Decimal Addition and
Subtraction
Objective To extend methods for whole-number addition and
subtraction to decimals.
s
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Analyzing Circle Graphs
• Model decimals through hundredths
with base-10 blocks. Math Journal 1, p. 88
Students compare population data
presented in circle graphs.
[Number and Numeration Goal 1]
• Express the values of digits in decimals. [Number and Numeration Goal 1]
• Add and subtract decimals to the
hundredths place. Math Boxes 4 5
Math Journal 1, p. 89
Students practice and maintain skills
through Math Box problems.
[Operations and Computation Goal 2]
• Judge the reasonableness of solutions to
decimal addition and subtraction problems. [Operations and Computation Goal 6]
Study Link 4 5
Math Masters, p. 119
Students practice and maintain skills
through Study Link activities.
Key Activities
Curriculum
Focal Points
Differentiation Options
READINESS
Investigating a Decimal Version
of the Number Grid
Math Masters, p. 427
Number-Grid Poster
Students use a decimal version of the
number grid to model decimal addition and
subtraction.
ENRICHMENT
Solving Hiking Trail Problems
Math Masters, pp. 120 and 121
Students compute various distances on a
hiking trail.
Students discuss different methods in which
to add and subtract decimals, including
modeling with base-10 blocks and using
algorithms.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Masters, page 118. [Number and Numeration Goal 1]
Ongoing Assessment:
Informing Instruction See page 263.
Materials
Math Journal 1, p. 87
Student Reference Book, pp. 178–178B
Study Link 44
Math Masters, p. 118; pp. 427 and 428
(optional)
base-10 blocks quarters, nickels, dimes,
pennies (optional) slate
Advance Preparation
For Part 1, copy and cut apart Math Masters, page 118 so that each student has one answer sheet for the
Math Message. Place these sheets near the Math Message.
Teacher’s Reference Manual, Grades 4–6 pp. 119 –126
260
Unit 4
Decimals and Their Uses
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP1, SMP2, SMP3, SMP5, SMP6, SMP7
Content Standards
Getting Started
4.OA.2, 4.MD.2
Mental Math and Reflexes
Pose decimal addition and subtraction problems within a money context. Suggestions:
$0.50 + $0.75 = $1.25
$1.20 + $0.25 = $1.45
$0.30 + $0.60 = $0.90
$1.00 - $0.70 = $0.30
$0.80 - $0.40 = $0.40
$1.39 + $0.46 = $1.85
$2.40 + $0.63 = $3.03
$0.64 - $0.33 = $0.31
$0.45 - $0.28 = $0.17
$1.18 + $0.10 = $1.28
$1.75 - $1.25 = $0.50
$1.41 - $0.30 = $1.11
Math Message Study Link 4 4 Follow-Up
Draw students’ attention to Problems 4 and 5. Problem 4 describes
what should be added to the length of one tunnel to get the length of
another. This is an example of a comparison situation involving addition.
Problem 5 describes what one tunnel length should be multiplied by to get another
tunnel length. This is an example of a comparison situation involving multiplication.
Take an answer sheet (Math
Masters, page 118 ) and
complete it.
Descriptions of these problem types are on Student Reference Book, pages 178–178B.
Refer to these pages as you lead a discussion about the difference between these two
types of comparisons. You might suggest that students sketch a situation diagram for
each problem.
1 Teaching the Lesson
Math Message Follow-Up
(Math Masters, p. 118)
WHOLE-CLASS
ACTIVITY
SOLVING
Have students discuss why the answer to the problem is incorrect.
There are many ways to explain the mistake. Mention the
following, if no one brings them up:
Model the problem with base-10 blocks or pictures of
base-10 blocks. (See margin.) This gives a total of 9 longs
and 6 cubes, or 0.96.
+
0.76
+ 0.2
Write the problem in dollars-and-cents notation.
0.76 = $0.76 and 0.2 = $0.20. Think of the 7 in $0.76 as
7 dimes and the 6 as 6 pennies. Think of the 2 in $0.20 as
2 dimes and the 0 as no pennies. This gives a total of 9 dimes
and 6 pennies, or $0.96.
Think in terms of place value.
0.76 = 7 tenths and 6 hundredths, and 0.2 = 2 tenths.
