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eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

590 Unit 7 Exponents and Negative Numbers

Advance PreparationFor Part 1, students need Fraction Cards (Math Journal 2, Activity Sheets 5–7), which were cut out

and used in Lesson 5-1.

Line PlotsObjective To provide experience creating and interpreting line

plots with fractional units.

��

Key Concepts and Skills• Identify equivalent fractions.

[Number and Numeration Goal 5]

• Identify fractions on a number line.

[Number and Numeration Goal 6]

• Add fractions and mixed numbers with

like and unlike denominators.

[Operations and Computation Goal 4]

• Create a line plot.

[Data and Chance Goal 1]

• Analyze a data set.

[Data and Chance Goal 2]

Key ActivitiesStudents make a line plot to display and

analyze a data set of measurements in

fractions of a unit. Students use equivalent

fractions and operations of fractions

including addition and subtraction to solve

problems involving information presented in

line plots.

MaterialsMath Journal 2, pp. 242 and 242A

Fraction Cards (Math Journal 2, Activity

Sheets 5–7)

Student Reference Book, pp. 119–121

(optional)

calculator � Probability Meter Poster

(optional)

Operations with Multidigit Whole Numbers and DecimalsMath Journal 2, p. 242B

Students practice solving problems

involving operations with multidigit

whole numbers and decimals.

Math Boxes 7�10Math Journal 2, p. 243

Students practice and maintain skills

through Math Box problems.

Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Number and Numeration Goal 6 and

Operations and Computation Goal 4]

Study Link 7�10Math Masters, p. 212

Students practice and maintain skills

through Study Link activities.

READINESS

Identifying Fractions on a Number LineMath Masters, p. 211

Students label fractions on number lines.

EXTRA PRACTICE

Plotting Rain Gauge DataMath Master, p. 213

Students read measures from pictures of rain

gauges, plot the data on a line plot, and then

answer questions about data landmarks.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

590_EMCS_T_TLG2_G5_U07_L10_576914.indd 590590_EMCS_T_TLG2_G5_U07_L10_576914.indd 590 3/1/11 11:54 AM3/1/11 11:54 AM

Lesson 7�10 591

Getting Started

1 Teaching the Lesson

▶ Math Message Follow-Up WHOLE-CLASS

ACTIVITY

(Math Journal 2, Activity Sheets 5–7)

Draw a number line on the Class Data Pad, and label the benchmarks 0, 1 _ 4 , 1 _ 2 , 3 _ 4 , and 1. Label the line plot Sorting Fraction Cards, the x-axis Fractions, and the y-axis Number of Cards. Place the title, Sorting Fraction Cards, above the number line, allowing enough room for data to be added for a line plot.

Tell students that the number line will be used to create a line plot displaying the results of the equivalent-fraction card sorting activity.

Ask students to share the results of their card sorting and justify their choices as you record the results on the Class Data Pad.

Possible questions to ask include the following:

● How many cards show a fraction equivalent to 1? eight: 2 _ 2 , 3 _ 3 , 4 _ 4 , 5 _ 5 , 6 _ 6 , 8 _ 8 , 10 _ 10 , 16 _ 16

● How do you know these fractions are all equivalent to 1? Sample answers: The front of each of these cards is fully colored. The numerator is equal to the denominator in each fraction.

● How many cards show a fraction equivalent to 1 _ 2 ? seven: 1 _ 2 , 2 _ 4 , 3 _ 6 , 4 _ 8 , 5 _ 10 , 6 _ 12 , 8 _ 16

● How do you know these fractions are all equivalent to 1 _ 2 ? Sample answers: The denominator in each of these fractions is twice the numerator. The number of spaces shaded blue on each of these cards is equal to the number of spaces that are white.

● How many cards show a fraction equivalent to 1 _ 4 ? three: 1 _ 4 , 2 _ 8 , 3 _ 12

● How many cards show a fraction equivalent to 3 _ 4 ? three: 3 _ 4 , 6 _ 8 , 9 _ 12

● How many cards show a fraction equivalent to 0? three: 0 _ 5 , 0 _ 10 , 0 _ 16

Math MessageSort the Fraction Cards to find the cards equivalent to 0, 1

_ 4 , 1 _ 2 ,

3

_ 4 , and 1. Use your slate to record the number of cards in each group. Be ready to justify your choices.

