Download Partial-Differences Subtraction

Partial-Differences Subtraction
Partial-differences subtraction builds on a skill most people use daily:
reading from left to right. The person using this algorithm begins at
the far-left side of the problem and subtracts the subtrahend (the lesser
number) from the minuend (the greater number) one place-value column
at a time until the final difference between the two numbers is reached.
Most students find it helpful to see the subtrahend expressed in expanded
notation, and many students find it natural to move from left to right
when performing mathematical operations.
Build Understanding
Subtraction
Review expanded notation: Write 2,638 on the board and explain how to write
the number in expanded form (2,000 + 600 + 30 + 8). Have students expand
the following numbers at their desks: 318; 1,967; 8,049. Ask volunteers to
write the answers on the board, and, if necessary, model a few of the numbers
using base-10 blocks.
Note: If students seem confused when one or more of the place values are zero,
explain two different ways they can handle the situation: Using 8,049 as an
example, students can expand the number either as 8,000 + 0 + 40 + 9 or as
8,000 + 40 + 9.
Using page 31, explain that with this method of subtracting, students will
begin on the far-left side of the problem and subtract one place-value column
at a time until they find the final difference between the minuend (the top
number) and the subtrahend (the bottom number). Use questions like the
following to guide students through the example (and through other examples
you provide):
• Which number will be broken down into its individual place values?
(the subtrahend)
• What is the greatest place value in the subtrahend?
• How will you subtract the second-greatest place value in the subtrahend?
(Write it in expanded notation and then subtract it from the minuend.)
1. 223
• What is the final difference between the minuend and the subtrahend?
Error Alert Make sure students understand that the second subtracted
number (100 in the example on page 31) has been “pulled out” from the
original subtrahend. If necessary, have students write each subtrahend in
expanded notation and then draw an arrow from each part of the expanded
notation to its counterpart in the recorded algorithm (the “solution column”).
2. 566
3. 361
Check Understanding
4. 211
Write 213 − 148 on the board. Have three volunteers take turns solving
each step of the problem to help emphasize the fact that three place values
are being subtracted, one at a time, in sequence. Work through as many
problems in this way as necessary until you are reasonably certain that most
of your students understand the algorithm. Then assign the “Check Your
Understanding” exercises at the bottom of page 31. (See answers in margin.)
5. 6,568
6. 768
7. 42,179
Copyright © Wright Group/McGraw-Hill
Page 31
Answer Key
8. 4,449
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Teacher Notes
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Name
Date
Time
Partial-Differences Subtraction
Subtract left to right, one column at a time. In some cases, the
larger number is on the bottom. When this happens and you
subtract, the difference is a negative number.
Example
9,328
- 5,170
First, write or think of 5,170 as
5,000 + 100 + 70 + 0.
(minuend)
(subtrahend)
9,328
- 5,170
Find the total.
→ (4,000 + 200 − 50 + 8) →
Copyright © Wright Group/McGraw-Hill
(9,000
(300
(20
(8
−
−
−
5,000)
100)
70)
0)
→ 4,000
200
→
50
→ 8
→
Multiplication
Subtract the hundreds.
Subtract the tens.
Subtract the ones.
→
→
→
→
Subtract the thousands.
4,158
Check Your Understanding
Solve the following problems.
1. 317 − 94
2. 582 − 16
3. 640 − 279
4. 835 − 624
5. 7,104 − 536
6. 2,952 − 2,184
7. 43,870 − 1,691
8. 15,033 − 10,584
Write your answers on a separate sheet of paper.
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