This gives a total of 9 tenths and 6 hundredths, or 0.96.
Name
LESSON
4 5
䉬
夹
Date
Time
Math Message
What’s wrong with this problem?
What is the correct answer?
0.76
0.2
0.78
Sample answer: The digits are not in
the correct columns. Six hundredths
plus 2 tenths is not 8 hundredths.
The correct answer is 0.96.
Math Masters, p. 118
Rename 0.2 as 0.20 so that both addends name hundredths.
Then use an addition algorithm.
0.76
+ 0.2
→
→
0.76
+ 0.20
0.96
(0.2 = 0.20)
Lesson 4 5
261
Ongoing Assessment:
Recognizing Student Achievement
Math Message
Use the Math Message to assess students’ understanding of the
values of decimal digits. Students are making adequate progress if
their responses indicate that the digit 6 stands for or represents 6 hundredths
and the digit 2 stands for or represents 2 tenths. Some students may be
able to describe how a ballpark estimate can be used to check the answer
to the problem.
[Number and Numeration Goal 1]
Algorithm Project In this lesson,
students use various methods to add
and subtract decimals. To teach U.S.
traditional addition and subtraction of
decimals, see Algorithm Projects 2 and 4
on pages A5 and A15.
Adding and Subtracting
WHOLE-CLASS
ACTIVITY
Decimals Using an Algorithm
Ask: Is it possible to use the same methods for adding and
subtracting decimals that you use for whole numbers? yes
As with whole numbers, all digits of a given place value must
be lined up correctly.
One way to make sure the digits align correctly is to rename the
numbers so that each has the same number of digits after the
decimal point. For example, if adding or subtracting decimals in
tenths and hundredths, rename the tenths as hundredths by
adding a zero to the end of the numbers. When the digits are
aligned correctly, the decimal points will also align.
Pose several decimal addition and subtraction problems. Ask
students to model their answers with base-10 blocks (or symbols).
Suggestions:
2.63 + 3.5 = ?
17 + 5.1 = ?
8.1 - 4.72 = ?
9 - 0.09 = ?
The zeros in boldface have been appended so both numbers have
the same number of digits after the decimal point.
2.63
+ 3.50
6.13
17.0
+ 05.1
22.1
8.10
- 4.72
3.38
9.00
- 0.09
8.91
Links to the Future
Do not be concerned if students use manipulatives such as base-10 blocks or
bills and coins to add and subtract decimals. Students will be expected to do so
without the use of manipulatives in Grade 5.
262
Unit 4 Decimals and Their Uses
Student Page
Practicing Decimal Addition
Date
INDEPENDENT
ACTIVITY
Time
LESSON
4 5
䉬
Decimal Addition and Subtraction
and Subtraction
Add or subtract mentally or with a paper-and-pencil algorithm.
Pay attention to the and symbols.
(Math Journal 1, p. 87)
1.
3.88
3. 2.4 3.01 0.26 5.67
5. 19 1.9 20.9
2.05 1.83 2.
4.
6.
34–37
5.84
2.31 1.88 0.43
1 0.67 0.33
3.04 2.8 Students solve decimal addition and subtraction problems.
Adjusting the Activity
ELL
Have base-10 blocks, coins and bills (Math Masters, page 428),
and a decimal number grid (Math Masters, page 427) available. Encourage
students to think in terms of the partial-sums algorithm.
2.05
+ 1.83
2+1
0.0 + 0.8
0.05 + 0.03
3 + 0.8 + 0.08
Add the 1s:
Add the 0.1s:
Add the 0.01s:
Find the total:
A U D I T O R Y
→
→
→
→
3.00
0.80
+ 0.08
7.
3.88
K I N E S T H E T I C
T A C T I L E
Choose one of the problems from above. Explain the method you used
to solve the problem.
Sample answer: Problem 6; I rewrote the problem as
$1.00 $0.67. Then I mentally thought how I would
make change. $0.03 $0.05 $0.25 $0.33.
V I S U A L
Math Journal 1, p. 87
Ongoing Assessment: Informing Instruction
Watch for students who do not correctly align the digits when adding and
subtracting. All digits of a given place value must be written in the same column.
