Decimal Addition and Subtraction - Everyday Math - Login

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260 Unit 4 Decimals and Their Uses

Advance PreparationFor 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

Key Concepts and Skills• Model decimals through hundredths

with base-10 blocks.

[Number and Numeration Goal 1]

• Express the values of digits in decimals.


• Add and subtract decimals to the

hundredths place.

[Operations and Computation Goal 2]

• Judge the reasonableness of solutions to

decimal addition and subtraction problems.

[Operations and Computation Goal 6]

Key ActivitiesStudents 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.

MaterialsMath Journal 1, p. 87

Student Reference Book, pp. 178–178B

Study Link 4�4

Math Masters, p. 118; pp. 427 and 428

(optional)

base-10 blocks � quarters, nickels, dimes,

pennies (optional) � slate

Analyzing Circle GraphsMath Journal 1, p. 88

Students compare population data

presented in circle graphs.

Math Boxes 4�5Math Journal 1, p. 89

Students practice and maintain skills

through Math Box problems.

Study Link 4�5Math Masters, p. 119

Students practice and maintain skills

through Study Link activities.

READINESS

Investigating a Decimal Version of the Number GridMath Masters, p. 427

Number-Grid Poster

Students use a decimal version of the

number grid to model decimal addition and

subtraction.

ENRICHMENTSolving Hiking Trail ProblemsMath Masters, pp. 120 and 121

Students compute various distances on a

hiking trail.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Decimal Addition andSubtraction

Objective To extend methods for whole-number addition and

subtraction to decimals.s

��

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

260_EMCS_T_TLG1_G4_U04_L05_576817.indd 260260_EMCS_T_TLG1_G4_U04_L05_576817.indd 260 2/28/11 3:29 PM2/28/11 3:29 PM

Lesson 4�5 261

Mental Math and Reflexes Pose decimal addition and subtraction problems within a money context. Suggestions:

LESSON

4 �5

Name Date Time

Math Message

What’s wrong with this problem?

What is the correct answer?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.

�0.76

� 0.2

0.78

Math Masters, p. 118

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

(Math Masters, p. 118)

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.

� 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.

� Rename 0.2 as 0.20 so that both addends name hundredths. Then use an addition algorithm.

0.76 → 0.76+ 0.2 → + 0.20 (0.2 = 0.20)

0.96

PROBLEMBBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEMMMMLEBLELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBBLBLBBLBLBLLBLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELELELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBB ELEELELEMMMMMMMMMOOOOOOOOOBBBLBLBLBBBLBBLOOROROROORORORORORORORORO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGGLLLLLLLLLLLLLVINVINVINVINNNNVINVINVINVINNVINVINVINVINV GGGGGGGGGGGOLOOOLOOLOLOLOO VVINVINLLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOOOLOLOLOLOLLOOO VVVLLLLLLLLLLVVVVVVVVVVOSOSOSOOSOSOSOSOSOSOOSOSOSOSOOOOSOOSOSOSOSOSOSOSOOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVLLLLLLLLVVVVVVVVVLLLVVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING

Getting Started

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.

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.

$0.50 + $0.75 = $1.25

$0.30 + $0.60 = $0.90

$1.00 - $0.70 = $0.30

$0.80 - $0.40 = $0.40

$1.20 + $0.25 = $1.45

$1.18 + $0.10 = $1.28

$1.75 - $1.25 = $0.50

$1.41 - $0.30 = $1.11

$1.39 + $0.46 = $1.85

$2.40 + $0.63 = $3.03

$0.64 - $0.33 = $0.31

$0.45 - $0.28 = $0.17

Math Message Take an answer sheet (Math Masters, page 118 ) and complete it.

�

++0.76 0.2

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Links to the Future

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.

Ongoing Assessment: Math Message �

Recognizing Student Achievement

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.


� Adding and Subtracting WHOLE-CLASS ACTIVITY

Decimals Using an AlgorithmAsk: 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 17.0 8.10 9.0 0 + 3.50 + 05.1 - 4.72 - 0.09 6.13 22.1 3.38 8.91

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.


