Addition of Whole
Numbers and Decimals
Objectives To review place-value concepts and the use of the
partial-sums and column-addition methods.
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Practice
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Game™
Teaching the Lesson
Key Concepts and Skills
• Write numbers in expanded notation. [Number and Numeration Goal 1]
• Use paper-and-pencil algorithms for
multidigit addition problems. [Operations and Computation Goal 1]
• Make magnitude estimates for addition. [Operations and Computation Goal 6]
Key Activities
Students review place-value concepts and
write numbers in expanded notation. They
review addition of whole numbers and
decimals with the partial-sums and columnaddition methods.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 33. Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Addition Top-It
(Decimal Version)
Student Reference Book, p. 333
per partnership: 4 each of the number
cards 1–10 (from the Everything Math
Deck, if available); 2 counters
Students practice place-value
concepts, use addition methods, and
compare numbers.
Math Boxes 2 2
Math Journal 1, p. 34
Students practice and maintain skills
through Math Box problems.
Study Link 2 2
Math Masters, p. 36
Students practice and maintain skills
through Study Link activities.
[Operations and Computation Goal 1]
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Building Numbers with Base-10 Blocks
Math Masters, p. 37
base -10 blocks
Students use base -10 blocks to explore the
partial-sums method of addition.
ENRICHMENT
Using Place Value to Solve Addition
Problems
Math Masters, p. 38
Students apply place-value and addition
concepts to solve problems.
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 142
Students define and illustrate the term
expanded notation.
Key Vocabulary
place value digit algorithm partialsums method place value expanded
notation column-addition method
Materials
Math Journal 1, pp. 32 and 33
Student Reference Book, pp. 13, 14, 28–30,
and 35
Study Link 21
Math Masters, p. 415
slate
Advance Preparation
Plan to spend two days on this lesson. Distribute copies of the computation grid on Math Masters, page 415
for students to use as they do addition problems. Make and display a poster showing expanded notation for a
whole number and a decimal.
Teacher’s Reference Manual, Grades 4–6 pp. 119–122
Lesson 2 2
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Getting Started
Mental Math and Reflexes
Math Message
Read the numbers orally and have students write them in expanded notation on
their slates. Remind students that expanded notation expresses a number as the
sum of the values of each digit. For example, 906 is equivalent to 9 hundreds + 0 tens +
6 ones, and 0.796 is equivalent to 7 tenths + 9 hundredths + 6 thousandths. In expanded
notation, 906 is written as 900 + 6, and 0.796 may be written as 0.7 + 0.09 + 0.006 or
1 +
1 +
1
9 ∗ (_
6 ∗ (_
as 7 ∗ (_
10 )
100 )
1,000 ). Encourage students to write the decimal numbers in
fraction notation. Sample answers are given.
1
35 30 + 5
241 200 + 40 + 1
0.109 1 ∗ (_
10 ) +
1
_
1
1
1
1
_
_
_
_
∗
9 ( 1,000 )
0.35 3 ∗ ( 10 ) + 5 ∗ ( 100 )
0.241 2 ∗ ( 10 ) + 4 ∗ ( 100 ) +
1
1
_
∗
1
(
)
0.708 7 ∗ (_
52 50 + 2
1,000
10 ) +
1
_
∗
8 ( 1,000 )
1
1
_
162 100 + 60 + 2
0.52 5 ∗ (_
10 ) + 2 ∗ ( 100 )
1
1
1
_
_
0.084 8 ∗ (_
0.467 4 ∗ ( 10 ) + 6 ∗ ( 100 ) +
100 ) +
1
_
1
_
∗
4 ( 1,000 )
7 ∗ ( 1,000 )
7,904 7,000 + 900 + 4
Use the information on
Student Reference Book, pages 28–30 to
solve the Check Your Understanding
Problems on the bottom of page 30.
Study Link 2 1
Follow-Up
Have partners discuss their strategies and
identify one thing that they did the same
and one thing that they did differently. Have
volunteers share their findings.
1 Teaching the Lesson
● On
Day 1 of this lesson, students should
complete the Mental Math and Reflexes and
the Math Message. They should review and
discuss the partial-sums addition method.
