CHAPTE R
7
Organize and
Display Data
connectED.mcgraw-hill.com
co
onn
The
BIG Idea
Investigate
How can I collect,
represent, and
interpret data in a
variety of graphs?
Animations
Vocabulary
Math Songs
Multilingual
eGlossary
Learn
Personal Tutor
Virtual
Manipulatives
Make this Foldable
to help organize
information about
data and graphs.
and
Organize
ata
Display D
Data
d Organize
Collect an
ian,
e, Medan
od
M
nd
Fi
d R ge
Outliers, an
Line Plots
le Bar Graphs
Bar and Doub
ility
ab
ob
Pr
Audio
Foldables
Self-Check Practice
eGames
Worksheets
Assessment
New Vocabulary
s
bar graph gráfica de barra
used to compare data by
using bars of different
s
heights to represent value
40
30
20
10
0
Under 5
Key Vocabulary
English
data
line plot
outcome
probability
324
Population of Kids
Number of Kids (millions)
Practice
Español
datos
esquema lineal
resultado
probabilidad
5–13
Age
14–17
When Will I Use This?
Ethan and Candace in
FIELD DAY DECISIONS
Field day is
coming up.
We need to
come up
with four
events. Any
ideas.
YA AA A AY !
How about a water
balloon toss?
Sack race!
Three-legged race!
Long
jump!
Obstacle
course!
What about
tug of war?
Wow, we have a lot of
events. Raise your
hand when I call the
event you want. You
get four votes.
Later...
I hope that event
doesn’t get many votes!
Ok, and the last one –
water balloon toss...
Field Day Event Votes
Event
Long jump
Obstacle course
Sack race
Three-legged race
Tug of war
Water balloon toss
Votes
7
15
17
11
18
Your Tthuiisrn!
You will sollve
err.
teer
problem in the chap
Organize and Display Data
325
Are You Ready
for the Chapter?
Text Option
You have two options for checking
Prerequisite Skills for this chapter.
Take the Quick Check below.
Make a tally chart for each situation.
1. Alexi took a survey to find
her friends’ favorite colors.
2. Mr. Bailey recorded the ages of the
students on the basketball team.
Favorite Colors
Ages of Basketball Players
red
yellow
green
10
11
9
blue
pink
red
9
10
11
green
blue
pink
10
9
10
red
blue
blue
10
10
10
Order from least to greatest.
3. 12, 17, 19, 15, 13
4. 87, 56, 72, 34, 94
5. 31, 60, 23, 87, 91
Use the graph to answer each question.
7. How does the number of students
who like music and gym compare to
the number of students who like art?
10
9
8
7
6
5
4
3
2
1
0
Students’ Favorite Class
Number of Students
6. How many more students like art
than gym?
Art
Gym
Class
Online Option
326
Take the Online Readiness Quiz.
Organize and Display Data
Music
Multi-Part
Lesson
1
Collect and Organize Data
PART
A
Main Idea
I will take a survey
and collect and
organize data.
Vocabulary
V
ssurvey
data
B
D
E
Collect and
Organize Data
A survey is a way to collect data or information that answers
a question. You can use a tally chart or a frequency table to
record data.
tally chart
frequency table
Organize Data
Get ConnectED
GLE 0406.5.1
Collect, record, arrange,
present, and interpret data
using tables and various
representations.
SPI 0406.5.1 Depict
data using various
representations (e.g.,
tables, pictographs, line
graphs, bar graphs). Also
addresses GLE 0406.1.7.
SCHOOL Ms. Alvarez
asked her students,
“What is your favorite
after school activity?”
The results are shown.
Organize the data in
a tally chart and a
frequency table.
Step 1 Draw a table with
two columns. Include a title.
Step 2 List each activity in the first column.
Step 3 Use tally marks or numbers to record the results.
Tally Chart
Frequency Table
Favorite After
School Activities
Favorite After
School Activities
Activity
Frequency
Playing a sport
Playing a sport
5
Reading
Reading
4
Watching T.V.
Watching T.V.
3
Activity
Tally
Each tally mark
represents a student.
Numbers are used
to record the results.
Lesson 1A Collect and Organize Data 327
You can take a survey and collect and represent data on charts
and tables.
Mini-Activity
Step 1 Write a survey question you can
ask your classmates. An example
is shown.
What type of pet is your favorite?
The tally marks used
to represent a value of
/ , not lllll.
5 are llll
a) dog
c) cat
b) fish
d) I do not like pets.
Step 2 Create a tally chart to record your results.
Step 3 Ask the question of each of your classmates.
Organize the data as you collect it.
Step 4 Use the information on your tally chart to create
a frequency table.
Analyze the data.
1. Write two sentences that describe your survey results.
2. Were the survey results what you expected? Explain.
1.
1 The data show the ways Mrs
Mrs. Jackson’s
students travel to school. Organize the
data in a tally chart. See Example 1
2.
2 Mary lists all the kinds of fish in her fish
tank. Organize the data below in a
frequency table. See Example 1
How Do You Travel to School?
Method
Frequency
Bicycle
Bus
Car
Walk
angelfish
angelfish
angelfish
clown fish
clown fish
3
6
9
5
3. Refer to Exercise 1. What is the most
popular way to travel to school? What
is the least popular? See Example 1
328
3
Mary’s Fish Tank
Organize and Display Data
4.
E
damsel
damsel
damsel
eel
eel
TALK MATH What are three
questions that you could use to
conduct a survey?
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Begins on page EP2.
Organize each set of data in a tally chart
chart. SSee EExample
l 1
5.
6.
Favorite Type of Pizza
Type of Movie
cheese
cheese
sausage
action
comedy
cheese
cheese
pepperoni
pepperoni
sausage
action
animated
comedy
comedy
Organize each set of data in a frequency table. See Example 1
7. Measurement Damián recorded the
items sold in the school store.
9. A survey was taken to see how
students spend their time at recess.
Items Sold at School Store
Item
Recess Activities
Tally
Eraser
Pencil
Scissors
8. Which item was the top seller?
kickball
drawing
swing
kickball
kickball
kickball
drawing
drawing
swing
swing
swing
swing
tag
tag
tag
10. How many students chose tag?
Use the information to solve the problem.
Field Day Decisions
Remember, my
students are voting
for Field Day
events. The four
events that receive
the most votes will
become the Field
Day events.
Now we have to
figure out which
four events received
the most votes.
Field Day Event Votes
Event
Long jump
Obstacle course
Sack race
Three-legged race
Tug of war
Water balloon toss
Votes
7
15
17
11
18
20
11. Which four events received the most votes?
12. OPEN ENDED Explain how a frequency table differs
from a tally chart. How are they alike?
13.
E
WRITE MATH Would it be better to use a frequency table or a tally
chart to organize data about your city’s population? Explain.
Lesson 1A Collect and Organize Data 329
Multi-Part
Lesson
1
PART
Collect and Organize Data
A
Main Idea
I will identify the mode,
median, outliers, and
range of a set of data.
Vocabulary
V
mode
median
outlier
B
Find Mode, Median,
Outliers, and Range
The mode of a set of data is the number or numbers that
occur(s) most often. If no number occurs more than once, there
is no mode. The median is the number in the middle when the
numbers have been arranged from least to greatest.
range
Get ConnectED
SPI 0406.5.3
Given a set of data or
a graph, describe the
distribution of the data
using median, range,
or mode.
Identify Mode
and Median
SCIENCE The largest spider in the world
is almost 1 foot long. Look at the table.
What are the mode and the median
of the data?
World’s Largest Spiders
Spider
Length (in.)
Goliath birdeater
11
Slate red ornamental
9
King baboon
8
Salmon pink birdeater
10
Colombian giant redleg
8
To find the mode, find the number that occurs most often.
11, 9, 8, 10, 8
8 appears twice.
So, the mode is 8.
To find the median, first arrange the numbers in order from
least to greatest. Then, find the middle number.
8, 8, 9, 10, 11
9 is the middle number.
So, the median is 9.
330
Organize and Display Data
An outlier is an item of data that is either much greater or much
less than the rest of the data. A data set may not have outliers.
The difference between the greatest and least values of a data
set is the range .
Identify Outliers
and Range
MOVIES What are the outlier and the range of the data?
M
Movie Tickets Sold
In some cases, when
no numbers repeat
in a data set, there is
no mode. There can
also be more than
Day
Sun.
Mon.
Tues.
Wed.
Thurs.
Fri.
Sat.
Tickets
285
110
232
236
235
252
306
To find the outlier, find the number that is either much
greater or much less than the rest of the data.
