Carried Numbers

[Fred Van Ackeren]

Hi,
Having scant information on carried numbers I was asked by someone how to they would work for a multiplication problem such as:

574
x823

By applying the basics I decided to “build” the problem in 2 steps. Step 1 will take care of the multiplication with each new carried line above the previous. Then in step 2, add the 3 lines which also has carried numbers.
In such a situation, one has to apply what one knows and hope that it’s presentation is clear to the student. TNs may help in this process as well, such as: Problem solved in 2 steps. And again perhaps one to explain the carried numbers in layers for the multiplication (see example).
There are 2 different ways shown to carry the numbers. The top problem is explained above.
The 2nd (bottom) solution is to add the 2nd carry line [u]under[/u] the 1st, then the 3rd carry line under the 2nd. What you end up with is still 3 carry lines but each “newest” line is kept close to the columns of numbers in the problem making it easier to do the math w/o the interference of previous carried numbers. This way you don’t have to look way at the top then then look way down to align numbers, they're right next to each other.
Lgically, this is the best way I came up with and anxious to hear your comments. TN’s of course will be needed but they don’t need to be long ones, more of identifiers such as “1st carried line”, “2nd carried line”, etc. as in the example.

Thanks,
Fred

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[dworthing]

Could you include a picture of your print?

[dworthing]

There is no print. It's a hypothetical question of the multiplication problem in the post.

[dworthing]

It is difficult to answer hypothetical questions. It is recommended that for multiplication problems with carried numbers we follow the guidelines for carried numbers in addition.

[Fred Van Ackeren]

Hi Dorothy,

Let's begin again. The question is: How are multiple lines of carried numbers in a multiplication problem brailled? You stated: "It is recommended that for multiplication problems with carried numbers we follow the guidelines for carried numbers in addition."

This is fine for basic information, but the problem is that it only pertains to only ONE level of carried numbers. Three numbers multiplied by three numbers will produce THREE levels of numbers to be carried. The addition guideline was the first I consulted and finding it lacking and no other examples I decided to bring it to your attention.

Since I don't have a print copy I created an example, 574 x 823. It is attached as a brailled spatial problem to illustrate carried numbers. I have inserted labels and solved in 2 steps, Step 1: multiplication and Step 2: addition, to demonstrate two distinct types of carried numbers. In theory the carried numbers for addition could have been added as a 4th level but seemed awkward, so I decided to keep them separate and more easily distinguished. The labels could also be used as TNs if needed for an actual text.

I hope I've done a better job explaining, looking forward to your reply.
thanks,
Fred

[Fred Van Ackeren]

I think I still need to see what your print looks like. Could you create it in a word doc?

[Fred Van Ackeren]

Hi Dorothy,
Sorry it took so long to reply, but health and work load have kept me busy. Attached is a .doc showing the solution in 2 steps. If you need anything else let me know.

Thanks,
Fred

[Fred Van Ackeren]

I'm sorry to be so thick about this. In your print version, if this were in a text, would those horizontal separation lines be present, or is this just your print interpretation of what you've done in braille? I would really need to see an actual print expression to offer an opinion. If you feel that your transcription adequately and clearly shows what is taking place in print, then you have probably answered your question.

[dworthing]

Dorothy,

A teacher had requested an explanation after a student had posed the question: "How would I do multiple carried numbers when more than one line is needed? He then submitted the sample problem (which I submitted to you). Evidently the student was concerned when asked to show steps to a solution and was confronted with how to show additional carried lines. The teacher had said the student had a page of 3 and 4 place numbers to be multiplied. They had studied the textbook "Introduction to Braille Mathematics" and found no solution and so posed the question to me. I suggested the format which I conveyed to you for your opinion. Basically, I just needed your input as to the correctness of my response to the teacher/student.

Thanks, Fred

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