▶ Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Student Reference Book, pp. 28–30)
● On
Day 2 of this lesson, do the Study
Link Follow-Up. Then review and discuss
the column-addition method. Finally, have
students complete the Part 2 activities.
Ask students to use the information they read in the Student
Reference Book to think of one true statement they could make
about the base-ten number system.
Adjusting the Activity
Student Page
Refer students to the place-value chart on page 30 of the Student
Reference Book. Ask them to look over the headings on the chart and describe
any patterns they see. The numbers decrease in size from left to right; the
columns on the right side of the chart have a decimal point and the left side does
not; the 0s increase by one for each column as you move outward from the
center in either direction.
Decimals and Percents
You use facts about the place-value chart each time you make
trades using base-10 blocks.
Suppose that a flat is worth 1. Then a long is
1
1
ᎏ
worth ᎏ10ᎏ, or 0.1; and a cube is worth ᎏ
100 , or 0.01.
For this example:
You can trade one long for ten cubes because
1
1
ᎏ
one ᎏ10ᎏ equals ten ᎏ
100 s.
A flat
You can trade ten longs for one flat because
1
ten ᎏ10ᎏs equals one 1.
A long is worth
1
ᎏᎏ
10
A cube is worth
or 0.01.
1
ᎏᎏ ,
100
You can trade ten cubes for one long because
1
1
ᎏ
ᎏᎏ
ten ᎏ
100 s equals one 10 .
is worth 1.
or 0.1.
one 100 ⫽
1
ᎏᎏ
10
of 1,000
one
1
ᎏᎏ
10
⫽
1
ᎏᎏ
10
of 1
one 10
⫽
1
ᎏᎏ
10
of 100
one
1
ᎏᎏ
100
⫽
1
ᎏᎏ
10
of
1
ᎏᎏ
10
one 1
⫽
1
ᎏᎏ
10
of 10
one
1
ᎏᎏ
1,000
⫽
1
ᎏᎏ
10
of
1
ᎏᎏ
100
a. 20,006.8
b. 0.02
c. 34.502
2. Using the digits 9, 3, and 5, what is
a. the smallest decimal that you can write?
b. the largest decimal less than 1 that
you can write?
c. the decimal closest to 0.5 that you
can write?
Check your answers on page 434.
Student Reference Book, p. 30
86
Unit 2
K I N E S T H E T I C
T A C T I L E
V I S U A L
Survey the class and use their responses to discuss the following:
Left to Right in the Place-Value Chart
Study the place-value chart below. Look at the numbers that
name the places. As you move from left to right along the chart,
1
each number is ᎏ1ᎏ0 as large as the number to its left.
1. What is the value of
the digit 2 in each of
these numbers?
A U D I T O R Y
Each place has a value that is 10 times the value of the place
to its right. For example, 1,000 is 10 times as much as 100; 100
is 10 times as much as 10; 10 is 10 times as much as 1; 1 is 10
times as much as 0.1; and 0.1 is 10 times as much as 0.01.
Each place has a value that is one-tenth the value of the place
1 of 1,000; 10 is _
1 of 100;
to its left. For example, 100 is _
10
10
1 of 10; 0.1 is _
1 of 1; and 0.01 is _
1 of 0.1.
1 is _
10
10
10
Ask students how these relationships guide them in writing the
decimals in Problem 2 on Student Reference Book, page 30. Sample
answers: Place the largest digits rightmost when forming the
smallest decimal; place the largest digits leftmost when forming
the largest decimal; place the 5 in the tenths place and the other
Estimation and Computation
EM3cuG5TLG1_086-090_U02L02.indd 86
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two digits so the larger is to the right to form the decimal that is
closest to 0.5. Explain that knowing these relationships also helps
with comparing and ordering numbers by their relative sizes.
Ask students to listen closely as you read the numbers from
Problem 1 on Student Reference Book, page 30. Tell them that you
will include some mistakes. Read the numbers as 200,068; 0.2;
and, 34.052. For each number, ask students to tell a partner what
mistake was made. Then ask volunteers to describe the mistake
and to read the number correctly. 200,068—no decimal point;
0.2—decimal point in the wrong position; 34.052 reverses the
tenths and hundredths.