The number of tickets sold on Monday was 110. The number
110 is an outlier because it is much less than the other data
items, which were between 232 and 306.
one mode.
To find the range, find the least number and the greatest
number. Then subtract.
306 – 110 = 196
So, the outlier is 110, and the range is 196.
Find the mode,
mode median,
median and range of each set of data.
data Identify any
outliers. See Examples 1 and 2
1.
2.
Shells Found on a Beach
Name
Shells Found
Fish Caught While Camping
Day
Fish Caught
Margo
9
Monday
3
Eva
7
Tuesday
6
Dani
9
Wednesday
2
Sondra
8
Thursday
4
Louis
7
Friday
7
The table shows the time
spent studying by fourth grade
students each day.
Time Spent Studying
Day
Time (min)
Mon.
Tues.
Wed.
Thurs.
Fri.
15
20
18
40
10
3. Identify the outlier.
4.
E
TALK MATH Give a possible explanation for an outlier in this
situation.
Lesson 1B Collect and Organize Data 331
EXTRA
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Begins on page EP2.
Find
the mode,
and
data.
Identify
Fi
d th
d median,
di
d range off each
h sett off d
t Id
tif
any outliers. See Examples 1 and 2
5.
Faces Painted at a Fair
Pints Sold
Day
Monday
18
Wednesday
Tuesday
14
Thursday
23
Wednesday
11
Friday
25
Thursday
16
Saturday
24
3
Sunday
28
Day
Friday
7.
6.
Pints of Strawberries Sold
8.
Scores in Golf Tournament
Faces Painted
8
Arts Festival Visitors
Player
Scores
Day
Visitors
Trisha
58
Wednesday
46
Marita
42
Thursday
40
Aashi
64
Friday
35
Ted
49
Saturday
12
Ciro
56
Sunday
40
9.
Theme Park Ticket Prices
Theme Park
A
B
C
D
E
F
G
Adult Ticket
$39
$59
$49
$45
$20
$50
$35
10.
Average High Temperatures for Each Month ( °F )
Month
Temp. ( °F )
August
September
October
November
December
January
February
85
78
68
50
45
42
45
11. Look at Exercise 9. What is the
difference in cost of one adult ticket
for parks C and G?
12. Measurement Look at Exercise 10.
How much warmer was it in August
than in September?
Science
The table at the right shows the
number of rings for five planets.
Planets with Rings
Planet
Rings
Uranus
11
13. Identify the mode and median of the data.
Jupiter
1
14. Identify the outlier.
Saturn
1,000
15. How many more rings does Saturn have than
Uranus? Neptune?
Neptune
6
Earth
0
332
3
Organize and Display Data
16. FIND THE ERROR Carmen is finding
the median of the data set 34,
51, 49, 27, and 38. Find and
34, 51, 49, 27, 38
correct her mistake.
median
17.
E
WRITE MATH A grocery store sold 15, 20, 10, 12,
and 5 pints of strawberries each of 5 days. Find the mode,
median, and range of the data set. Write a sentence to
compare this data with the data from Exercise 5.
Test Practice
18. Which sentence best describes the
data? (Lesson 1A)
19. What is the median of the
data set? (Lesson 1B)
Favorite Animals
Animal
Math Test Scores
Student
Number of Students
Dolphin
Score
Angela
89
Carmen
93
Elephant
Edgardo
85
Lion
Rafiq
78
Justin
89
Snake
A. Thirteen students were surveyed.
B. Lions are least popular.
F. 78
G. 85
C. Elephants are most popular.
H. 89
D. Three students like snakes.
I. 93
20. Miss Moore recorded the jersey sizes for the
girls volleyball team. Organize the information
in a frequency table. (Lesson 1A)
Jersey Sizes
extra small
small
medium
large
21. How many more medium shirts than extra small
shirts were ordered? (Lesson 1A)
To assess mastery of SPI 0406.5.3, see your Tennessee Assessment Book.
333
Multi-Part
Lesson
2
Line Plots and Line Graphs
A
PART
B
C
D
E
Problem-Solving Strategy:
Make a Table
Main Idea I will solve problems by making a table.
The music club at Steven’s school is going
to a concert. There are 2 teachers going to
the concert for every 9 students. If there
are 16 teachers, how many students are
going to the concert?
Understand
What facts do you know?
• There are 2 teachers going for
every 9 students.
• The total number of teachers going is 16.
What do you need to find?
• Find how many students are going to the concert.
Plan
You can make a table to solve the problem.
Solve
Make a table to show that there are 2 teachers for every
9 students going.
+2
Teachers
Students
2
9
+9
+2
4
18
+9
+2
6
27
+9
+2
8
36
+9
+2
10
45
+9
+2
12
54
14
63
+9
+2
16
72
+9
So, 72 students are going to the concert.
Check
Divide the total number of teachers by the number of teachers
per group.
16 ÷ 2 = 8
There are 8 groups. There are 9 students in each group.
So, there are 8 × 9 = 72 students going altogether. The answer
is correct. GLE 0406.3.2 Use mathematical language and modeling to develop descriptions, rules and extensions
of patterns.
334
Organize and Display Data
Refer to the problem on the previous page.
1. Explain how a table was used to find
the number of students going to the
concert.
3. Suppose 1 teacher was going for every
3 students. How many teachers would
be going on the trip with 72 students?
2. What pattern is shown in the table?
4. Refer to Exercise 3. Check your answer.
How do you know that it is correct?
EXTRA
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Begins on page EP2.
Solve. Use the make a table strategy.
5. Algebra Kenya’s school day is
6 hours long. Copy and complete the
table to find if her school day is more
or less than 300 minutes.
Hours
1
2
Minutes
60
120
3
4
5
6
6. Malik buys a $2 lunch every day at
school. How many lunches can Malik
purchase for $17?
7. Martín sold some of his old toys on the
Internet. The cost of shipping each
item is shown. If he paid $32 in
shipping, how many of his toys did
he ship?
9. Elki received her first paycheck from a
job. She earns $150 every 2 weeks.
How many weeks will it take her to
earn more than $1,000?
10. The state sales tax is $7 for every
$100 spent on certain items. Takara’s
mother is charged $21 in tax at the
store. What was the total cost of all
the items she purchased?
11. Algebra Don spends 40 minutes on
homework every night. How many
minutes of homework does he
complete in 5 days?
Day
Shipp
ing
Cost:
$4
Monday
40
Tuesday
80
Wednesday
120
Thursday
8. Jenna scored 24 points in her last
basketball game. She made 2 baskets
for every 5 shots she took. If one
basket is equal to 2 points, how
many shots did she take for the
entire game?
Friday
12.
Total Homework
n)
Time (min)
E
WRITE MATH Explain why the
make a table strategy is a good
problem-solving strategy to use for
Exercise 10.
Lesson 2A Line Plots and Line Graphs 335
Multi-Part
Lesson
2
Line Plots and Line Graphs
PART
A
Main Idea
I will represent and
interpret data in a
line plot.
Vocabulary
V
B
C
D
E
Line Plots
You have used tally charts and frequency tables to show
data. A line plot is a way to show data using Xs above a
number line.
line plot
Get ConnectED
Make a Line Plot
GLE 0406.5.1
Collect, record, arrange,
present, and interpret data
using tables and various
representations.
SPI 0406.5.3 Given a
set of data or a graph,
describe the distribution
of the data using median,
range, or mode.
SCIENCE Vijay went
camping in Pennsylvania
Wilds. He recorded
the number of elk
he saw in a tally
chart. Represent
the data in a
line plot.
Elk Observed
Day
Tally
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Step 1 Draw and label a
number line.
1
2
3
4
5
6
7
8
Step 2 Mark an X above the number line to show each data
item. Add a title.
Elk Observed
X
X
X
1
336
3
Organize and Display Data
2
3
The two Xs represent the
two days he saw 4 elk.
X
X
X
4
5
X
6
7
8
Read a Line Plot
READING Bianca’s class took part in a reading
competition. The results are shown below. Identify the
mode, median, range, and any outliers for the data set.
The least and greatest
numbers included in
the line plot should fit
Books Read
the data being
displayed.
median
outlier
X
2
3
4
X
X
X
5
mode
X
X
X
X
X
X
X
6
7
8
Range is 8 – 2.
So, the mode is 7, the median is 6, the range is 6,
and the outlier is 2.
Organize each set of data in a line plot. See Example 1
1.
2.
Ages of Students
Time Spent on Chores
Student
Time (h)
11
11
10
12
10
11
11
11
Mac
3
10
11
11
10
Julio
1
Tala
2
Peyton
3
Identify the mode, median, range, and any outliers for each set of data. See Example 2
3.
