690
Contents
NC SCS
5.02b
Inequalities (Use after Lesson 6-6)
4.01d
Mean (Use after Lesson 7-1)
4.01b
Stem-and-Leaf Plots (Use after Lesson 7-7)
4.01b
Select an Appropriate Display (Use after Lesson 7-7)
2.03
Elapsed Time (Use after Lesson 11-7)
691
Inequalities
MAIN IDEA
I will write inequalities
and determine if a
number is a solution of
an inequality.
NC SCS
5.02 b) Demonstrate
an understanding of
equality and
inequality.
New Vocabulary
inequality
NC Math Online
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• Extra Examples
• Personal Tutor
• Self-Check Quiz
Rashid used a number
line to graph his four
math scores. Then he
wrote the following
statements comparing
his test scores.
79
82
79
78
84
80
82
82
82
84
84
90
90
86
88
90
84
Recall that an equation is a number sentence containing an
equals sign, showing that two expressions are equal. An
inequality is a number sentence containing an inequality symbol
showing that two expressions may not be equal. These inequality
symbols are , , , and .
Inequalities
Words
Key Concept
is less than
than or is greater than
is greater than is less
equal to
or equal to
Symbols
In Lesson 1-2, you used , , and to compare whole numbers.
Inequalities can also be used to compare a number to a variable
such as x 7 or a 5.
EXAMPLES
Write an Inequality
Use a variable to write an inequality for each sentence.
1 Daria’s age is less than 10.
Let the variable d represent Daria’s age. Choose the symbol
to represent the phrase is less than.
An inequality is d
10.
2 Jason’s biking speed is greater than or equal to 8 miles
per hour.
Let the variable s represent Jason’s biking speed. Choose the
symbol to represent the phrase is greater than or equal to.
An inequality is s
692
8.
A balance scale can be used to demonstrate an inequality. On the balance
scale below, a cup containing an unkown number of counters is placed on
the left scale. Three postive counters are placed on the right scale.
Note that the left side of the scale weighs more than the right scale. So, x
The number of counters in the cup is greater than 3.
3.
Check possible values of x.
x
3 Write the inequality.
2 3 No
3 3 No
4 3 Yes
5 3 Yes
x
6 3 Yes
So, the solution of the ineqality is any number greater than 3.
If two postive counters are added to each side of the balance scale,
note that the left scale still weighs more than the right scale. So, x 2
5.
Check possible values of x.
x
2
5 Write the inequality.
2
2 5 No
3
2 5 No
4
2 5 Yes
5
2 5 Yes
6
2 5 Yes
x
Possible values of x include 4, 5, and 6 but do not include 2 and 3. So, the
solution of the inequality x 2 5 is x 3.
Note that the possible values of x did not change when the same number
of counters are added to each side.
You can use substitution to determine if a certain value is a solution of an inequality.
EXAMPLE
Solution of an Inequality
3 Given the inequality x > 11, determine whether x = 9 is a solution.
x
11 Write the inequality.
9 11 Replace x with 9.
9 ≯ 11 Determine if the inequality is true or false. Nine is not greater than 11.
The sentence is false, so 9 is not a solution of the inequality.
Inequalities 693
EXAMPLE
Solution of an Addition Inequality
4 Given the inequality a 3 5, determine whether a
solution.
a 3 5 Write the inequality.
2
2 is a
3 5 Replace a with 2.
5
5 Simplify. Determine if the inequality is true or false.
Although the inequality 5 5 is false, the equation 5
So, 2 is a solution of the inequality.
5 is true.
Use a variable to write an inequality for each sentence. See Examples 1–2 (p. 692)
1. Your height is greater than 4 feet.
2. The car’s speed is less than 50 miles per hour.
3. Children under the age of 3 are admitted free.
4. A package must be less than or equal to 20 pounds.
Determine whether the given value of the variable is a solution of
each inequality. Write yes or no. See Examples 3–4 (pp. 693–694)
5. x
7; x
8. b
1
5
6; b
6. b > 3; b
7
9. s
4
2
1; s
5
7. w
13; w
10
10. 5x
15; x
2
11. You must be 36 inches or taller to ride a certain ride at an
amusement park. Use the symbol to write an inequality for
this situation.
Use a variable to write an inequality for each sentence. See Examples 1–2 (p. 692)
12. Your age is greater than 9.
13. The runner’s speed is less than 6 miles per hour.
14. A package must be less than or equal to 5 pounds.
15. The cost must be less than $15.
16. The test score must be greater than or equal to 85%.
17. The baker must bake 200 or more muffins.
694
Determine whether the given value of the variable is a solution of each inequality.
