U.S. Traditional Subtraction
(Standard)
U.S. traditional subtraction (standard) is familiar to most adults and
many children. A person using this algorithm subtracts from right to left,
one place-value column at a time, regrouping as necessary.
The traditional method for teaching this algorithm is to begin with
concrete models (such as base-10 blocks) and then gradually move toward
the use of symbols (that is, numerals) only.
Build Understanding
Subtraction
Write the following number on the board (leaving out the comma and adding
a fair amount of space between the digits): 28,143. (Fifth and sixth grade
students might be ready for a larger number, such as 5,092,411, but, again,
be sure to omit all commas and add extra spacing between the digits.) Ask a
volunteer to read the number. If the student has difficulty, ask the class what
might be done to make the number easier to read. Elicit from students the
need for one or more commas, and have another volunteer label each place
value with a letter abbreviation (Th, H, T, or O) above each digit.
Using page 29, explain that with this method of subtracting, students will
begin with the place value on the far right—the ones. Use questions like the
following to guide students through the examples:
• What are the first numbers you will work with? (the ones)
• As you study the problem, how many times do you think you will have
to rename one of the digits?
• How many digits do you think might be in the answer?
Error Alert Watch for students who write the regrouped number over the
correct place-value column but forget to cross out the original number. Keep in
mind, however, that some students are able to regroup correctly without the
aid of visual reminders.
Check Understanding
Make sure students understand what to do when they need to regroup a
place value that is a zero. Write the following problem vertically on the board:
701 − 358. Make sure students understand that they must actually regroup
the tens place two times. Have a volunteer work through the problem out
loud while you write on the board what the student dictates. When you are
reasonably certain that most of your students understand the algorithm,
assign the “Check Your Understanding ” exercises at the bottom of page 29.
(See answers in margin.)
1. 574
2. 741
3. 266
4. 6,339
5. 4,024
Copyright © Wright Group/McGraw-Hill
Page 29
Answer Key
6. 49
7. 22,908
8. 2,746
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Teacher Notes
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Name
Date
Time
FOCUS
ALGORITHM
U.S. Traditional Subtraction (Standard)
Start with the ones column, and subtract one column at a time.
Regroup (rename) as necessary.
Example 1
Think: Can I subtract 9 ones from 5 ones? (no)
Regroup the 5 tens and 5 ones as 4 tens and 15 ones.
Then subtract 9 ones from 15 ones.
4 15
855
-439
416
Subtraction
Think: Can I subtract 3 tens from 4 tens? (yes)
Subtract 3 tens from 4 tens.
Then subtract the hundreds.
416 is the difference.
Example 2
Copyright © Wright Group/McGraw-Hill
Think: Can I subtract 6 ones from 2 ones? (no)
Regroup the 7 hundreds and 0 tens as 6 hundreds
and 10 tens. Then regroup the 10 tens and 2 ones
as 9 tens and 12 ones.
Then subtract 6 ones from 12 ones.
9
6 10 12
702
-586
116
Think: Can I subtract 8 tens from 9 tens? (yes)
Subtract 8 tens from 9 tens.
Then subtract the hundreds.
116 is the difference.
Check Your Understanding
Solve the following problems.
1. 601 − 27
2. 815 − 74
3. 529 − 263
4. 7,195 − 856
5. 9,113 − 5,089
6. 1,248 − 1,199
7. 32,084 − 9,176
8. 15,643 − 12,897
Write your answers on a separate sheet of paper.
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