Links to the Future

Adjusting the Activity

Decimal Addition and SubtractionLESSON

4 �5

Date Time

Add or subtract mentally or with a paper-and-pencil algorithm.

Pay attention to the � and � symbols.

1. 2.05 � 1.83 � 2. 3.04 � 2.8 �

3. 2.4 � 3.01 � 0.26 � 4. 2.31 � 1.88 �

5. 19 � 1.9 � 6. 1 � 0.67 � 0.3320.9

0.435.67

5.843.88

7. Choose one of the problems from above. Explain the method you used

to solve the problem.

make change. $0.03 � $0.05 � $0.25 � $0.33.

$1.00 � $0.67. Then I mentally thought how I would

Sample answer: Problem 6; I rewrote the problem as

34–37

Math Journal 1, p. 87

Student Page

Circle GraphsLESSON

4 �5

Date Time

Percent urban is the number of people out of 100 who live in towns or cities. Percentrural 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.

Source: The United Nations

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 �1

2� of their people living

in urban areas and �1

2� of their people living in rural areas?

5. Write a question that can be answered from the information in the graphs. Then answer the

question.

Question:

Answer: Namibia

of its population living in rural areas?

Which country has about two-thirds

Congo, Cameroon

Burundi, Uganda

Gabon

urb

an

rural

Burundi

urbanrural

Cameroon

urbanrural

Central AfricanRepublic

urbanrural

Congo

urban

rural

Gabon

urban

rural

Lesotho

urbanrural

Namibia

urban

rural

Rwanda

urbanrural

South Africa

urb

an

rural

Uganda

Try This


Student Page

Lesson 4�5 263

� Practicing Decimal Addition INDEPENDENTACTIVITY

and Subtraction(Math Journal 1, p. 87)

Students solve decimal addition and subtraction problems.

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

Add the 1s: 2 + 1 → 3.00

Add the 0.1s: 0.0 + 0.8 → 0.80

Add the 0.01s: 0.05 + 0.03 → + 0.08

Find the total: 3 + 0.8 + 0.08 → 3.88

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

Ongoing Assessment: Informing InstructionWatch 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

� Analyzing Circle Graphs INDEPENDENTACTIVITY

(Math Journal 1, p. 88)

Students compare population data presented in circle graphs. To support English language learners, discuss the terms population, urban, and rural.

Creating and interpreting circle graphs are Grade 5 and Grade 6 Goals.

ELL

ELL



STUDY LINK

4�5 Addition and Subtraction of Decimals

34–37

Name Date Time

Add or subtract. Show your work.

1. 96.45 � 23.96 � 2. 1.06 � 0.4 �

3. 9.87 � 4.69 � 4. 0.4 � 0.37 � 0.035.18

1.46120.41

Write �, �, or � to make each statement true.

5. 2.78 � 9.1 3.36 � 8.49 6. 0.08 � 0.97 1.04 � 0.03

7. 13.62 � 4.9 9.4 � 1.33 8. 9.4 � 5.6 8.3 � 4.7

9. Name two 3-digit numbers whose sum is 6.54. � � 6.54

10. Name two 3-digit numbers whose difference is 1.52. � � 1.52

11. 13 � 7 � s s � 12. 8 º g � 24 g �

13. 36 / p � 6 p � 14. m / 9 � 8 m � 726

36

5.316.83

4.212.33��

��

Sample answers:

Practice


Study Link Master

89

Math Boxes LESSON

4 �5

Date Time

1. Insert �, �, or �.

a. 0.96 0.4

b. 0.50 0.500

c. 1.3 1.09

d. 0.85 0.86

e. 0.700 0.007�

�

�

�

�2. a. Measure the length of this line segment

to the nearest �1

2� centimeter.

About cm

b. Draw a line segment

3 centimeters long.