4.
Distance Live from School (miles)
X
X
X
X
X
X
X
X
1
2
3
4
Time Spent on Homework (min)
X
X
X
X
X
X
X
X
10 11 12 13 14 15 16 17 18 19 20
5
6
7
8
9
The line plot shows weekly allowances.
Friends’ Allowances
5. What is the most money a person receives?
6.
E
TALK MATH Sumi’s weekly
allowance is $4. Should she use the
line plot to convince her parents to
increase her allowance? Explain.
X
X
X
X
X
X
X
X
X
X
$5
$6
$7
$8
X
$9
$10
Lesson 2B Line Plots and Line Graphs 337
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EXTRA
Begins on page EP2.
Organize each set of data in a line plot
plot. See Example 1
7.
8.
Crickets Caught
Day
Test Scores
Student
Crickets
Score
Monday
6
Darin
95
Tuesday
3
Janna
91
Wednesday
8
Grace
90
Thursday
6
Arnoldo
95
Friday
6
Lali
86
9.
10.
Points Scored per Game
Magazine Subscriptions Sold
4
4
6
10
12
15
9
16
8
3
4
5
11
10
12
8
6
5
2
4
15
11
10
11
Identify the mode, median, range, and any outliers for each set of data. See Example 2
11.
12.
Shoe Sizes
X
X
X
X
X
X
4
5
6
7
13.
X
8
9
X
1
2
3
X
10 11
X
X
X
X
X
X
4
5
15
14.
Goals for Chase’s Team
Time Spent Walking Dogs (min)
6
XX
17
19
X
X
X
X
X
X
X
X
5
6
7
Mr. Simmons recorded the
height of each player on his basketball team.
Organize and Display Data
23
27
25
X
8
9
10 11 12
Height (in.)
15. How many players are 58 inches tall?
338
3
X
X X
Pencils on Mr. Wilkenson’s Desk
Measurement
16. The median height of the players of the
Los Angeles Clippers is 80 inches.
Compare this height to the median height
of the players on Mr. Simmons’s team.
21
X XX
X
53
54
X
X
X
X
X
55
56
X
X
X
X
X
X
X
57
58
59
60
17. OPEN ENDED Create a survey question to ask your classmates.
Ask your question. Collect and represent the data on a line plot.
18.
E
WRITE MATH How would the median change if the lowest
score in Exercise 8 was replaced with 93?
Test Practice
19. What is the median of the data in the
frequency table? (Lesson 1B)
20. What is the mode of the data on
the line plot? (Lesson 2B)
Garden Vegetables
Vegetable
Backpack Weights (lbs)
Frequency
Carrots
49
Celery
25
Cucumbers
28
Lettuce
32
Onions
44
A. 49
C. 32
B. 44
D. 28
X
X
X
1
X
X
X
X
X
X
X
X
X
2
3
4
5
6
F. 2
H. 4
G. 3
I. 8
7
8
21. There are eight hamburger buns in a package. How many
packages of hamburger buns should Mr. Green buy to make
43 hamburgers? (Lesson 2A)
Refer to the table to the right.
It lists the items in Ella’s school
supply box. (Lesson 1B)
22. Find the mode of the set of data.
23. Find the median of the set of data.
24. Identify any outliers in the set of data.
Ella’s School Supply Box
Supply
Frequency
Crayons
36
Erasers
5
Glue
1
Pencils
7
Scissors
1
Lesson 2B Line Plots and Line Graphs 339
Multi-Part
Lesson
2
Line Plots and Line Graphs
PART
A
B
C
D
E
Stem-and-Leaf Plots
Main Idea
I will construct and analyze
stem-and-leaf plots.
A stem-and-leaf plot is another way to organize data. The
data in a stem-and-leaf plot is ordered from least to greatest
and is organized by place value.
Vocabulary
V
sstem-and-leaf plot
stem
leaf
Get ConnectED
GLE 0406.5.1
Collect, record, arrange,
present, and interpret data
using tables and various
representations.
SPI 0406.5.1 Depict
data using various
representations (e.g.,
tables, pictographs, line
graphs, bar graphs).
NATURE Mr. Myren’s
class went on a hike.
Five students recorded
the number of birds
they saw in a table.
Make a stem-and-leaf
plot of the data.
Step 1
Step 3
Allison
Benny
Dave
Emily
Jackie
Terrence
18
15
24
38
27
27
Order the data from
least to greatest.
15
Step 2
Birds Observed
Student
Number of
Birds
18
24
27
27
Order the tens digits
in a column from
least to greatest
to form the stems .
Write each ones digit
in order to the right
of its tens digit. The
ones digits form
the leaves .
38
Stem
1
2
3
Stem
Each tens digit is
called a stem.
Leaf
1
2
3
5 8
4 7 7
8
3
8 = 38 birds
Always add each leaf even if it repeats.
Step 4
340
Organize and Display Data
Include a key to show what each
stem and leaf represents.
Key
About It
1. Explain the difference between a stem and a leaf in a stem-andleaf plot.
2. If another student saw 42 birds, how would your stem-and-leaf
plot change?
and Apply It
Organize each set of data in a stem-and-leaf plot.
3.
Hours of Television Watched
Each Week
10
5
16
14
15
7
10
12
12
18
20
8
4.
Temperatures (°F)
67
85
73
65
68
79
70
82
66
77
71
69
55
70
59
71
Use the stem-and-leaf plot that shows prices of guitars.
5. How much is the least
expensive guitar?
Prices of Guitars
Stem
6. How much is the most
expensive guitar?
7. How many guitars cost
more than $100?
8. Write a sentence that describes
the data.
Leaf
7
8
9
10
11
12
5
4
4
1
0
0
9
10
9 = $109
5
5
5
1
8 9
9
7 8
5 7
Use the stem-and-leaf plot that shows the number
of butterflies observed in a garden by students.
9. What was the least number of
butterflies observed?
10. What was the greatest number of
butterflies observed?
11. What number of butterflies was
counted most often?
12. Write a sentence that describes the data.
13.
E
Number of Butterflies Observed
Stem
Leaf
0
1
2
3
4
5
8
2
0
2
1
0
9
5
1
3
1
1
5 = 15 butterflies
8
1 1 5 9
4 6
5 8
WRITE MATH Write a sentence to
describe the data in Exercise 4.
Lesson 2C Line Plots and Line Graphs 341
Multi-Part
Lesson
2
Line Plots and Line Graphs
PART
A
Main Idea
I will interpret data in a
line graph.
Vocabulary
V
B
D
C
E
Line Graphs
A line graph shows how data changes over time. You can use
a line graph to make predictions about future events.
line graph
Interpret a Line Graph
GLE 0406.5.1
Collect, record, arrange,
present, and interpret data
using tables and various
representations.
SPI 0406.5.2 Solve
problems using estimation
and comparison within a
single set of data. Also
addresses GLE 0406.1.1.
FLOWERS The graph shows the growth of a flower
over four months. How tall did the flower grow in
four months?
Find the fourth month shown on the graph. It is June.
Flower Growth
10
Height (in.)
Get ConnectED
8
6
4
2
0
March
April
May
June
Month
Move up to find where the point is located on the graph.
Then compare the height of the point to the scale on the left.
Flower Growth
Height (in.)
10
8
6
4
2
0
March
April
May
June
Month
The point is located between 8 and 10 on the graph’s scale.
So, the flower grew about 9 inches in four months.
342
3
Organize and Display Data
Interpret a Line Graph
MEASUREMENT The graph shows the growth of a baby
panda over four weeks. How much weight did the baby
panda gain between the first week and the fourth week?
Growth of Panda
Weight (lb)
14
13
12
11
10
0
1
2
3
4
Week
You need to subtract the panda’s weight at week 1
from its weight at week 4.
During week 1, the panda weighed 11 pounds. During
week 4, the panda weighed 14 pounds.
14 - 11 = 3
So, the baby panda gained 3 pounds between the first week
and the fourth week.
Use the line graph. See Examples 1 and 2
1. At what time is the least amount of
snow on the ground?
3. How many more inches of snow were
on the ground at 9 P.M. than at 6 P.M.?
Depth (in.)
2. How much snow is on the ground
at 8:00 P.M.?
Amount of Snow
12
10
8
6
4
2
0
6 P.M. 7 P.M. 8 P.M. 9 P.M. 10 P.M.
Time
4. How many fewer inches of snow were
on the ground at 7 P.M. than at 10 P.M.?