Write yes or no. See Examples 3–4 (pp. 693–694)
18. c
2; c
1
19. h
8; h
7
20. p
9; p
9
21. x
2; c
1
22. b
5; b
4
23. t
20; t
22
24. n
2
5; n
25. d
1
27. h
7
18; h
5
8
28. 4s
10; d
8; s
10
2
26. 2y
29. x
13; y
5
7
;x
20
30. A first class letter must be less than or equal to 1 ounce in weight for
a single first class stamp to be required. Use the symbol to write
an inequality for this situation.
31. Over the summer, Kayla must spend at least 60 minutes a week
reading. Use the symbol to write an inequality representing the
time Kayla must spend reading each week.
32. An elevator has a sign that the maximum weight is 2,000 pounds.
Use the symbol to write an inequality for this situation.
33. In North Carolina, you can get a driver’s license if you are at least 16
years old. Use the symbol to write an inequality for the age of
drivers in North Carolina.
34. OPEN ENDED Describe a si tuation that could be represented by the inequality
x 10.
35. FIND THE ERROR Sophia and Marvin are writing an inequality for the expression
two hours or more of homework. Who is correct? Explain.
Marvin
–<
h
–> 2
36. CHALLENGE Write an inequality to represent the following sentence. Then give a
number that is a solution of the inequality.
Five more than a number is greater than or equal to eight.
37.
Explain the difference in n
5 and n
5.
Inequalities 695
Mean
MAIN IDEA
I will use the mean to
describe a set of data.
NC SCS
4.01 d) Explore the
mean as a measure
of center and its
interpretation as a
fair share.
New Vocabulary
measures of center
NC Math Online
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• Extra Examples
• Personal Tutor
• Self-Check Quiz
Four friends set up lemonade stands
in four different locations throughout
their neighborhood. The table shows
how much money each friend collected.
The mean amount earned was $6.
Carter
$4
Kasha
$7
Madeline
$9
Thomas
$4
In Lesson 7-1, you learned how to find the mean, median, and
mode of a data set. These three measures are called measures of
center because they describe the center of a data set. The mean
is also called the average because it represents the average value
of a data set if each data value is distributed equally. Because the
mean is the sum of the data values divided by the number of
pieces of data, the mean represents a fair share of the data
values.
You can find the mean of data represented in a graph to give a
fair measure of center of the data.
EXAMPLE
Find the Mean
1 CIVICS Find the
mean number of
Representaives for
the four states
shown in the
pictograph.
METHOD 1
2007 Representatives to U.S. Congress
Move the figures.
2007 Representatives to U.S. Congress
696
Lemonade Stand Earnings
Move the figures
to equally
distribute the
total number of
Representatives
among the four
states.
METHOD 2
Write and simplify an expression.
← sum of the data
← number of data items
Simplify.
EXAMPLE
Distribute Data Fairly
2 Sabrina collected 12 pieces of candy from a piñata. Meagan
collected 15 pieces of candy, and Kim collected 18 pieces of
candy. The three friends decided to combine their candy and
split it evenly among them so that they each had a fair share.
How many pieces of candy will each girl receive?
To find the amount candy each girl will receive, find the mean of
the data.
12
15
45
3
18
15
45
Find the sum of the data.
Divide by the number of girls.
So, each girl will receive 15 pieces of candy.
Find the mean of the data represented in each model. See Example 1 (p. 696)
Number of Pairs of Shoes
Elise
Gloria
Maxwell
Toby
2.
Hours Spent Reading
Number of Hours
1.
14
12
10
8
6
4
2
0
Aida Dante Nicholas Rosa
Student
3. The table shows the number of points each of five friends
received while playing games at an arcade. The points can be
redeemed for prizes. The friends decided to combine the points
and then split them equally amongst themselves. How many
points will each friend receive to use for prizes?
Friend
Tyler
Points
Ally
105
Brandon
135
Lucy
170
Miko
120
Ruben
95
Mean 697
Find the mean of the data represented in each model. See Example 1 (p. 696)
Number of Siblings
Elise
Juan
Maggie
5.
Books Checked Out of Library
Number of Books
4.