Tell students that clocks operate on a base-60 number system for
minutes, and base-12 or base-24 (with military clocks) for hours.
Have volunteers compare these systems and the base-10 systems.
▶ Reviewing Algorithms:
WHOLE-CLASS
DISCUSSION
Partial-Sums Method
(Math Journal 1, p. 32; Student Reference Book,
pp. 13, 29, and 35; Math Masters, p. 415)
Most fifth-grade students have mastered an algorithm of their
choice for addition. If they are comfortable with that algorithm,
there is no reason for them to change it. However, all students are
expected to know the partial-sums method for addition. This
method helps students develop their understanding of place
value and addition. In the partial-sums method, addition is
performed from left to right, column by column. The sum for each
column is recorded on a separate line. The partial sums are added
either at each step or at the end.
Ask students to read Student Reference Book, page 29 and then
write the numbers 348 and 177 in expanded notation. 300 +
40 + 8 = 348 and 100 + 70 + 7 = 177 Provide additional
examples for students to write in expanded notation if needed.
Then refer to page 13 in the Student Reference Book and
demonstrate adding 348 + 177 using the partial-sums method.
Ask students to describe any relationships they see between the
expanded notation and the partial-sums method. Sample answer:
Both methods use the value of the digits.
Algorithm Project The focus of this
lesson is the partial-sums and column-addition
methods for adding whole numbers and
decimals. To teach U.S. traditional addition
with whole numbers and with decimals, see
Algorithm Project 1 on page A1 and Algorithm
Project 2 on page A6.
Expanded Notation
Number
Expanded Form
34.15
3 ∗ 10 + 4 ∗ 1 + 1 ∗ 0.1 + 5 ∗ 0.01
27.94
2 ∗ 10 + 7 ∗ 1 + 9 ∗ 0.1 + 4 ∗ 0.01
18.795
1 ∗ 10 + 8 ∗ 1 + 7 ∗ 0.1 +
9 ∗ 0.01 + 5 ∗ 0.001
72.089
7 ∗ 10 + 2 ∗ 1 + 0 ∗ 0.1 +
8 ∗ 0.01 + 9 ∗ 0.001
Expanded form may also be written with fractions
instead of decimals. For example: 34.15 = 3 ∗ 10 +
1
1
_
4 ∗ 1 + 1 ∗ (_
10 ) + 5 ∗ ( 100 ).
NOTE Display a poster showing the
expanded notation of a whole number and
of a decimal to provide students with a readily
accessible example.
Language Arts Link The word
algorithm is used to name a step-bystep procedure for solving a
mathematical problem. The word is derived
from the name of a ninth-century Muslim
mathematician, Al-Khowarizimi. Encourage
students to research the etymology of other
mathematical terms.
Ask students to write the numbers 4.56 and 7.9 in expanded
notation. 4 + 5 ∗ 0.1 + 6 ∗ 0.01 = 4.56 and 7 + 9 ∗ 0.1 = 7.9
Provide additional decimal examples for students to write
in expanded notation if needed. Then refer to page 35 in the
Student Reference Book and demonstrate adding 4.56 + 7.9
using the partial-sums method. Ask: What are the similarities
and differences between expanded notation and the partial-sums
method with whole numbers and with decimals? Sample answers:
Both methods for whole numbers and decimals use the value of
the digits. With decimals, you have to line up the places correctly,
either by affixing 0s to the end of the numbers, or by aligning the
digits in the ones place.
Have students independently solve the problems on journal
page 32 and then check each other’s answers.
Lesson 2 2
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Student Page
Date
Time
LESSON
2 2
䉬
▶ Reviewing Algorithms:
Adding with Partial Sums
Column-Addition Method
Write the following numbers in expanded notation.
1.
432:
2.
56.23
400 30 2
50 6 0.2 0.03
Write an estimate for each problem. Then use the partial-sums method to find the
exact answer.