5. How much snow fell over the 4-hour
period shown on the graph?
6.
E
TALK MATH Predict how much snow will be on the ground
at midnight.
Lesson 2D Line Plots and Line Graphs 343
EXTRA
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Begins on page EP2.
Use the
the
h graph
h that
h shows
h
h number
b off words
d read.
d See Examples 1 and 2
7. How many words were read in two
minutes?
Words
8. How many words were read in five
minutes?
Words Read
9. At this rate, how many words will be
read in six minutes?
600
500
400
300
200
100
0
1
2
3
4
5
Minutes
10. How many fewer words were read in
two minutes than in four minutes?
11. How many more words were read in
five minutes than in one minute?
12. How many miles did the car travel in
two hours?
13. How many miles did the car travel in
three hours?
14. What distance did the car travel between
two and four hours?
Distance Traveled (miles)
Use the graph that shows the distance a car travels. See Examples 1 and 2
Distance Traveled by Car
300
250
200
150
100
50
0
1
2
15. How long does it take the car to travel
200 miles?
3
4
5
Time (hours)
16. How many more miles did the car travel
in five hours than in two hours?
18.
E
WRITE MATH The graph shows the
rate of a submarine’s descent
underwater. Write two sentences
that describe the data.
Submarine Descent
Feet Below Sea Level
17. OPEN ENDED Give an example of a set
of data that is best represented in a
line graph.
1,200
1,000
800
600
400
200
0
2
4
6
Time (min)
344
3
Organize and Display Data
8
10
Multi-Part
Lesson
2
Line Plots and Line Graphs
PART
A
B
C
D
E
Make a Line Graph
Main Idea
I will represent data in
a line graph.
In the following activity, you will collect and represent
data in a line graph.
Materials
Step 1
Get ConnectED
GLE 0406.5.1
Collect, record, arrange,
present, and interpret data
using tables and various
representations.
SPI 0406.5.1 Depict
data using various
representations (e.g.,
tables, pictographs, line
graphs, bar graphs).
Time
Collect weather
data from one
day. Record the
temperatures
in a table like
the one shown.
grid paper
newspaper
Collect data.
Step 2
Temperature (°F)
9 A.M.
10 A.M.
11 A.M.
12 P.M.
1 P.M.
Create a graph.
Draw and label two axes. Then write a title at the
top of the graph. Choose an appropriate scale for
your graph.
One Day’s Temperatures
Temperature (°F)
colored pencils
Label the
axes.
80
75
70
65
60
0
9 A.M. 10 A.M. 11 A.M. 12 P.M. 1 P.M.
Time
Lesson 2E Line Plots and Line Graphs
345
Graph the data.
Step 4
Temperature (°F)
Above 9 A.M., place
a point at the correct
temperature. For example,
if the high was 60, then
place a point at 60.
Continue graphing the
rest of the data. An
example is shown.
One Day’s Temperatures
80
75
70
65
60
0
9 A.M. 10 A.M. 11 A.M. 12 P.M. 1 P.M.
Time
Draw a line.
Connect the points
with straight lines.
One Day’s Temperatures
Temperature (°F)
Step 3
80
75
70
65
60
0
9 A.M. 10 A.M. 11 A.M. 12 P.M. 1 P.M.
Time
About It
1. Describe how a line graph shows how data changes over time.
2. Explain how you labeled the axes and chose a scale for the data.
and Apply It
Represent each data set in a line graph.
3.
5.
Plant Growth
4.
One Day’s Temperatures
Week
Height (in.)
Time
Temperature (˚F)
1
1
12 P.M.
62°
2
2
1 P.M.
65°
3
3
2 P.M.
72°
4
5
3 P.M.
66°
5
8
4 P.M.
64°
E
WRITE MATH Give an example of a set of data that is best
displayed in a line graph.
346
3
Organize and Display Data
Mid-Chapter
Check
1. Organize the set of data in a tally chart
and in a frequency table. (Lesson 1A)
Sandwiches for a Picnic
Peanut butter
Turkey
Ham
Ham
Turkey
Ham
Turkey
Peanut butter
Ham
For Exercises 2 and 3, use the tally chart
below. (Lesson 1A)
Solve. Use the make a table strategy.
(Lesson 2A)
6. It costs $32 for 2 admissions to a
museum. Ebony and her father invite
10 friends for opening night. At this
rate, how much would it cost for
everyone to go to the museum?
7. Organize the set of data in a line
plot. (Lesson 2B)
Where Do You Read?
Place
Time It Takes to Walk Home (min)
Tally
Outside
Bedroom
10
11
12
15
12
15
8
7
10
8
10
9
Library
2. Where do most students like to read?
8. MULTIPLE CHOICE About how many
more pages did Julian read on Day 3
than on Day 4? (Lesson 2D)
Number of Pages Read
Living room
3. How many students read in their
bedrooms or at the library?
4. MULTIPLE CHOICE What is the mode
of the data set {4, 5, 8, 8, 4, 3, 4}?
(Lesson 1B)
A. 3
C. 5
B. 4
D. 8
250
200
150
100
50
0
Day 1
F. 50 pages
G. 75 pages
5. Find the mode and median of the
data. Identify any outliers. (Lesson 1B)
Movies Rented During a Week
1
2
3
4
5
Day
29 58 62 55 64
Movies
Julian’s Reading Log
9.
Day 2 Day 3
Day
Day 4
H. 100 pages
I. 200 pages
E
WRITE MATH Explain the
difference between a line plot and
a stem-and-leaf plot. (Lesson 2C)
Mid-Chapter Check 347
Multi-Part
Lesson
3
Bar Graphs
PART
A
Main Idea
I will interpret a bar
graph.
Vocabulary
V
bar graph
B
C
D
E
Bar Graphs
A bar graph is used to compare data by using bars of different
heights or lengths to represent values. You can interpret data that
is displayed in a bar graph.
Get ConnectED
MEASUREMENT The students in Mrs. Smith’s class
measured their heights in inches. What was the most
common height?
Heights of Students
Number of Students
GLE 0406.5.1
Collect, record, arrange,
present, and interpret data
using tables and various
representations.
SPI 0406.5.2 Solve
problems using estimation
and comparison within a
single set of data.
Interpret a Bar Graph
10
9
8
7
6
5
4
3
2
1
0
52 53 54 55 56 57 58
Height in Inches
The tallest bar represents the height of the most students.
Number of Students
Heights of Students
10
9
8
7
6
5
4
3
2
1
0
52 53 54 55 56 57 58
Height in Inches
So, the most common height was 55 inches tall.
348
3
Organize and Display Data
Interpret a Bar Graph
Ohio Cities’ Land Area
City
Cincinnati
Cleveland
Columbus
Dayton
To write a statement
that describes the
data in a bar graph,
you need to
compare the lengths
of the bars in the graph.
0
In grade 3 you learned
that a scale is a set of
numbers that
represents data.
MEASUREMENT
The bar graph
shows the land
area of four cities
in Ohio. Write a
statement that
describes the
data.
50
100
150
200
Land Area (Square Miles)
The bar for Columbus is the longest. So, you can write
that Columbus has the largest land area of the four cities
shown.
Use the
h graph shown. See Examples 1 and 2
1. During which grade was Janet absent
the most days?
3. How many more days was Janet
absent in second grade than in third
grade?
4. How many days has Janet been
absent since she finished the first
grade?
Grade Level
2. What grade was Janet in when she
was absent for 3 days?
Janet’s School Absences
3
2
1
K
0
2
4
6
8
10
12
Number of Days Absent
5. Write a statement that describes the
data in the graph.
6.
E
TALK MATH Refer back to Exercise 4. How did you find
the answer?
Lesson 3A Bar Graphs 349
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Measurement The graph shows the
160
140
120
100
80
60
40
20
0
Tornado Frequency
AL AR KS MN MS TX WI
State
(s
ho Pi
rtf lot
in
ne
d)
in
ke
M
H
um
0
pb
ac
k
120
100
80
60
40
20
Number of Tornadoes
Whale Lengths
Bl
ue
Average Length of Whale (ft)
lengths of certain whales. See Examples 1 and 2
The graph shows the states with the most
tornadoes in a recent year. See Examples 1 and 2
Whale
7. Which type of whale is the
shortest?
11. Which states appear to have had the
same number of tornadoes?
8. Which whale is about 50 feet long?
12. About how many more tornadoes
were in Texas than in Alabama?
9. Why is the scale set in intervals of
20 feet?
13. About how many more tornadoes
were in Kansas than in Wisconsin?