Study Link 7�9 Follow-UpHave partners compare answers and resolve differences.

Mental Math and Reflexes Have students rename fractions as decimals and as percents. Suggestions:

3 _ 10

0.3; 30%

4

_ 8 0.50; 50%

3

_ 4 0.75; 75%

1 _ 3 0. ⎯ 3 ; 33. ⎯ 3 %

2

_ 5 0.40; 40%

1

_ 8 0.125; 12.5%

3

_ 8 0.375; 37.5%

2

_ 3 0. ⎯ 6 ; 66. ⎯ 6 %

4

_ 4 1.00; 100%

14

12

34

10

Fractions

Sorting Fraction Cards

Num

ber

of

Card

s

14

12

34

10

XXX

XXX

XXXXXXX

XXX

XXXXXXXX

Fractions


Num

ber

of C

ard

s

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Ask volunteers to label the fractions 1 _ 8 , 3 _ 8 , 5 _ 8 , and 7 _ 8 on the line plot. Ask students to explain their reasoning for the placement of each fraction as it is recorded.

Have students continue to sort the Fraction Cards to find those that are equivalent to the fractions for eighths that were just added to the number line. Continue discussing students’ findings as you complete the line plot. Ask:

● How many cards did you find for each new fraction we marked on the number line? There are 2 cards for each: 1 _ 8 is equal to 2 _ 16 , 3 _ 8 is equal to 6 _ 16 , 5 _ 8 is equal to 10 _ 16 , and 7 _ 8 is equal to 14 _ 16 .

● How can you use the line plot to find the total number of cards sorted? Count all the Xs in the line plot.

▶ Using a Line Plot to

WHOLE-CLASS ACTIVITY

Analyze Data (Student Reference Book, pp.119–121)

Refer students to Student Reference Book, pages 119–121 to review data landmarks, if necessary.

Have students use slates to record information about the data on the Sorting Fraction Cards line plot. Ask students to share their thinking as they analyze the data. As they determine the various landmarks, label them on the line plot on the Class Data Pad.

● Which number on the line plot has the most equivalent fractions? 1 whole, or 1 What do we call the landmark for the value or values that occur with the greatest frequency in a set of data? mode

● What is the maximum value in the set of data? 1 What is the minimum value in the set of data? 0

● What is the range of data displayed on the line plot? 1 How did you find the range? I subtracted the minimum from the maximum: 1 – 0 = 1.

● What is the median? 1 _ 2 How did you find the median? I started at each end and then worked toward the center until I found the middle number.

● How many cards do we have in our data set? 32

● If the blue shading on the cards represents blue liquid in a beaker, for how many beakers do we have data? 32

● What landmark would tell us how much liquid each beaker would have if the liquid were distributed equally among all the beakers? mean

● If you actually had these beakers of liquid, what would you do to distribute the liquid equally among all beakers? Sample answer: I’d pour liquid from the beakers with more liquid into the beakers with less liquid until the liquid levels in all of the beakers were equal.

● How do you find the mean for a set of data? Sample answer: Add all of the data values, and then divide the sum by the number of data values.

18

14

38

12

58

34

78

10

XXX

XX

XXX

XX

XXXXXXX

XX

XXX

XX

XXXXXXXX

Fractions


Nu

mb

er

of

Ca

rds

18

14

38

12

58

34

78

10

XXX

XX

XXX

XX

XXXXXXX

XX

XXX

XX

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Fractions


Num

ber

of C

ard

s

mode andmaximum

minimum medianmean


Date Time

Line Plots and Data in Fractional Units cont.LESSON

7�10

The table below shows rainfall for 10 days in one of the driest cities. Organize

the data in a line plot. Then analyze the data to answer questions about the

plotted rainfall.

Rainfall Data

Day 1 2 3 4 5 6 7 8 9 10

Rainfall (in.) 3

_ 8 1 _ 2 0 0 1

_ 8 5

_ 8 3

_ 4 0 0 0

8. Label the approximate locations on the line plot for 1 _ 8 , 2

_ 8 , 3

_ 8 , 4 _ 8 ,

5

_ 8 , 6

_ 8 , and 7 _ 8 .

