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Hi, My DS7 is at lesson 91 in Level C, multi-digit subtraction. He did very well in the previous lessons using the abacus and symbols to subtract, and figured out trading quickly.
But - he wants to do what I was always taught - start subtraction from the right, trading as necessary as you go along. It seems more convoluted to start from the left. For example, the book says to compare the numbers in each place value ahead of time to determine if a trade will be necessary. But, if two numbers are the same, you might now know right off whether a trade will be needed.
For example: 3453 - 1259
If I just compare place values, I don't need a trade to perform subtraction in the tens, but because I will need a trade for the ones, I do end up needing a trade for the tens. Does that make sense?
I guess my real question is - what is the value in subtracting left to right?
Thanks so much,
Linda
Hello Linda,
Thank you for your question.
I as understand it. The method taught in Level C is the preferred method to be taught in this program.
The fact is subtracting from right to left (the way we were taught) is not the only way to teach multi-digit subtraction. In fact, many other countries teach their kids to subtraction from left to right.
The concept behind it has some interesting reasons.
First, when we add we add from right to left, and we trade up.
Being that subtraction is the opposite of addition and we are trading down, it makes sense to be going from left to right.
Second reason is, going from left to right you can spot your mistake in the place value column it is in sooner then having to go through the whole problem and doing borrowing.
Third reason is, it shows the child that there is more than one way to solve a math problem.
Fourth reason is, they will be more likely to be able to mentally compute the numbers learning it this way, as they will go from the higher place value to the lower place value.
The following is a note that Dr. Cotter has made for parents where this program is taught in a classroom environment. You may find it helpful.
SIMPLIFIED SUBTRACTION
The children in the second grade mathematics program are learning to
subtract 4-digit numbers. They are using methods that may be new to
you, in which the work proceeds from left to right like division, rather
than right to left like addition. The methods are explained below.
2-Digit Numbers First the children learned to subtract mentally 2-digit numbers. In everyday
life most people do not reach for paper and pencil or even a calculator
for such computations; instead, they do them in their heads.
There are many good shortcuts that can be used; however, a good general
procedure is the following. To subtract 86 – 52, think 86 – 50, which is 36;
then 36 – 2, giving 34. Next try 86 – 57; again think 86 – 50, which is 36;
then 36 – 7, giving 29.
4-Digit Numbers Before the children attempted subtraction on paper, they worked extensively
with written symbols and abacuses to understand the process.
According to research, it is easier for most children to complete the work
for trading, or borrowing, before performing the actual subtracting.
In the following example two trades are necessary.
8572
-6913
First consider the thousands; is a thousand going to be needed for a trade
to get more hundreds. Yes, because 913 is more than 572, 1 thousand will
be traded for 10 hundreds. Indicate it by underlining the 8.
8572
-6913
8572
-6913
Next look at the hundreds; is a hundred needed to make more tens. No,
because 13 is less than 72, a trade is not necessary.
Finally, consider the tens; will 1 ten need to be traded to get 10 more ones.
Yes, a ten is must be traded because 3 is more than 2. Underline the 7 as
shown above.
Now the actual subtraction can take place; 8 thousand – 6 thousand = 2
thousand, but write 1 in the thousand place. See below. Note that the line
under the number indicates subtracting an extra 1. Next 15 hundreds – 9
hundreds is 6 hundreds; write 6. Continue with 7 tens – 1 ten = 6 tens, but
7 is underlined so write 5. For the ones, 12 – 3 = 9.
8572
– 6913
1
8572
– 6913
16
8572
– 6913
165
8572
– 6913
1659
4808
– 3457
1
4808
– 3457
1351
8002
– 4567
3
8002
– 4567
3435
I think I get it now! Using the poster's example
3453
-1259
__________
It's not immediately obvious you need to trade in the 100s column b/c there are 5s in the tens column. But, in that lesson, it mentions letting the child discover the following method: that 59 is more than 53. Looking at it that way, it's obvious you need to trade in the 100s place.
Is that right?
Hello Captuhura,
That is correct!
That is one of several ways you can see that you need to trade, but that is by far the easiest way to see it, well that's my opinion.
Thank you for giving your child a RightStart in Math,
Carissa
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