10. Can you find the exact difference
between the lengths of a humpback
whale and a minke whale by using
this bar graph? Explain.
14. Which two states had a combined total
of about 220 tornadoes? Explain how
you found your answer.
15. OPEN ENDED Where have you seen bar graphs used outside the
classroom? What information was being described?
16. NUMBER SENSE Why is it sometimes necessary to estimate when
reading a bar graph?
17.
350
3
E
WRITE MATH Refer to the graph used for Exercises 11–14.
Would this graph be easier to read if the scale was changed to intervals
of 100? Explain.
Organize and Display Data
Graphs
A circle graph, or pie chart, is another way to organize data.
Make a Circle Graph
FRUIT A bag contains 8 of the following apples:
4 red apples, 2 green apples, and 2 yellow apples.
Make a circle graph to show these data.
Step 1
Draw a circle. Place connecting
cubes to represent the apples
on the outline of the circle.
When interpreting a
graph:
1
is __4
Step 2
Place a point in the center of
the circle. Draw line segments
from the center of the circle to
the points of the circle
where the colors change.
1
is __3
1
is __2, and
3
is __4
Apple Colors
Step 3
Shade and label each section.
Write a title for the graph.
red
apples green
apples
yellow
apples
For Exercises 18 and 19, use the circle graph above.
18. Most of the apples in the bag are what
color?
19. What fraction of the apples is red or
green?
20. Use the data in the table at the right to
make a circle graph.
21.
E
WRITE MATH Survey eight of your
classmates. Ask each to name his or her
favorite field trip. Display the results in a
circle graph. Write 2 sentences to interpret
your data.
Favorite Pizza Toppings
Topping
Students
Cheese
4
Pepperoni
1
Other
1
To assess mastery of SPI 0406.5.1, see your Tennessee Assessment Book.
351
Multi-Part
Lesson
3
Bar Graphs
PART
A
B
C
D
Make Double Bar Graphs
Main Idea
Double bar graphs are used to compare two sets of related data.
I will display data in
double bar graph.
Step 1
colored pencils
Create a frequency
table that shows
the number of
minutes you and
a partner spend
studying or doing
homework each
day over the span
of a school week.
graph paper
Get ConnectED
Collect data.
Step 2
GLE 0406.5.1
Collect, record, arrange,
present, and interpret data
using tables and various
representations.
SPI 0406.5.1 Depict
data using various
representations (e.g.,
tables, pictographs, line
graphs, bar graphs).
Create
a graph.
Time Spent
Studying/Homework
Day
Student 1
Draw and
label the axes.
s.
Tues.
Wed.
Thurs.
Fri.
Time Spent Studying/Homework
Student 1
Student 2
Key
Mon.
Tues.
Wed.
Day
Draw and label two axes. Write a
title at the top. Choose a color for
each set of data and make a key.
352
Organize and Display Data
a
Student 2
Mon.
Minutes
Materials
Thurs.
Fri.
Step 3
Choose a scale.
The scale should include the least and the greatest
number from your data.
Time Spent Studying/Homework
Minutes
This scale goes
from 0 to 90 by 15s.
Start the
scale at zero.
90
75
60
45
30
15
0
Student 1
Student 2
Mon.
Tues.
Wed.
Thurs.
Fri.
Day
Draw bars.
Time Spent Studying/Homework
Draw the bars for your
data on the graph. Then
draw the bars for your
partner’s data on the
graph.
Minutes
Step 4
90
75
60
45
30
15
Student 1
Student 2
0
Mon.
Tues.
Wed.
Thurs.
Fri.
Day
About It
1. Tell how you can use a double bar graph to compare data.
2. Explain how you choose a scale and intervals.
and Apply It
Represent each set of data in a double bar graph.
3.
Month
5.
4.
Books Read
Allowance
Miki
Alicia
Age
Morgan
Eli
May
3
2
7
$2
$0
June
5
6
8
$3
$1
July
4
5
9
$4
$3
August
6
4
10
$5
$5
E
WRITE MATH Look at Exercises 3 and 4. Write a comparison
sentence that describes the data in each table.
Lesson 3B Bar Graphs 353
Multi-Part
Lesson
3
Bar Graphs
PART
A
Main Idea
I will interpret double bar
graphs to answer
questions.
Vocabulary
V
B
C
D
E
Double Bar Graphs
A double bar graph displays two sets of related data using
bars of different colors and heights.
double bar graph
d
Read Double Bar Graphs
Get ConnectED
SCHOOL The double bar graph shows the number of
boys and girls selling magazines for a fundraiser.
About how many
students will sell
magazines in the
second grade?
There are about 40
boys and about 45 girls
in the second grade.
40 + 45 = 85
So, about 85 students
will sell magazines in
second grade.
Magazine Sales
Boys
50
Number of Students
GLE 0406.5.1
Collect, record, arrange,
present, and interpret data
using tables and various
representations.
SPI 0406.5.2 Solve
problems using estimation
and comparison within a
single set of data.
Girls
40
30
20
10
0
1st
2nd 3rd
Grade
4th
How many more fourth grade girls will sell magazines
than fourth grade boys?
Subtract the number of fourth grade boys selling magazines
from the number of fourth grade girls.
fourth grade boys
40 – 30 = 10
fourth grade girls
So, 10 more fourth grade girls will sell magazines than
fourth grade boys.
354
3
Organize and Display Data
CLIMATE The double bar graph shows the average
temperatures of two cities over four months. On average,
which city has a warmer summer?
Look at the bar graph.
In April, Seattle is slightly warmer. In May, June, and July,
Chicago is warmer.
So, on average, Chicago has a warmer summer.
When reading a
double bar graph,
always look at the
scale and the key.
Average Temperatures
Chicago
Seattle
Month
July
June
May
April
0
10
20
30 40 50 60
Degrees Fahrenheit
70
80
90
For Exercises 1–4, use the graphs shown. See Examples 1–3
Library Books
Third Grade
Fourth Grade
Sports
Type of Books
Learning to Play Instruments
Boys
10
Girls
8
Students
Mystery
Animals
6
4
2
Adventure
0
10
20
30
40
50
60
Number of Books
0
Clarinet Drum Flute Guitar Trumpet
Instrument
1. About how many students checked out
adventure books?
3. What is the least popular instrument
for boys?
2. About how many more fourth graders
checked out mystery books than third
graders?
4. What is the total number of students
surveyed?
5.
E
TALK MATH
Explain the difference between a bar graph and a double bar graph.
Lesson 3C Bar Graphs 355
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6. Which sport do most students
play?
7. Do more fourth grade students or
fifth grade students play a
sport?
Sports Played
25
Number of Students
Use the bar graph that shows the
number of students who play
each sport. See Examples 1–3
fourth grade
fifth grade
20
15
10
5
0
soccer
8. How many fourth and fifth grade
students play a sport?
baseball basketball volleyball
Sport
9. If the students who play soccer joined the baseball team,
would baseball have as many student players as basketball?
Use the double bar graph that shows the
number of tickets sold for a high school
play. See Examples 1–3
Play Tickets Sold
Adult
Number Attended
10. Which day had the highest total
attendance?
11. Did more adults or children attend on
Friday?
12. About how many adults attended in all?
20
15
10
5
0
Thursday Friday Saturday Sunday
13. Suppose adult tickets cost $4 and child
tickets cost $2. On which day was more
than $100 made in ticket sales?
Day of Week
E
WRITE MATH The graph shows the
value of stocks for three companies.
Write two sentences that describe
the data.
15. OPEN ENDED Describe a set of data
that could not be shown in a double
bar graph.
Stocks for Three Companies
June 2007
100
90
June 2008
80
70
60
50
40
0 Pizza Express ABC Bank Star Movies
Stock Prices
14.
Child
Company
356 To assess mastery of SPI 0406.5.2, see your Tennessee Assessment Book.
3
Graph
Race
Create a Bar Graph
You will need:
0–5 number cube, grid paper
Get Ready!
Players: 2 players
Get Set!
Draw a bar graph on grid paper
as shown.
Go!
Roll. The greater number
goes first.
Player 1 rolls the number
cube and graphs the
number on the bar graph.
If a 0 is rolled, it is Player 2’s
turn.
Player 2 rolls the number
cube and graphs the
number on the bar graph.
Player 1 rolls the number
cube again and adds the
result to his or her previous
amount.
Play continues until a
player’s bar goes over
45. That player wins.
Game Time Graph Race 357
Multi-Part
Lesson
1
3
PART
Bar Graphs
A
B
D
C
E
Problem-Solving Investigation
Main Idea I will solve problems by choosing the best strategy.