5.5

3. Fill in the missing numbers.

a. 28, 35, 42, , ,

Rule:

b. 56, 48, 40, , ,

Rule:

c. 81, , 63, , 45,

Rule:

365472

162432

6356494. Solve each open sentence.

a. 5.9 � T � 5 T �

b. 9.4 � K � 3 K �

c. 0.81 � M � 0.43 M �

d. F � 2.1 � 6.8 F �

e. 2.43 � S � 1.06 S �

f. R � 12.2 � 4.65 R � 16.85

1.37

8.9

0.38

6.4

0.9

5. Add 9 tens, 8 hundredths, and 3 tenths

to 34.53.

What is the result? 124.91

6. Add mentally or with a paper-and-pencil

algorithm.

a. 6 b. 54

40 180

150 240

� 1,000 � 800

32 33 128

160 161

36

148

10 11

1,196 1,274

�7

�8

�9


Student Page

� Math Boxes 4�5 INDEPENDENTACTIVITY

(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.

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.

� Study Link 4�5 INDEPENDENTACTIVITY

(Math Masters, p. 119)

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 SMALL-GROUP ACTIVITY

� Investigating a Decimal 5–15 Min

Version of the Number Grid(Math Masters, p. 427)

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.


Name Date Time

Number Grid (Decimal Version)

0

0.100.090.080.070.060.050.040.030.020.01

0.200.190.180.170.160.150.140.130.120.11

0.300.290.280.270.260.250.240.230.220.21

0.400.390.380.370.360.350.340.330.320.31

0.500.490.480.470.460.450.440.430.420.41

0.600.590.580.570.560.550.540.530.520.51

0.800.790.780.770.760.750.740.730.720.71

0.700.690.680.670.660.650.640.630.620.61

0.900.890.880.870.860.850.840.830.820.81

1.000.990.980.970.960.950.940.930.920.91


Teaching Aid Master

Lesson 4�5 265

LESSON

4�5

Name Date Time

A Hiking Trail continued

34–37

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.

How can you check your answers?

Sample answer: Finding the sum of the twoentries on each line should give you the distance of the whole trail: 47.60 km.

Batona Trail

Point of Interest Distance from Distance fromCarpenter Spring (km) Washington Road (km)

Carpenter Spring 0 47.60

Deep Hollow Pond 1.91 45.69

Route 70 3.37 44.23Lebanon Headquarters 4.66 42.94Pakim Pond 9.91 37.69Route 72 12.10 35.50Route 563 14.04 33.56

Route 532 19.53 28.07Apple Pie Hill Fire Tower 21.31 26.29Carranza Memorial 27.80 19.80

Hay Road 33.05 14.55Quakerbridge 37.92 9.68

Washington Road 47.60 0


Teaching MasterLESSON

4 �5

Name Date Time

A Hiking Trail

542

532

72

70

Carpenter Spring

Map of Batona Trail

Lebanon

Headquarters

& Fire TowerN

CHATSWORTH

FOREST

BATSTO Batsto Historical Area

STATE

Apple Pie Hill

Fire Tower

Scale of Kilometers

0 1 2 3 4

Quakerbridge

Area of

this map

Source: Batona Hiking Club of Philadelphia

NewJersey

Wash

ington R

oad

BATONA

TRAIL

Deep HollowPond

PakimPond

BatstoLake

Bats

to R

iver

563

Carranza

Memorial

Hay R

oad

WHARTON

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.

The trail crosses several roads, so it

can be reached by car at a number

of places.

Carpenter Spring is at the north end

of the trail. Washington Road, near

Batsto, is at the trail’s south end.

Go to Math Masters, page 121.


Teaching Master

Ask students to solve addition or subtraction problems by counting on the grid.

Examples:

� Write 0.02 + 0.07 on the board.

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

� Write 0.14 + 0.10 on the board.

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

ENRICHMENT PARTNER ACTIVITY

� Solving Hiking Trail 5–15 Min

Problems(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.


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Decimal Addition and Subtraction - Everyday Math - Login