9. Plot the rainfall data from the table.

Numberof

Days

X X X X X XXXXX

Rainfall Data

Rainfall (in.)

0 118

28

38

48

58

68

78

10. Identify the following landmarks for the rainfall data:

a. mode: 0 in.

b. range: in.

c. median: in.

d. mean (as a decimal, rounded to the nearest hundredth inch): 0.24 in.

6 _

8 or 3 _

4

1 _ 16

209-247_EMCS_S_MJ2_G5_U07_576434.indd 242A 3/18/11 5:26 PM

Math Journal 2, p. 242A

Student Page

Date Time

Use the data in the table below to create a line plot.

1. Place an X on the line plot below to represent the annual rainfall in each of the 10 driest

cities in the United States. Label the line plot with the mixed numbers for the data.

Numberof

Cities X X XX

XX

XXXX

Rainfall in the Driest U.S. Cities

Annual Rainfall (in.)

2 3 4 5 6 7 832 414 4

35 4 17 8

17 2 37 4

Now analyze the data from the table and line plot to answer the questions

about the annual rainfall in the 10 driest U.S. cities.

2. What is the minimum amount of annual rainfall? in.

3. What is the range of annual rainfall? 5 in.

4. What is the mode of annual rainfall? in.

5. What is the median annual rainfall? in.

6. What is the combined annual rainfall for the 10 driest cities? in.

7. What is the mean annual rainfall for the 10 driest cities? 6.35 in.

Line Plots and Data in Fractional UnitsLESSON

7�10

Source: National Climatic Data Center

City and State Annual Rainfall (in.) City and State Annual Rainfall (in.)

Yuma, Arizona 2 3

_ 4 Alamosa, Colorado 7 1 _ 8

Las Vegas, Nevada 4 1 _ 4 Reno, Nevada 7 1

_ 2

Bishop, California 5 3

_ 4 Winslow, Arizona 7 3

_ 4

Bakersfield, California 5 3

_ 4 El Paso, Texas 7 3

_ 4

Phoenix, Arizona 7 1 _ 8 Winnemucca, Nevada 7

3

_ 4

Rainfall in the Driest U.S. Cities

63 1

_ 2

7 3

_ 4

7 1

_ 8

2 3

_ 4

209-247_EMCS_S_MJ2_G5_U07_576434.indd 242 3/18/11 5:26 PM

Math Journal 2, p. 242

Student Page

Adjusting the Activity

Adjusting the Activity

Lesson 7�10 593

▶ Finding the Mean PARTNER ACTIVITY

Ask students to work with a partner to find the sum of the data values using various strategies. 18 1 _ 2 Ask students to share their strategy for finding the sum.

Students who need a visual model to find the sum

of the fractions may benefit from using the Fraction Cards.

Have students match cards that together add to a sum

of 1 whole. For example, 7 _ 8 and 1

_ 8 add to 1 whole. Using

this method, all cards except for one of the 1 _ 2 cards has a

“match” to make 1 whole.

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

Students then use a calculator to find the mean of the set of data. Students may convert 18 1 _ 2 to a decimal and then use the calculator to divide the sum by 32 to find the mean. Ask students to round the quotient in the calculator display to the nearest hundredth. 18.5 / 32 = 0.578125, or about 0.58 Ask:

● Between which two fractions on your line plot does 0.58 fall? Between 1 _ 2 and 5 _ 8

● Which fraction on your line plot is 0.58 closest to? How do you know? Sample answer: 0.58 is closest to 5 _ 8 because 5 _ 8 = 0.625, and 0.625 - 0.58 = 0.045. This is less than the distance between 0.58 and 0.5, which is 0.08.

Students then use estimation to determine an approximate placement on the line plot for the mean of the set of data.

Students who need a visual model to estimate the placement of the

mean on the line plot may benefit from referring to the Probability Meter Poster.

After determining the approximate location of the decimal on the decimal side

of the probability meter, students look on the opposite side of the meter to

determine the fraction that is closest to the one found on the line plot. Students

should notice that 0.58 is greater than 0.5 and less than 0.625, and that it is

closer to 0.625.