JAKE: I can earn 20,000 points in each
level of my video game. How many total
points can I earn by the third level of
my video game?
YOUR MISSION: Find how many points Jake
can earn by the third level of his
video game.
Understand
Jake can earn 20,000 points in each level of his video game.
Find how many points he can earn by the third level.
Plan
Organize the data to show the total number of points that
can be earned by each level.
Jake
Solve
Rule: t = 20,000 g
Level
Total
1
20,000
2
40,000
3
60,000
Jake can earn 60,000 points.
Check
Since 20,000 + 20,000 + 20,000 = 60,000,
you know that the answer is correct.
GLE 0406.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation,
and reasonableness of the solution. Also addresses GLE 0406.3.2.
358
3
Organize and Display Data
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• Choose an operation.
• Determine whether an answer
is reasonable.
• Make a table.
Use any strategy to solve each problem.
5. A black bear weighs 25 pounds more
than a gorilla. Use the information in
the table to find how much a black
bear weighs. Write and solve an
equation.
Large Animal Weights
1. Turi burns about 350 calories for every
hour he skis. The last time he skied, he
burned 1,200 Calories. Did he ski
more than 3 hours? Explain.
2. About 200,000 aluminum beverage
cans and 100,000 steel cans are
used in a state each day. Write a
number between the two given
numbers.
Animal
Gorilla
Black bear
Lion
Weight (pounds)
400
x
440
6. Each bag holds the lemons shown
below. Marisa needs 80 lemons.
How many bags of lemons should
she buy?
3. Every teacher at Elmwood Elementary
School is provided with the paper
shown below.
7. Skylar copied the predicted high
temperature (°F) for each of the
following 10 days. What is the range
of her set of data? {75, 78, 84, 82,
86, 90, 88, 74, 76, 77}
How many sheets of paper do the
40 teachers have altogether?
4. In one weekend, a movie made
$838,392. Round this number to the
nearest hundred thousand.
8.
E
WRITE MATH You need 132,000
pennies to make $1,320. You need
133,000 pennies to make $1,330. The
answer is 134,000. What is the
question?
Lesson 3D Bar Graphs 359
Height (ft)
360
25
20
15
10
5
0
Door
Organize and Display Data
Fourth Giraffe Sunflower
Grade
Student
Object
Sunflowers are giants in the
plant world. The tallest sunflower
grew to a total height of 25 feet
5 inches. The size of the largest
sunflower head is 32 inches across.
This is almost three feet across!
an important source of food.
Sunflower oil is a valued and
healthy vegetable oil. In addition,
sunflower seeds are enjoyed as a
healthy, tasty snack and a
nutritious ingredient in many
foods.
Sunflowers can be used for
decoration, but they are also
The shortest
sunflower on
record measured
just over
2 inches tall.
Use the information on the previous page to solve each problem.
1. What is the tallest object on the
bar graph? How tall is this object?
2. What is the difference in height of
a sunflower and a giraffe?
3. What is the shortest object on the
bar graph? How tall is this object?
4. Look at Exercise 3. Explain how
you found the answer.
5. What is the difference between the
tallest and shortest objects on the
bar graph?
6. The height of how many fourth
grade students equals the height
of a sunflower?
Problem Solving in Science 361
Multi-Part
Lesson
4
obability
Probability
PART
A
B
C
E
Possible Outcomes
Main Idea
I will explore the
possible outcomes of
an experiment.
Possible outcomes are all the results that could occur from an
experiment. In this activity, you will explore the possible
outcomes of an experiment.
Materials
spinner labeled 1–4
Get ConnectED
Use a spinner to create multi-digit numbers.
Step 1
SPI 0406.5.4
List all possible outcomes
of a given situation or
event. Also addresses
GLE 0406.1.3.
362
Spin a spinner like the one shown two times.
1
2
4
3
Step 2
Create two-digit numbers.
Use each digit once to make as many two-digit
numbers as possible. Record the numbers.
Step 3
Create three-digit numbers.
Spin the spinner a third time. If it lands on a digit
already spun, spin again. Use the two digits spun in
Step 1 and the digit you just spun to make as many
three-digit numbers as possible. Remember to use
each digit only once. Record the numbers you made.
Step 4
Create four-digit numbers.
Spin a fourth digit to go with the three digits you
previously spun. If the spinner lands on a digit you
already have, spin again. Use the fourth digit to
create as many numbers as possible.
Organize and Display Data
About It
1. How many two-digit numbers can be made with two digits,
if each digit is used only once?
2. How many three-digit numbers can be made with three digits,
if each digit is used only once?
3. How many four-digit numbers can be made with four digits,
if each digit is used only once?
4. Describe the strategy you used to find the numbers you made.
and Apply It
Determine all the possible outcomes for each situation.
5. What are all the possible outcomes if
the spinner is spun twice?
6. Describe an outcome that is not
possible if two connecting cubes are
chosen from the bag at a time.
M
H
T
7. What are all the possible outcomes if
the coin is flipped twice?
9.
8. What are all the possible outcomes if
two counters are each flipped once?
E
WRITE MATH Create an experiment using two spinners. What
are all the possible outcomes for that experiment? How did you find
all the possible outcomes? What predictions can you make?
Lesson 4A Probability 363
Multi-Part
Lesson
4
Probability
PART
A
Main Idea
I will use pictures to
find all the possible
outcomes in a problem
situation.
Vocabulary
V
outcome
o
B
C
Determine Possible
Outcomes
In the previous Explore activity, you learned that an outcome
is a result in an experiment. You can use a grid to help you
find outcomes.
tree diagram
Determine Outcomes
Get ConnectED
SPI 0406.5.4
List all possible outcomes
of a given situation or
event.
SPORTS In a basketball game, Samantha went to the
free-throw line. She shot two free throws. How many
possible outcomes does Samantha have for her two
free throws?
One way to find the possible outcomes is by making a grid.
On a grid, each outcome is shown where each row and
column intersect.
First Shot
Second Shot
Make
Miss
Make
Make,
Make
Make,
Miss
Miss
Miss,
Make
Miss,
Miss
These are Samantha’s possible outcomes.
So, there are 4 possible outcomes.
364
Organize and Display Data
Another way to find the possible outcomes is by using a tree
diagram . A tree diagram uses “branches” to show all the
possible outcomes.
Possible Outcomes
A student is spinning
two spinners. How
many possible
outcomes are
there?
Make a branch for
each possible
outcome.
A tree diagram can be used to find all the possible
outcomes for spinning both spinners.
First
Spinner
Second
Spinner
Outcomes
Orange
Red
Blue
Orange, Red
Orange, Blue
Purple
Red
Blue
Purple, Red
Purple, Blue
Yellow
Red
Blue
Yellow, Red
Yellow, Blue
So, there are 6 possible outcomes.
1. Draw a grid to find the number of
possible outcomes if the spinner is
spun twice. See Example 1
3.
E
GLUE
PEN
BOOK
PENCIL
2. Draw a tree diagram to find the
number of possible outcomes if the
coin is tossed and the spinner is
spun. See Example 2
TALK MATH In Exercise 2, what generalization can be
made about determining all possible outcomes?
Lesson 4B Probability 365
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
D
Draw
a grid
id tto fi
find
d th
the number
b off possible
ibl outcomes
t
ffor each
h
situation. See Example 1
4. How many outcomes are possible if
the spinner below is spun twice?
4
1
3
2
5. How many outcomes are possible if the
5–10 number cube is rolled twice?
Draw a tree diagram to find the number of possible outcomes
for each situation. See Example 2
6. How many outcomes are possible if
the spinners are spun?
7. How many outcomes are possible if the
0–5 number cube is rolled and the
spinner is spun?
The shells in the table are found in Louisiana and
other states along the Gulf Coast.
8. Make a tree diagram to show all the twoshell combinations that are possible from
the shells listed in the table if each shell is
used once.
1
2
4
3
Shells of the Gulf Coast
Atlantic Shark Eye
Banded Tulip
Horse Conch
Lightning Whelk
9. After you take out shell combinations that are
the same, how many combinations are left?
10. OPEN ENDED Create two spinners with at least three colors, including
red, on each spinner. The possible combinations of the spinners
must include red more often than any other color.
11.
366
3
E
WRITE MATH In Exercise 10, what generalization can you make
about determining all possible combinations?
Organize and Display Data
Test Practice
12. About how many more moons does
Saturn have than Uranus? (Lesson 3A)
13. If Ellis spins the arrow twice, which of
these is NOT a possible outcome?