Encourage students to use computation grid paper and record the place-value
heading above each column.
2 Ongoing Learning & Practice
Date
Time
LESSON
4 5
䉬
Circle Graphs
Percent urban is the number of people out of 100 who live in towns or cities. Percent
rural is the number of people out of 100 who live in the countryside. Each circle graph
below represents the percent of the urban and rural population of an African country.
Burundi
Cameroon
Central African
Republic
Congo
rural
Lesotho
urban
Namibia
rural
Rwanda
urban
Links to the Future
rural
urban
rural
urban
South Africa
urban
Uganda
an
rural
Gabon
rural
urban
rural
urban
rural
urb
Students compare population data presented in circle graphs. To
support English language learners, discuss the terms population,
urban, and rural.
Student Page
an
(Math Journal 1, p. 88)
INDEPENDENT
ACTIVITY
ELL
urb
Analyzing Circle Graphs
rural
urban
rural
Source: The United Nations
Creating and interpreting circle graphs are Grade 5 and Grade 6 Goals.
1.
For each pair, circle the country with the larger urban population.
a.
Congo
Uganda
b.
Rwanda
Gabon
c.
Burundi
South Africa
d.
Namibia
Lesotho
2.
Which country has the greatest percentage of people living in urban areas?
3.
Which two countries have the greatest percentage
of people living in rural areas?
4.
Which two countries have about of their people living
2
1
in urban areas and of their people living in rural areas?
1
2
Gabon
Burundi, Uganda
Congo, Cameroon
Try This
5.
Write a question that can be answered from the information in the graphs. Then answer the
question.
Which country has about two-thirds
of its population living in rural areas?
Answer: Namibia
Question:
Math Journal 1, p. 88
Lesson 4 5
263
Student Page
Date
Math Boxes
4 5
䉬
1.
Math Boxes 4 5
Time
LESSON
Insert , , or .
2. a.
0.4
0.50 0.500
1.3 1.09
0.85 0.86
0.700 0.007
Measure the length of this line segment
1
to the nearest centimeter.
2
0.96
a.
b.
c.
d.
e.
5.5
About
b.
128
Fill in the missing numbers.
49 , 56 , 63
b.
9.4 K 3
K
c.
0.81 M 0.43
M
Rule:
d.
F 2.1 6.8
F
81,
e.
2.43 S 1.06
S
f.
R 12.2 4.65
R
7
56, 48, 40,
32 , 24 , 16
8
72 , 63, 54 , 45, 36
9
Rule:
c.
Solve each open sentence.
5.9 T 5
Rule:
b.
4.
a.
28, 35, 42,
a.
T
Add 9 tens, 8 hundredths, and 3 tenths
to 34.53.
Study Link 4 5
148
6.
124.91
What is the result?
Writing/Reasoning Have students write a response to the
following: Explain how you found the value of S in Problem
4e. Sample answer: Since I knew the whole (2.43) and
one of the parts (1.06), I subtracted 1.06 from 2.43 to find the
value of S.
0.9
6.4
0.38
8.9
1.37
16.85
160 161
5.
(Math Journal 1, p. 89)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 4-7. The skill in Problem 6
previews Unit 5 content.
cm
Draw a line segment
3 centimeters long.
32 33
3.
INDEPENDENT
ACTIVITY
Add mentally or with a paper-and-pencil
algorithm.
a.
6
40
150
1,000
b.
1,196
54
180
240
800
INDEPENDENT
ACTIVITY
(Math Masters, p. 119)
1,274
36
10 11
89
Math Journal 1, p. 89
Home Connection Students add and subtract decimals.
They also write <, >, or = symbols to make true number
sentences.
Encourage students to continue bringing examples of decimals to
display in the Decimals All Around Museum.
3 Differentiation Options
READINESS
Investigating a Decimal
Date
(Math Masters, p. 427)
Time
Addition and Subtraction of Decimals
STUDY LINK
4 5
䉬
Add or subtract. Show your work.
1.
96.45 23.96 3.
9.87 4.69 120.41
5.18
2.
1.06 0.4 4.
0.4 0.37 5–15 Min
Version of the Number Grid
Study Link Master
Name
SMALL-GROUP
ACTIVITY
1.46
0.03
34 –37
To explore the use of a visual organizer for understanding the
base-ten place-value system for decimals, have students use a
decimal version of the number grid.