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

▶ Displaying and Analyzing PARTNER ACTIVITY

Data on a Line Plot(Math Journal 2, pp. 242 and 242A)

Students work with a partner. Have students solve the problems on journal pages 242 and 242A involving plotting data points on a line plot with fractional units and analyzing the data with landmarks. Circulate and assist.

+


Date Time

Operations with Multidigit Whole Numbers and DecimalsLESSON

7�10

1. Use the standard algorithm to complete the multiplication problem shown at right.

2. $7,550 is shared equally among 25 people.

a. Write an open number sentence to show how much money each person gets.

7,550 ÷ 25 = m b. Will a reasonable estimate for the quotient be

in the tens, hundreds, or thousands?

In the hundreds c. Each person gets $ 302 .

3. In a store, Denny picks out jeans for $34.98 and a shirt for $16.49. He has $50 with him.

a. Does he have enough money to buy the jeans and shirt? no b. If not, how much more money does he need? $1.474. a. The correct digits for the product are given. Write the decimal point in the product

without actually multiplying.

0.98 ∗ 39.39 = 3 8.6 0 2 2

b. Explain how you decided where to place the decimal point. Sample answer: 0.98 is almost 1, so I knew that the product would be close to 39.5. a. Explain how you could use the shading in the grid to find

the quotient 0.65 ÷ 0.05.

Sample answer: The shading shows 13 groups of 0.05 in 0.65.

b. What whole number division problem has the same quotient?

Sample answer: 65 ÷ 5

8 2 83 51 0 0

1 71 1 8

+

45º

702

4 º 207

50 º 207,

,

209-247_EMCS_S_MJ2_G5_U07_576434.indd 242B 3/28/11 3:24 PM

Math Journal 2, p. 242B

Student Page

Date Time

5. A large jar of drink mix holds 1.75 kg. How much drink mix will 12 jars of the same size hold?

6. 36 stamps per package. How many in . . .

a. 3 _ 4 of a package? b. 5 _ 6 of a package? c. 2 _ 9 of a package? d. 7 _ 12 of a package? e. 2 _ 3 of a package?

1. Write the following number in standard notation.

Nine billion, one hundred two million, three thousand, sixty-two

3. Shade 3 _ 8 of the fraction stick.

a. Is this more or less than 1 _ 2 ? b. Is this more or less than 1 _ 4 ? c. 3 _ 8 + 1 _ 2 =

4. Write the next two numbers in each pattern.

a. 1 _ 4 , 3 _ 4 , 5 _ 4 , ,

b. 6, 12, 24, ,

c. –16, –13, –10, ,

d. 7 _ 5 , 14 _ 5 , 28 _ 5 , ,

2. Fill in the blanks.

a. (8 ∗ 7) + (8 ∗ 4) = ∗ (7 + 4)

b. 23 ∗ ( – ) =(23 ∗ 3.2) – (23 ∗ 2)

c. ∗ (12 + 21) = (6 ∗ 12) + (6 ∗ 21)

d. (9 ∗ ) – (9 ∗ ) =

∗ (11 – 3)5

66 67

38–40 75

230

219

Math BoxesLESSON

7�10

�

7 _ 8

7 _ 4 9 _ 4

56 _ 5 112 _ 5

9,102,003,062

9 3 11

6

2 3.2 8

more less

48 96–7 –4

27 stamps30 stamps8 stamps21 stamps24 stamps

21 kg

209-247_EMCS_S_MJ2_G5_U07_576434.indd 243 3/28/11 3:24 PM

Math Journal 2, p. 243

Student Page


2 Ongoing Learning & Practice

▶ Operations with Multidigit

INDEPENDENT ACTIVITY

Whole Numbers and Decimals(Math Journal 2, p. 242B)

Students practice solving problems involving operations with multidigit whole numbers and decimals.

▶ Math Boxes 7�10


(Math Journal 2, p. 243)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 7-7. The skills in Problem 6 previews Unit 8.