(Lesson 4B)
Planets’ Moons
Planet
Jupiter
Neptune
Saturn
Uranus
0
10 20 30 40 50 60
Number of Moons
F. Blue, blue
G. Red, purple
A. 2
C. 10
H. Yellow, red
B. 5
D. 15
I. Green, blue
14. On Monday, 2,367 students bought lunch. On Wednesday,
2,745 students bought lunch. If 45 more students bought lunch
on Tuesday than Monday, how many lunches were sold on
those three days in all? (Lesson 3D)
Use the graph that shows speeds of land
animals. (Lesson 3B)
Speeds of Land Animals
15. How fast can an antelope run?
17. How much faster can a cheetah run
than a lion?
18. Which animal can run twice as
fast as an elephant?
Animal
16. Which animal can run 35 miles per hour
faster than an elephant?
Antelope
Cheetah
Elephant
Lion
0 10 20 30 40 50 60 70 80
Speed (miles per hour)
Write the mode, median, and range of each set of data. (Lesson 1B)
19. Bowling scores: 124, 115, 110, 145,
115
20. Number of push ups: 12, 17, 10, 26,
12, 28, 16
Lesson 4B Probability 367
Multi-Part
Lesson
4
Probability
PART
A
Main Idea
I will describe
probability with words
and numbers.
Vocabulary
V
B
C
Probability
The chance that an outcome will occur is its probability . The
words certain, likely, equally likely, unlikely, and impossible can
describe probability.
probability
Get ConnectED
GLE 0406.5.2
Use probability to describe
chance events.
certain to
choose red
likely to
choose red
unlikely to
choose red
equally likely to
choose red or blue
impossible to
choose red
Use Words to
Describe Probability
Sophie knows the colors of the
marbles in a bag. She asks Marta
to choose a marble without looking.
How likely is it that Marta will
choose a yellow marble?
The bag has 8 marbles, and
2 are yellow.
In the bag, fewer than half of
the marbles are yellow. So, it is
unlikely that Marta will choose
a yellow marble.
368
Organize and Display Data
Use Words to
Describe Probability
Find the total number
of possible outcomes
before determining
the probability of a
particular outcome.
MONEY The table shows
the coins Tucker has in
his hand. Suppose he
drops a coin on the
ground. Describe the
probability that the coin he
drops is a dime.
Coin
Frequency
Quarter
1
Dime
5
Penny
2
TOTAL
8
Of the 8 coins in Tucker’s pocket, 5 are dimes.
So, it is likely that Tucker drops a dime.
You can also use numbers to describe probability.
Use Numbers to Describe Probability
The letter tiles below spell out mathematics. Use numbers
to describe the probability of choosing a vowel without
looking.
MA T H E MA T I C S
Four out of eleven letters are vowels.
So, the probability of choosing a vowel is 4 out of 11.
The
h spinner is spun. What is the probability of each outcome?
Write certain, likely, equally likely, unlikely, or impossible.
7
See Examples 1 and 2
5
1. odd number
2. even number
3. number less than 3
4. the number 5, 11, or 13
11
13
9
3
For Exercises 5 and 6, use the cubes at the right. See Example 3
5. Use numbers to describe the probability of choosing a cube
that is not yellow without looking.
6.
E
TALK MATH Omar reaches into the bag and chooses one
cube without looking. Are there any colors that are more likely
to be chosen? Explain.
Lesson 4C Probability 369
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
A marble is chosen from the bag without looking. What is the
probability of each outcome? Write certain, likely, equally likely,
unlikely, or impossible. See Examples 1 and 2
7. green
8. yellow
9. red, yellow, or green
10. blue
11. not green
12. red or green
The spinner is spun. Use numbers to describe the probability
of each outcome. See Example 3
B
A
C
13. A
14. not E
15. consonant
16. vowel
17. not A or B
18. letter in the name LILY
19. Sancho spun a spinner 21 times. The
tally chart shows his results.
20. Erin dropped 32 plastic cups. The table
shows how the cups landed.
Color
Results
E
How Cup Landed
Blue
D
Number
10
Green
18
Orange
4
Suppose Sancho spins the spinner
one more time. Describe the
probability that the spinner will
land on orange.
Suppose Erin drops one more cup.
Describe the probability that the cup
will land on its side.
21. OPEN ENDED Make a spinner with 8 equal parts in which green
is most likely to be landed on and so that red and blue are unlikely
to occur.
22.
370
3
E
WRITE MATH Describe a probability situation in which an
outcome is certain to happen.
Organize and Display Data
Probability
You can also use the number line below to describe probability with
numbers. If the chance of an event happening is impossible, use 0.
If the chance of an event happening is certain, use 1. You can also use
fractions to describe probability.
1
2
0
impossible
1
certain
Describe Probability
12
A spinner is spun. Use numbers to describe
the probability of each outcome.
even number
2
4
10
8
6
blue
Step 1 Find the number of possible
outcomes.
There are 6 possible sections
for the spinner to land on.
Step 1
Find the number of possible
outcomes.
You know there are 6 sections
for the spinner to land on.
Step 2 Count the number of sections
with an even number.
Of those 6 possible sections,
all 6 have even numbers.
Step 2
Count the number of sections
that are blue.
Of those 6 possible sections,
3 sections are blue.
So, the probability of landing on an even
number is 6 out of 6, or 1.
So, the probability of landing on blue is
3
1
3 out of 6, _ , or _.
6
2
A marble is chosen from the bag without looking. Use numbers
to describe the probability of each outcome.
23. orange
24. yellow
25. orange or blue
26. yellow or blue
27. yellow, orange, or blue
28. red, green, or purple
To assess mastery of SPI 0406.5.4, see your Tennessee Assessment Book.
371
Chapter Study
Guide and Review
Key Vocabulary
Be sure the following Key
Concepts are noted in
your Foldable.
bar graph
data
outcome
probability
survey
tree diagram
Organize and
Display Data
Collect and Organize
Data
Find Mode, Media
n,
Outliers, and
Range
Line Plots
Bar and Double
Bar Graphs
Probability
Vocabulary Check
Complete each sentence with the
correct vocabulary word.
Key Concepts
1. A survey is a way to collect
?
.
Collect and Organize Data
• A survey is a way to collect data. Data
can be organized in different ways, such as
a tally chart and a frequency table. (Lesson 1)
Line Plots and Line Graphs
• A line graph shows how data changes
over time. (Lesson 2)
Bar Graphs
• A bar graph is used to compare data by
using bars of different heights to represent
data. (Lesson 3)
Probability
• Probability describes the likelihood of an
event taking place. (Lesson 4)
First Coin
• The probabilityy of
two coins
landing on
Heads
heads is
unlikely, or
Tails
1 out of 4.
372
3
Second Coin
Heads
Tails
heads,
heads
heads,
tails
tails,
heads
tails
tails
Organize and Display Data
2.
?
describes the
likelihood of an event taking
place.
?
is used to compare
3. A
data by using bars of different
heights to represent values.
?
4. A
is a way to collect
information that answers a
question.
?
5. A
uses “branches” to
show all possible combinations
of a probability situation.
6. A grid can be used to find the
?
of a situation.
Multi-Part Lesson Review
Lesson 1
Collect and Organize Data
Collect and Organize Data
(Lesson 1A)
Organize the data shown in a tally
chart and a frequency table.
7. Family members were asked what
they wanted to do after dinner.
After Dinner Activity
EXAMPLE 1
Organize the data shown in a tally
chart and a frequency table.
Favorite Sports
basketball
basketball
track
nap
read
game
basketball
softball
volleyball
game
nap
read
basketball
softball
volleyball
game
game
read
basketball
softball
volleyball
read
game
game
basketball
track
volleyball
8. Fourth graders voted for Student
Council President.
Favorite Sports
Sport
Votes for President
Tom
Monica
Lamar
Monica
Tom
Tom
Tom
Monica
Monica
Lamar
Monica
Lamar
9. Hours of practice each week: 3, 8, 2,
4, 3
10. Wild birds seen at a state park: 54,
17, 15, 16, 15
11. The number of students in Mr.
Parker’s class who brought lunches
on each day of the week: 8, 6, 5, 7,
17
Sport
Frequency
Softball
Softball
3
Track
Track
2
Basketball
Basketball
6
Volleyball
Volleyball
4
Find Mode, Median, Outliers, and Range
Find the mode, median, and range of
the set of data. Identify any outliers.
Tally
Favorite Sports
(Lesson 1B)
EXAMPLE 2
Find the mode, median, and range of
the data 50, 53, 95, 50, 51. Identify any
outliers.