Example:
400
Estimate:
Estimate:
700
4.
Estimate:
Estimate:
Demonstrate the method using examples like those on pages 13
and 35 of the Student Reference Book. In this method, each
column of numbers is added separately, and in any order.
100
10.31
32.04
59.61
214
475.2
600.0
80.0
9.0
0.2
689.2
5.
90.00
11.00
0.90
0.06
101.96
60
6.
Estimate:
28.765
31.036
47.84
21.023
50.000
9.000
0.700
0.090
0.011
59.801
60.000
8.000
0.800
0.060
0.003
68.863
If adding results in a single digit in each column, the sum has
been found.
70
If the sum in any column is a 2-digit number, it is renamed and
part of it is added to the sum in the column on its left.
This adjustment serves the same purpose as “carrying” in the
traditional algorithm.
Math Journal 1, p. 32
NOTE Remind students always to say aloud,
or to themselves, the numbers that they are
adding when they use the partial-sums
method. For example: 500 + 200, not 5 + 2;
70 + 60, not 7 + 6.
Student Page
Date
Time
LESSON
2 2
䉬
Methods for Addition
夹
Solve Problems 1–5 using the partial-sums method. Solve the rest of the problems
using any method you choose. Show your work in the space on the right. Compare
answers with your partner. If there are differences, work together to find the correct
solution.
1.
714 465 2.
253 187 3.
8,999
1,179
440
5,312 3,687
6,211
729
5. 475 139 115 1,254 217 192 309 536
6.
48.05
7. 38.47 9.58 97.16 32.06 65.1
8.
53.21
9. 43.46 7.1 2.65 4.
10.
3,416 2,795 Alana is in charge of the class pets. She spent
$ 43.65 on hamster food,
$ 37.89 on rabbit food,
$ 2.01 on turtle food, and
$ 7.51 on snake food.
How much did she spend on pet food?
Estimate:
Solution:
(Student Reference Book, pp. 13 and 35;
Math Masters, p. 415)
The column-addition method is similar to the traditional
algorithm most adults know. It can become an alternate method
for students who are still struggling with addition.
325.022
134.527
400.000
50.000
9.000
0.500
0.040
0.009
459.549
3.
SMALL-GROUP
ACTIVITY
About $90
$91.06
Ask students to compare the examples of column addition on
pages 13 and 35 of the Student Reference Book. Assign each small
group one of the following problems to solve using the column
addition method. Encourage students to use concrete models
or drawings and strategies based on place value, properties
of operations, and/or the relationship between addition and
subtraction. Have students write about their method and explain
the reasoning they used to solve the assigned problem. Volunteers
share the group’s solution using the board or a transparency.
39 + 23 62
607 + 46 + 239 892
7,069 + 3,481 10,550
0.7 + 0.29 0.99
1.56 + 8.72 10.28
48.26 + 7.94 56.2
▶ Adding Whole Numbers
PARTNER
ACTIVITY
and Decimals
(Math Journal 1, p. 33; Student Reference Book,
pp. 13, 14, and 35; Math Masters, p. 415)
Encourage students to estimate and solve the problems
independently and then check each other’s work. Using the
computation grid helps students line up digits and/or decimal
points. Encourage students to try the methods described on
pages 13, 14, and 35 of the Student Reference Book.
Ongoing Assessment:
Recognizing Student Achievement
Journal
Page 33
Problems 1 and 2
Use journal page 33 to assess students’ ability to solve multidigit addition
problems. Students are making adequate progress if they correctly use the
partial-sums method to solve Problems 1 and 2.
[Operations and Computation Goal 1]
Math Journal 1, p. 33
88
Unit 2
Estimation and Computation
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Student Page
▶ Sharing Results
WHOLE-CLASS
DISCUSSION
(Math Journal 1, pp. 32 and 33)
Date
Time
LESSON
Math Boxes
22
䉬
1.
Round to the nearest tenth.
a.
45.52 ⫽
Bring the class together to share solutions. Some possible
discussion questions include the following:
b.
60.18 ⫽
c.
123.45 ⫽
d.
38.27 ⫽
●
e.