Have students compare the Number-Grid Poster with the decimal
version. Ask: What are some similarities and differences? Possible
answers: Patterns in the digits are similar in that the hundredths
digit stays the same as you move down a column, and the tenths
digit stays the same as you move across a row. The numbers
increase by 0.01 as you move a step to the right; the numbers
increase by 0.1 as you move a step down.
Write , , or to make each statement true.
1.04 0.03
8.3 4.7
Sample answers:
2.33 4.21 6.54
Name two 3-digit numbers whose sum is 6.54.
6.83 5.31 1.52
Name two 3-digit numbers whose difference is 1.52.
5.
2.78 9.1
7.
13.62 4.9
9.
10.
3.36 8.49
6.
0.08 0.97
9.4 1.33
8.
9.4 5.6
Practice
11.
13 7 s
s
13.
36 / p 6
p
6
6
12.
8 º g 24
g 14.
m/98
m
3
72
Math Masters, p. 119
264
Unit 4 Decimals and Their Uses
Teaching Aid Master
Ask students to solve addition or subtraction problems by counting
on the grid.
Name
Date
Time
Number Grid (Decimal Version)
Examples:
0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Write 0.02 + 0.07 on the board.
0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20
Have students put their fingers on 0.02 and count by
hundredths as they move their fingers 7 steps to the
right—one step for each hundredth. 0.09
0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30
0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40
0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
Write 0.14 + 0.10 on the board.
0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60
0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70
Have students put their fingers on 0.14 and count by
hundredths as they move their fingers 10 steps to the
right—one for each hundredth. Or, move down one row
for each tenth. 0.24
0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80
0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.90
0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00
PARTNER
ACTIVITY
ENRICHMENT
Solving Hiking Trail
5–15 Min
Problems
Math Masters, p. 427
(Math Masters, pp. 120 and 121)
To apply students’ understanding of computation with decimals
to the hundredths place, have them find distances on a hiking map.
Teaching Master
Name
LESSON
4 5
䉬
Teaching Master
Date
Time
Name
A Hiking Trail
Date
LESSON
4 5
䉬
Map of Batona Trail
The Batona Trail is a hiking trail in
southern New Jersey. The Batona
Hiking Club measured the trail very
carefully and found that it is about
47.60 kilometers long.
A Hiking Trail
Point of Interest
Lebanon
Headquarters
& Fire Tower
N
Pakim
Pond
72
IL
A
TR
Go to Math Masters, page 121.
563
Carpenter Spring is at the north end
of the trail. Washington Road, near
Batsto, is at the trail’s south end.
Distance from
Carpenter Spring (km)
0
47.60
Deep Hollow Pond
1.91
45.69
Route 70
3.37
Lebanon Headquarters
4.66
44.23
42.94
37.69
35.50
Pakim Pond
yR
Ha
d
oa
Batsto River
Carranza
Memorial
9.91
FOREST
Quakerbridge
New
Jersey
ad
BATSTO
12.10
Route 563
14.04
33.56
Route 532
19.53
28.07
26.29
Carranza Memorial
Hay Road
STATE
Batsto
Lake
Route 72
Apple Pie Hill Fire Tower
0 1 2 3 4
Scale of Kilometers
n
gto
Ro
hin
as
W
Batsto Historical Area
2
54
Area of
this map
Distance from
Washington Road (km)
Carpenter Spring
532
NA
CHATSWORTH
BATO
Apple Pie Hill
Fire Tower
WHARTON
34 –37
Batona Trail
Deep Hollow
Pond
70
continued
The following table shows distances from several points of interest from
the north to the south end of the trail. Fill in the missing distances.
Carpenter Spring
The trail crosses several roads, so it
can be reached by car at a number
of places.
Time
21.31
27.80
19.80
33.05
14.55
Quakerbridge
37.92
9.68
Washington Road
47.60
0
How can you check your answers?
Sample answer: Finding the sum of the two
entries on each line should give you the
distance of the whole trail: 47.60 km.
Source: Batona Hiking Club of Philadelphia
Math Masters, p. 120
Math Masters, p. 121
Lesson 4 5
265