8
6
4
2
0
Nina
Jordan
Patrick
Collin Brianna
Chen
Student
Tyron
For Exercises 6–8, use the table at the right. It lists the greatest
depths of the oceans. See Example 2 (p. 697)
6. What is the mean of the data?
7. Which data value is farthest away from the mean than the
other data values?
Ocean
Depth (ft)
Pacific
15,215
Atlantic
12,881
Indian
13,002
Arctic
Southern
3,953
14,749
8. Describe how including this data value in the calculation of the
mean affects the mean’s interpretation as a fair share of the data.
9. The graphic at the right shows the
5-day forecast as shown on the local news.
What is the difference between the mean high
and mean low temperatures for the 5-day
period? Justify your answer.
10. Refer to Exercise 3. Suppose a sixth friend,
Antwon, was included. If Antwon received 155
points, how many points would each friend
receive if they split the number of points
equally amongst themselves?
11. The table shows the amount of money Quentin earns for
mowing 5 different lawns in his neighborhood. His friend asked
him the average amount of money he receives for mowing a
lawn. What amount should Quentin tell his friend?
698
Lawn
Earnings ($)
1
10
2
18
3
13
4
15
4
9
Real-World PROBLEM SOLVING
The table at the right shows the monthly
average high temperatures in Greensboro, North Carolina.
Average High Temperature,
Greensboro, North Carolilna
Month
12. What temperature could describe the average high
during the summer (June, July, and August) in
Greensboro?
Temperature (°F)
January
47
February
52
March
60
13. What temperature could describe the average high
temperature during the winter months (December,
January, and February)?
April
70
May
77
June
84
July
88
14. Daniel’s grandparents spend October through February
in Greensboro. What is the average high temperature
during these months?
August
86
September
79
October
70
November
60
December
51
Number of Songs Downloaded
Number of Songs
15. FIND THE ERROR The graph at the
right shows the number of songs
that five students downloaded from
the Internet. Byron and Dimitri both
found the mean of the data in the
bar graph. Who is correct? Explain.
14
12
10
8
6
4
2
0
Alvin
Claire
Nate Parker
Student
Sally
Dimitri
+
16.
+ + + =
10 + 14 + 10 + 6 + 8 = 9.6 songs
5
The table shows the number of
students in each fifth grade homeroom at Dartwell
Elementary. For the school field day, the teachers want each
homeroom to have the same number of students. Explain
what the teachers can do so that each homeroom has a fair
number of students participating in the events.
Number of Students in
Fifth Grade Homerooms
24
28
25
27
26
26
Mean 699
Stem-and-Leaf Plots
You can use a stem-and-leaf plot to organize large data
sets so that they are easier to analyze and interpret. In a
stem-and-leaf plot, the data are ordered from least to
greatest and organized by place value.
MAIN IDEA
I will make and
interpret stem-and-leaf
plots.
NC SCS
4.01 b) Collect,
organize, analyze,
and display data
using various
representations,
including stem-andleaf plots.
• The leaf is the last digit of the number.
• The other digits to the left of the leaf form the stem.
For the numbers 21, 24, 35, and 38, 2 and 3 are the stems.
The numbers 1, 4, 5, and 8 are the leaves.
The stem-and-leaf plot at the right shows
scores from a math test. The plot shows that
the test scores were 74, 85, 87, 96, 96, and
100. The information can be used to find the
mean, median, and mode.
New Vocabulary
Mean
74
85
87
stem-and-leaf plots
Median
87
96
183
stems
Mode
96
leaves
key
96
2
96
100
Math Test Scores
Stem Leaf
7 4
8 5 7
9 6 6
10 0
8 5 85
538
6
89.7
91.5
You can construct a stem-and-leaf plot from data given in a table.
EXAMPLE
Construct a Stem-and-Leaf Plot
1 INSTANT MESSAGING Make a
stem-and-leaf plot of the data in
the table.
Step 1 Order the data from least
to greatest.
Number of Instant Messages
Sent Each Day for 21 Days
35
27
17
21
12
24
14
33
21
32
20
27
25
45
2
10
21
3
5
31
7
Step 2 Draw a vertical line and write the tens digits from least to
greatest to the left of the line. These digits form the stems.
Since the least value is 2 and the greatest value is 45, the
stems are 0, 1, 2, 3, and 4.
Step 3 Write the ones digits in order to the right of the line with
the corresponding stem. The ones digits form the leaves.
700
In these data, the tens
digits form the stems.