56.199 ⫽
●
●
What are some of the advantages or disadvantages of different
methods for addition?
2.
45.5
60.2
123.5
38.3
56.2
46
3.
When might a particular method be useful? When might it not
be useful?
The temperature at midnight was 25⬚F.
The wind chill temperature was 14⬚F.
How much warmer was the actual
temperature than the wind chill
temperature?
11⬚F
b.
7 ⴱ 60 ⫽
c.
70 ⴱ 60 ⫽
d.
8 ⴱ 10 ⫽
e.
8 ⴱ 70 ⫽
f.
80 ⴱ 70 ⫽
70
420
4,200
80
560
5,600
18
Complete.
a.
354 ⫽ 300 ⫹ 50 ⫹
b.
867 ⫽ 800 ⫹
c.
975 ⫽
e.
5.
Complete.
60
4
⫹7
900 ⫹ 70 ⫹ 5
1,256 ⫽ 1,000 ⫹ 200 ⫹ 50 ⫹ 6
6,704 ⫽ 6,000 ⫹ 700 ⫹ 4
13
6.
6
a.
A person 74 in. tall is
b.
A person who runs a mile runs
d.
▶ Playing Addition Top-It
7 ⴱ 10 ⫽
15–17
203
c.
2 Ongoing Learning & Practice
a.
d.
How did students use their estimates on journal page 32? Did
they make estimates for any subsequent problems?
Ask students to explain the reasoning they used to solve some of
the problems on Math Journal 1, page 33.
4.
Multiply.
5,280
ft
2
in.
Match.
a.
Straight angle
<90°
b.
Obtuse angle
>90°
c.
Right angle
90°
d.
Acute angle
180°
ft.
A person who runs 1,760 yd runs
5,280
ft.
A person who grew
the summer grew
1
ᎏᎏ
2
ft over
6
in.
184
139
Math Journal 1, p. 34
PARTNER
ACTIVITY
(Decimal Version)
NOTE Remind students of the benefits of
(Student Reference Book, p. 333; Math Masters, p. 493)
Addition Top-It (Decimal Version) provides practice adding
decimals, comparing numbers, and understanding place-value
concepts. Direct students to play a decimal version of Addition
Top-It, Student Reference Book, page 333. Use this variation:
making estimates prior to solving problems.
Estimation as an ongoing practice helps
students to become flexible with mental
computation and to check their answers for
reasonableness.
Each player draws 4 cards and forms 2 numbers that each has
a whole-number portion and a decimal portion. Players should
consider how to form their numbers to make the largest sum
possible. Use counters or pennies to represent the decimal point.
Study Link Master
Name
Each player finds the sum of the 2 numbers and then writes
the sum in expanded form.
Each player records his or her sum on Math Masters, page 493
to form a number sentence using >, <, or =.
STUDY LINK
22
䉬
Date
Time
Number Hunt
Reminder: A
means Do not use a calculator.
13–17
Use the numbers in the following table to answer the
questions below. You may not use a number more than once.
Sample answers:
★ 571
✓19 85.2 533
88.2
525
20
17.5
X
400
261
20.5
125
★
30
X7 ✓23 901 X
1. Circle two numbers whose sum is 832.
2. Make an X in the boxes containing three
The player with the largest sum takes all of the cards.
numbers whose sum is 57.
3. Make a check mark in the boxes containing
two prime numbers whose sum is 42.
4. Make a star in the boxes containing two numbers whose sum is 658.
▶ Math Boxes 2 2
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 34)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 2-4. The skill in Problem 6
previews Unit 3 content.
Writing/Reasoning Have students write a response for the
following: Leroy rounded 56.199 to 60. Rosina said that he
was incorrect. Do you agree or disagree with Rosina? Sample
answer: It depends on whether Leroy intended to round to the
nearest 10 or the nearest whole number; 56.199 rounded to the
nearest 10 is 60; 56.199 rounded to the nearest whole number is 56.
5. Make a triangle in the boxes containing two numbers whose sum is 105.7.
Explain how you found the answer.
