Download Partial-Sums Addition for Decimals

FOCUS
ALGORITHM
Partial-Sums Addition for Decimals
Addition
Just as they do with whole numbers, problem solvers add decimals by
adding values of digits one place-value column at a time—whether tens or
tenths, hundreds or hundredths, and so on. The partial-sums algorithm
and the column-addition algorithm used for adding multidigit whole
numbers can easily be applied to decimal addition as long as the problem
solver is careful to keep track of the place values—both whole-number and
decimal place values.
Students will feel empowered as they discover that they can apply their
number sense and understanding of whole-number addition to decimal
situations. The key, as with whole-number addition, is to pay attention
to the place values, and consequently the decimal point, in each of the
addends.
Build Understanding
Discuss equivalent decimals like 7.3, 7.30, and 7.300. Then have students
annex zeros to find equivalent decimals for 6.7, 0.4, 0.023, and 9. You may also
want to review the whole-number versions of this algorithm on pages 4–7.
As you work through Example 1 on page 17, point out that the partial sums
should be written with the same number of decimal places as the addend with
the greater (or greatest) number of decimal places. Use questions like the
following to guide students through the examples:
• Does it matter which place-value column you add first? (no)
• In Example 1, why are 6 ones written as 6.000? (Zeros are added to show
the same number of decimal places as the addend with the greater number
of decimal places. In this example, both 4.658 and 2.761 happen to have
the same number of decimal places—three.)
Error Alert
Watch for students who do not write all the partial sums and
the answer with the same number of decimal places. If students have difficulty
with this, they may first need to review place value.
Check Understanding
1. 6.166
Write 5.298 + 3.44 on the board. Have a volunteer work the problem using
the partial-sums algorithm. Encourage the student to “ narrate” his or her
thought process. Encourage the class to ask questions, and guide the volunteer
in answering as necessary. When you are reasonably certain that most of your
students understand the algorithm, assign the “Check Your Understanding”
exercises at the bottom of page 17. (See answers in margin.)
2. 67.84
3. 1.002
4. 0.034
5. 6.291
Copyright © Wright Group/McGraw-Hill
Page 17
Answer Key
6. 18.029
7. 102.02
8. 5.914
16
Teacher Notes
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Name
Date
Time
FOCUS
ALGORITHM
Partial-Sums Addition for Decimals
Use what you already know about adding whole numbers.
Add one place-value column at a time.
→
→
→
→
→
4.658
+ 2.761
6.000
1.300
0.110
+ 0.009
7.419
→
→
→
→
→
9.682
+ 1.506
10.000
1.100
0.080
+ 0.008
11.188
Example 1
Add
Add
Add
Add
Add
the
the
the
the
the
ones.
tenths.
hundredths.
thousandths.
partial sums.
→
→
→
→
→
(4.000 + 2.000)
(0.600 + 0.700)
(0.050 + 0.060)
(0.008 + 0.001)
(6.000 + 1.300 + 0.110 + 0.009)
Copyright © Wright Group/McGraw-Hill
Example 2
Add
Add
Add
Add
Add
the
the
the
the
the
ones.
tenths.
hundredths.
thousandths.
partial sums.
→
→
→
→
→
(9.000 + 1.000)
(0.600 + 0.500)
(0.080 + 0)
(0.002 + 0.006)
(10.000 + 1.100 + 0.080 + 0.008)
Addition
Remember to pay attention to the place values of the addends
to record the decimal point in the sum.
Check Your Understanding
Solve the following problems.
1. 3.441 + 2.725
2. 60.45 + 7.39
3. 0.906 + 0.096
4. 0.006 + 0.028
5. 2.4 + 3.891
6. 12.34 + 5.689
7. 89.22 + 12.8
8. 5 + 0.034 + 0.88
Write your answers on a separate sheet of paper.
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Student Practice
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