Order from least to greatest.
50, 50, 51, 53, 95
Mode
occurs most often
50
Median number in the middle
51
Range
difference between the greatest
number and the least number
45
Outlier
number that lies outside the data 95
Chapter Study Guide and Review
373
Chapter Study Guide and Review
Lesson 2
Line Plots and Line Graphs
Problem-Solving
SGR_DIR SGR_DIR Strategy: Make a Table
(Lesson 2A)
Solve the problems using a table.
EXAMPLE 3
12. At Riverside Elementary, there are
346 students in the school who take
the bus each day.
Students are going on a class trip.
There are 140 students going, and 28
students fit on each bus. How many
buses are needed?
1 bus = 40 students
What is the least number of buses the
school will need to transport children
to and from the school?
13. Thirty-six students are going rafting.
Each raft holds 7 students. How many
more students are needed to fill each
raft with 7 people?
Line Plots
Bus
Students
1
28
+28
2
56
+28
3
84
+28
4
112
+28
5
140
So, 5 buses are needed.
Check
Subtracting 28 from 140 five times equals 0.
So, the answer makes sense. (Lesson 2B)
Organize each set of data in a line plot.
EXAMPLE 4
14.
Organize the
information from
the frequency
table in a line
plot.
Phone Calls Made Each Day
Day
15.
374
Calls
Monday
2
Tuesday
2
Wednesday
5
Thursday
3
Friday
2
Children at the Park
1
5
6
6
3
3
2
3
4
2
2
4
5
2
6
3
6
7
7
2
1
6
5
6
6
5
Children at the Park
Canned Goods
Collected Each Month
27
26
24
24
30
33
28
26
25
29
30
28
Organize and Display Data
X
X
X
X
X
X
X
X
X
X
X
1
2
3
X
X
X
X
X
X
X
X
X
X
X
X
X
4
5
6
7
Line Graphs
(Lesson 2D)
Measurement For Exercises 16 and
EXAMPLE 5
17, use the line graph below.
Measurement Use the graph below.
What temperatures occur twice?
48
40
Monday’s Temperature
Temperature (°F)
16. What was the highest height the tree
reached?
17. How old was the tree when it was 16
feet tall?
P.
M
.
6
The temperature that occurs twice is 75°F.
Bar Graphs
Bar Graphs and Double Bar Graphs
For Exercises 18 and 19, use the graph.
Favorite Vacation Spots
8
Students
Time
Look for the points on the graph that
represent the same temperature.
Boys
Girls
(Lessons 3A, 3B, 3C)
EXAMPLE 6
About how many rolls of wrapping
paper did the fourth grade sell?
6
Sale Results
4
50
2
40
0
Beach Mountains Other
Spots
Theme
Park
18. What is the most popular spot?
19. What is the difference in number
of students who liked the most
popular and the least popular
vacation spots?
Students
Lesson 3
4
8
A.
M
.
Years
P.
M
.
75
0
P.
M
.
10 15 20 25 30
2
5
80
P.
M
.
8
0
85
A.
M
.
16
90
12
32
10
Height (ft)
Sequoia’s Growth
Boys
Girls
30
20
0
1st
2nd
3rd
Grade
4th
35 + 40 = 75.
So, about 75 rolls of wrapping paper
were sold.
Chapter Study Guide and Review 375
Chapter Study Guide and Review
Problem-Solving Investigation: Choose a Strategy
(Lesson 3D)
Use any strategy to solve.
EXAMPLE 7
20. Bruce has 19 baseball hats. Rashid
has 5 more than Bruce. Shelly has 2
less than Rashid. How many baseball
hats does Shelly have?
Pia wants to earn $75. If she earns $15
each time she babysits, how many
times will she have to babysit in order
to earn $75?
21. Geometry What four shapes come
next in the pattern if it continues?
Day
Money Earned
1
$15
2
$30
3
$45
4
$60
5
$75
Pia will have to babysit 5 times to earn
$75.
Lesson 4
Probability
Determine Outcomes and Probability
Draw a tree diagram to find the
number of possible outcomes for the
situation.
22. Jeff has a nickel and a spinner with
four equal sections. One section is
red, one is blue, one is orange, and
one is purple. How many outcomes
are possible if the coin is tossed and
the spinner is spun?
The spinner is spun. Describe the
probability of each outcome. Write
certain, likely, equally
3
likely, unlikely, or
1
5
impossible.
11
7
23. 3 or 5
9
24. Identify an outcome that is certain.
376
Organize and Display Data
(Lessons 4A, 4B, and 4C)
EXAMPLE 8
Angie can use clay or paper for an art
project. Her project can be blue or
yellow. What are all the outcomes of
the art project?
Use a tree diagram.
Material
Color
Combination
clay
blue
yellow
clay, blue
clay, yellow
paper
blue
yellow
paper, blue
paper, yellow
There are 4 possible outcomes.
Practice
Chapter Test
Tell whether each statement is true
or false.
1. A double bar graph displays two sets
of related data using bars of different
colors.
One piece of fruit is chosen without
looking. Use words and a number to
describe the probability of each
outcome.
2. A tree diagram uses “branches” to
show all possible combinations of a
probability situation.
3. MULTIPLE CHOICE Reggie will spin
the arrow on a spinner twice like the
one shown below.
6. orange
7. apple or peach
8. MULTIPLE CHOICE The graph shows
the number of touchdowns made in
four different games.
Touchdowns in Games
1
Game
If the spinner lands on a different
section on each spin, which of the
following is NOT a possible outcome?
A. Red, Blue
2
3
4
B. Green, Green
0
C. Red, Red
1
2
3
4
Touchdowns
5
6
D. Green, Red
According to the graph, how many
more touchdowns were made in
game 4 than in game 1?
Make a table to solve each problem.
4. A car needs an oil change every
3 months. Joe’s car has had 4 oil
changes so far. How many months
have passed?
5. How much money will Kendall save if
he saves $35 a month for a year?
9.
F. 2
H. 4
G. 3
I.
5
E
WRITE MATH Write two sentences
to describe the graph in Exercise 8.
Practice Chapter Test
377
Test Practice
Marla asked her classmates about their
favorite class trips. She made a bar graph to
show the results.
How many more students prefer
going to the zoo than to the science
museum?
C. 7
B. 6
D. 9
Favorite Class Trips
Aquarium
Location
A. 3
Subtract to find how many
more.
Read the Question
Art
Museum
Science
Museum
Zoo
You need to find how many more students
prefer going to the zoo than to the science
museum.
0
2
4
6
8
Students
10 12 14
Solve the Question
Look at the graph. Thirteen students prefer the
zoo. Four students prefer the science museum.
Subtract to find the difference.
13 – 4 = 9
So, 9 more students prefer going to the zoo than
to the science museum.
The answer is D.
Read each question. Then fill in the correct answer on the answer
sheet provided by your teacher or on a separate sheet of paper.
1. What is the median of the shoe sizes
shown in the data set below?
{6, 4, 5, 7, 8, 5, 6}
A. 3
C. 5
B. 4
378
D. 6
Organize and Display Data
2. Kari has a bag of 20 blocks. Six are blue,
4 are red, 7 are green, and 3 are yellow.
If Kari chooses a block without looking,
which color is most likely to be chosen?
F. green
H. red
G. blue
I. yellow
3.
6. A mountain is 9,485 feet tall. A climber
has hiked 6,208 feet. How many more
feet does the climber need to hike to
reach the top of the mountain?
GRIDDED RESPONSE What is
36,249 rounded to the nearest
hundred?
4. Ron sold lemonade at soccer practice.
On which two days did he sell the
least amount of lemonade?
A. 15,693
C. 3,277
B. 15,267
D. 3,183
Lemonade Sales
Day
Tally
7. A piggy bank has the coins shown
below in it. If a coin is selected at
random, what is the probability in
numbers that the coin will be a
penny?
Monday
Tuesday
Wednesday
Thursday
Friday
A. Monday and Friday
B. Wednesday and Friday
F. 1 out of 14
H. 1 out of 11
C. Tuesday and Thursday
G. 3 out of 14
I. 3 out of 11
D. Thursday and Friday
5. Nadia tossed a number cube labeled
0–5. What is the probability that she
will toss an even number?
8.
GRIDDED RESPONSE Larisa has
three pairs of pants and two sweaters.
Larisa’s Outfits
F. 2 out of 6
G. 3 out of 6
H. 4 out of 6
Pants
tan, black, navy
Sweaters
red, stripe
How many different outfits can Larisa
wear?
I. 5 out of 6
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Test Practice 379