Sample answer: Since the sum has a 7 in
the tenths place, look for numbers with
tenths that add to 7: 85.2 ⫹ 20.5 ⫽ 105.7;
and 88.2 ⫹ 17.5 ⫽ 105.7.
Solve Problems 6–9 using any method you want. Show your work in the space below.
6. 3,804 ⫹ 768 ⫽
4,572
246
8. 33 ⫹ 148 ⫹ 65 ⫽
Practice
10. 73 ⫺ 26 ⫽
12. 27 ⫼ 9 ⫽
47
3
7. 2.83 ⫹ 1.57 ⫽
9. 1.055 ⫹ 0.863 ⫽
4.4
1.918
208
8 R2
11. 727 ⫺ 519 ⫽
13. 4 冄3
苶4
苶∑
Math Masters, p. 36
Lesson 2 2
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Teaching Master
Name
Date
LESSON
Time
䉬
▶ Study Link 2 2
Modeling with Base-10 Blocks
22
INDEPENDENT
ACTIVITY
(Math Masters, p. 36)
Example:
100s
10s
1s
2
3
1
3
4
5
5
0
0
7
0
Add 100s
Add 10s
Add 1s
100s
10s
1s
Home Connection Students practice finding sums.
Students can solve problems using any method they
choose.
+
6
5
7
6
500
+ 70 +
6
Work with a partner. Choose a problem below. Use the base-10 blocks to model the
problem. Have your partner solve the problem and record the answer using the partial-sums
method. Compare your model with your partner's solution. Reverse roles and continue until
all problems are solved.
456
53
1.
400
100
9
509
Add 100s
Add 10s
Add 1s
Copyright © Wright Group/McGraw-Hill
2.
3.
Add 100s
Add 10s
Add 1s
271
653
Add 10s
Add 1s
900
60
12
972
4.
800
120
4
924
Add 100s
Add 100s
Add 10s
Add 1s
764
208
521
455
900
70
6
976
3 Differentiation Options
READINESS
▶ Building Numbers with
PARTNER
ACTIVITY
15–30 Min
Base-10 Blocks
(Math Masters, p. 37)
To explore place value and expanded notation using concrete
models, have students use base-10 blocks to model numbers. After
students complete Math Masters, page 37, discuss the relationship
between expanded notation and base-10 block representations.
Have students also share how they used the blocks to add the
numbers.
Math Masters, p. 37
ENRICHMENT
▶ Using Place Value to Solve
PARTNER
ACTIVITY
15–30 Min
Addition Problems
(Math Masters, p. 38)
Teaching Master
Name
LESSON
22
䉬
Date
Time
Place-Value Strategies
Use your favorite addition algorithm to solve the first problem in each column. Then use the
answer to the first problem in each column to help you solve the remaining problems.
1.
3,058
2,182
2.
5,240
a.
3,058
2,282
10,060
a.
5,340
b.
3,058
2,082
3,058
2,582
b.
3,058
2,181
5,239
3.
7,401
2,669
10,070
c.
5,640
d.
7,401
2,679
10,080
5,140
c.
7,401
2,659
To apply students’ understanding of place value and addition
algorithms, have them use the sum of one problem to help them
find the solution of other problems. After students complete
Problems 1 and 2 on Math Masters, page 38, discuss their
strategies. Ask students to explain how these strategies might be
useful when solving addition problems. Sample answer: I could
find related addends that are easier to work with than those in the
original problem and use what I know about place value to help
me solve the problem.
7,401
2,689
10,090
d.
7,401
2,699
10,100
Explain the strategy you used to solve the problem sets above.
I identified which digit in the second number
changed. Then I adjusted the sum of the
original problem by that amount.
ELL SUPPORT
▶ Building a Math Word Bank
SMALL-GROUP
ACTIVITY
5–15 Min
(Differentiation Handbook, p. 142)
To provide language support for number notation, have students
use the Word Bank Template found on Differentiation Handbook,
page 142. Ask students to write the term expanded notation, draw
pictures relating to the term, and write other related words. See
the Differentiation Handbook for more information.
Math Masters, p. 38
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Unit 2
Estimation and Computation
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