Ongoing Assessment Math Boxes

Problem 3 �Recognizing Student Achievement

Use Math Boxes, Problem 3 to assess students’ ability to add fractions with unlike denominators and to use benchmarks to compare fractions. Students are making adequate progress if they can compare the fraction 3 _ 8 to 1 _ 2 and find the sum of the two fractions. Some students may be able to compare the fraction to 1 _ 4 . [Number and Numeration Goal 6 and Operations and Computation Goal 4]


STUDY LINK

7�10 Scouting for Insects

Name Date Time

Some insects are harmful to

farmers’ crops. The insects listed

in this table are harmful to alfalfa

crops. Farmers scout their crops

and randomly collect sample plants.

They regularly observe the plants

and gather data to determine if the

insect population is growing or

remaining stable.

The table shows the result of

one farmer’s insect scouting.

Plot and label the lengths of the insects from the scouting sample on the

line plot below. Use the line plot to find the following data landmarks:

1. Minimum insect length 1

_ 8 in. 2. Maximum insect length 1

1

_ 4 in.

3. Range of insect lengths 1

1

_ 8 in. 4. Median insect length 1

_ 8 in.

5. Mean insect length 1

_ 4 in.

Type of Insect Average Length Number of of Insect (in.) Insects

Alfalfa Weevil Larvae

4

Fall Armyworm 1 1

_ 4 1

Meadow Spittlebug 1

_ 4 3

Pea Aphid 1

_ 8 6

Potato Leafhopper 1

_ 8 6

Number

ofInsects

X XXX

XXX

X

XXXX

XXXXXXXX

Insect Lengths

Average Length (in.)

0 114

38

18

114

11212

34

3

_ 8

187-220_EMCS_B_MM_G5_U07_576973.indd 212 2/25/11 9:20 AM

Math Masters, p. 212

Study Link Master

LESSON

7�10

Name Date Time

Identifying Fractions on a Number Line

Label each number line with the correct fractions.

1.

13

23

0 1

2.

15

25

35

45

0 1

3.

18

28

38

48

58

68

78

0 1

4. Draw and label the following points on this number line. The first one is done

for you.

A: 1 2

_ 4 B:

1

_ 4 C:

4

_ 4 D:

8

_ 4 E: 2

3

_ 4

0 1 2 3 4

AB C D E214 32 4

14 4

484

5. Jay, Kay, and Mae are in a 3-mile walk-a-thon. So far, Jay has walked 3

_ 4 mi,

Kay has walked 1 1

_ 2 mi, and Mae has walked

5

_ 2 mi. Draw and label points on

the number line below to show their approximate locations.

34

11252

0 3

Jay Kay Mae

187-220_EMCS_B_MM_G5_U07_576973.indd 211 2/25/11 9:20 AM


Teaching Master

LESSON

7�10

Name Date Time

Plotting Rain Gauge Data

3

2

1

in.

0 1 2

Rainfall (in.)

3

X

Example: Read the rain gauge pictured above and place an X on

the line plot to show how much rain has been collected.

1. Read each rain gauge to find out how much rain fell each day.

Write the amount of rain on the line below the gauge.

Sun Mon Tue Wed Thu Fri Sat

3

2

1

in.3

2

1

in.3

2

1

in.3

2

1

in.3

2

1

in.3

2

1

in.3

2

1

in.

1

_ 2 in. 1

_ 4 in. 1

1

_ 2 in. 0 in. 1

_ 4 in. 1

_ 4 in. 1

_ 2 in.

2. Use the number line

to make a line plot

recording daily rainfall

for 1 week. Label the

tick marks on the

number line. Place an

X to represent each

rain amount.

3. Analyze the rain gauge data to answer the questions below.

a. What is the mode amount of rain that fell each day? 1 _ 4 in.

b. What is the range of the rainfall during the week? 1 1 _

2 in.

0 1

Rainfall (in.)

Number

of

Days

Daily Rainfall

2

X XX

X XX

X

314112

11434

12

14

187-220_EMCS_B_MM_G5_U07_576973.indd 213 3/16/11 2:50 PM


Teaching Master

Lesson 7�10 595

▶ Study Link 7�10


(Math Masters, p. 212)

Home Connection Students practice making line plots with fractional increments using insect data.

