he could plunk down a 3 in a certain column, and then physically swap it out for a 4 if necessary.

Obviously that does not get you to a concise written notation, but it might work in the short term as he further solidifies his understanding.  Ultimately I would try to get him comfortable using the standard algorithm.

Wendy

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Can you have him write the new problem underneath instead of immediately adding it to the column to the left and erasing? It's not compact, but it's essentially what he's doing. It would be about the same as a multiple-digit multiplication problem in writing, which may be too much for him at this point though. 

Using Wendy's example of

     182
   +279
   +  45
-------------
 

he would write down:

    182

+  279

+   45

______

    3

+  19

+   16

______

  4

+ 10

+    6

_____

  506 

 

Edited by beckyjo

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5 hours ago, wendyroo said:

Does he need to actually write the numbers, or would a different form of "notation" work.  What about if the problem was written fairly large (perhaps on a small white board) and then he used magnetic numbers as the answers.  Then he could plunk down a 3 in a certain column, and then physically swap it out for a 4 if necessary.

Obviously that does not get you to a concise written notation, but it might work in the short term as he further solidifies his understanding.  Ultimately I would try to get him comfortable using the standard algorithm.

Wendy

He would love it if he didn't have to write numbers!!  Great idea!  Thanks!

 

Edited by domestic_engineer

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3 hours ago, beckyjo said:

Can you have him write the new problem underneath instead of immediately adding it to the column to the left and erasing? It's not compact, but it's essentially what he's doing. It would be about the same as a multiple-digit multiplication problem in writing, which may be too much for him at this point though. 

Using Wendy's example of

     182
   +279
   +  45
-------------
 

he would write down:

    182

+  279

+   45

______

    3

+  19

+   16

______

  4

+ 10

+    6

_____

  506 

 

Thanks for the idea!  It's a possibility, but it kinda muddies the idea of place value.  And understanding place value is very important in my tiny realm of teaching.

Perhaps if he wrote:

 300

+190

+ 16

-------

 

oooof.... I don't think I like that, especially since this problem would need another layer below what I typed.  This technique would be called "really, really Long addition."   😄 haha.

oh, please let this stage pass by quickly!!!! 😉

 

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On 9/12/2019 at 11:13 PM, domestic_engineer said:

At this point, yes, it's important for the child to notate.  We're just starting multi-digit addition and careless addition mistakes are the norm.

^This is what we started doing, but all the (incomplete)  erasing was driving me a bit batty.  I mean, he was getting the concept (yay!) but the paper was a mess!

We've tried Tanton's technique of noting the sum as 3 | 19 | 16 =4 | 9 | 16 = 5 | 0 | 6 = 506  with pretty decent results.

This afternoon, I tried "previewing" where the explosions/trading will occur and making "reminder tallies" in the appropriate column, but it got a lukewarm reception and still a bit of confusion as to where the reminder tally goes.  Maybe it's really tricky, maybe it's just the initial confusion (like the notation for left-to-right subtraction).  Shrug.  I'm still holding out hope for a glorious, elegant notation to solve all the confusion.  😄

Is there any particular reason why the calculation needs to resolved and stated all in the same line?

Starting with the example of

    182
   279
 +  45, this problem can be solved in stages. Just add by place value where it's most logical to the kid.
   300
    190
+    16, which becomes
   490
+    16, which becomes the total of
  506

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