3 Differentiation Options

READINESS

SMALL-GROUP ACTIVITY

▶ Identifying Fractions on a 5–15 Min

Number Line(Math Masters, p. 211)

Students label fractions on number lines.

EXTRA PRACTICE SMALL-GROUP

ACTIVITY

▶ Plotting Rain Gauge Data 5–15 Min

(Math Masters, p. 213)

Students use rain gauge data to practice creating a line plot with fractional increments and then answer questions about the landmarks of the data set.


Copyright

© W

right

Gro

up/M

cG

raw

-Hill

211

LESSON

7�10

Name Date Time

Identifying Fractions on a Number Line

Label each number line with the correct fractions.

1. 0 1

2. 0 1

3. 0 1

4. Draw and label the following points on this number line. The first one is done

for you.

A: 1 2

_ 4 B:

1

_ 4 C:

4

_ 4 D:

8

_ 4 E: 2

3

_ 4

0 1 2 3 4

A

214

5. Jay, Kay, and Mae are in a 3-mile walk-a-thon. So far, Jay has walked 3

_ 4 mi,

Kay has walked 1 1

_ 2 mi, and Mae has walked

5

_ 2 mi. Draw and label points on

the number line below to show their approximate locations.

0 3

187-220_EMCS_B_MM_G5_U07_576973.indd 211187-220_EMCS_B_MM_G5_U07_576973.indd 211 2/25/11 9:20 AM2/25/11 9:20 AM

Copyrig

ht ©

Wrig

ht G

roup/M

cG

raw

-Hill

212

STUDY LINK

7�10 Scouting for Insects

Name Date Time

Some insects are harmful to

farmers’ crops. The insects listed

in this table are harmful to alfalfa

crops. Farmers scout their crops

and randomly collect sample plants.

They regularly observe the plants

and gather data to determine if the

insect population is growing or

remaining stable.

The table shows the result of

one farmer’s insect scouting.

Plot and label the lengths of the insects from the scouting sample on the

line plot below. Use the line plot to find the following data landmarks:

1. Minimum insect length in. 2. Maximum insect length in.

3. Range of insect lengths in. 4. Median insect length in.

5. Mean insect length in.

Type of Insect Average Length Number of of Insect (in.) Insects

Alfalfa Weevil Larvae

4

Fall Armyworm 1 1

_ 4 1

Meadow Spittlebug 1

_ 4 3

Pea Aphid 1

_ 8 6

Potato Leafhopper 1

_ 8 6

Number

ofInsects

Insect Lengths

Average Length (in.)

0 1 11212

34

3

_ 8

187-220_EMCS_B_MM_G5_U07_576973.indd 212187-220_EMCS_B_MM_G5_U07_576973.indd 212 2/25/11 9:20 AM2/25/11 9:20 AM

Copyright

© W

right

Gro

up/M

cG

raw

-Hill

213

LESSON

7�10

Name Date Time

Plotting Rain Gauge Data

3

2

1

in.

0 1 2Rainfall (in.)

3

Example: Read the rain gauge pictured above and place an X on

the line plot to show how much rain has been collected.

1. Read each rain gauge to find out how much rain fell each day.

Write the amount of rain on the line below the gauge.

Sun Mon Tue Wed Thu Fri Sat3

2

1

in. 3

2

1

in. 3

2

1

in. 3

2

1

in. 3

2

1

in. 3

2

1

in. 3

2

1

in.

in. in. in. in. in. in. in.

2. Use the number line

to make a line plot

recording daily rainfall

for 1 week. Label the

tick marks on the

number line. Place an

X to represent each

rain amount.

3. Analyze the rain gauge data to answer the questions below.

a. What is the mode amount of rain that fell each day? in.

b. What is the range of the rainfall during the week? in.

0 1

Rainfall (in.)

Numberof

Days

Daily Rainfall

2

187-220_EMCS_B_MM_G5_U07_576973.indd 213187-220_EMCS_B_MM_G5_U07_576973.indd 213 3/16/11 2:50 PM3/16/11 2:50 PM

line plots - everyday math · pdf filedate time line plots and data in fractional units cont....

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