Number of Instant Messages
Sent Each Day for 21 Days
Stem Leaf
0 2 3 5 7
1 0 2 4 7
The ones digits of the
2 0 1 1 1 4 5 7 7
data form the leaves.
3 1 2 3 5
4 5
2 7 27 text messages
Step 4 Include a key that explains the stems and leaves.
Stem-and-leaf plots are useful in analyzing data because you can see all
the data values, including the greatest and least.
Real-World EXAMPLE
Analyze Plots
2 WATERFALLS The stem-and-leaf plot shows
the approximate height of the twenty tallest
waterfalls in the world. Write a few sentences
that analyze the data.
The tallest waterfall in the world is about
980 meters. Two of the waterfalls listed
are about 490 meters tall. Half of the
waterfalls are at least 610 meters tall.
Approximate Height of the
20 Tallest World Waterfalls
Stem Leaf
4 6 7 9 9
5 0 3 6 8
6 0 1 1 5 6
7 0 4 6 7
8 0
9 5 8 4 6 460 meters
You can describe the data that is displayed in a stem-and-leaf plot by first
finding the range, median, and mode of the data.
EXAMPLE
Describe Data
3 CHESS The stem-and-leaf plot shows
the number of chess matches won by
members of the Avery Middle School
Chess Team. Find the range, median,
and mode of the data. Then a few
sentences describing the data.
range
greatest wins least wins
61 8 or 53
median
middle value, or 35 wins
mode
most frequent value, 40
Chess Matches Won
Stem
0
1
2
3
4
5
6
Leaf
8 8 9
9
0 0 2 4 4 8 9
1 1 2 4 5 5 6 6 7 7 8
0 0 0 3 8 9
2 4
1
3 | 2 = 32 wins
The data ranges from 8 wins to 61 wins. The most frequently
occurring number of wins was 40. Half of the number of wins was
less than 35 and half of the number of wins was greater than 35.
Stem-and-Leaf Plots 701
Make a stem-and-leaf plot of each set of data. See Example 1 (pp. 700–701)
1. minutes spent on homework: 37, 28, 25, 29, 31, 45, 32, 31, 46, 39
2. miles traveled to reach weekend vacation destination:
81, 76, 55, 90, 71, 80, 83, 85, 79, 99, 70, 75, 70, 92
For Exercises 3–5, use the stem-and-leaf at the right.
See Examples 1–3 (pp. 700–701)
3. How many snack foods listed have more than 250
Calories?
4. How many Calories are in the snack food listed with
the most number of Calories?
Number of Calories in
Selected Snack Foods
Stem
24
25
26
27
28
Leaf
0 4 4 8
0 0 5 7 8
4 5
5
4
24 4
244 Calories
5. Write a few sentences that analyze the data.
Make a stem-and-leaf plot of each set of data. See Examples 1–3 (pp. 700–701)
6. bus ride in minutes: 24, 14, 25, 28, 47, 13, 9, 17, 30, 35, 16, 39
7. video game score: 53, 64, 15, 22, 16, 42, 12, 38, 68, 63, 23, 35, 30, 33, 34, 35
8. calories per serving: 62, 65, 67, 67, 62, 67, 51, 73, 72, 70, 63, 72, 78, 61, 54
9. test scores: 76, 82, 70, 93, 71, 80, 63, 73, 90, 92, 74, 79, 82, 91, 95, 93, 75
For Exercises 10 and 11,
use the plot below.
World’s Longest Tunnels
Stem Leaf
6 3 8 9 9
7 0 1
8 0 7
9
10 2
11 2
12
13
14
15 2
6 3 6.3 mi
For Exercises 12 and 13,
use the plot below.
Shows Performed by the
Top 25 Musical Tours
Stem Leaf
2 3 4 5
3 8 8
4 3 3 3
5 0 1 2 5 6 6 9
6 7
7 0 3 3 5 5 7
8 0 5
9 9
3 8 38 shows
10. How long is the world’s
longest tunnel?
12. How many tours performed
more than 50 shows?
11. Write a few sentences that
analyze the data.
13. Write a few sentences that
analyze the data.
702
Points Scored
Tigers
Stem
Eagles
0 3 4 8 8
8 4 2
5
2 6 7
6 5
6
0 2 5
8 7 4 0
7
2
9 8 6 0
8
5 4 54 points
5 0 50 points
For Exercises 14 and 15, use the back-to-back stemand-leaf plot at the right and the information below.
A back-to-back stem-and-leaf plot can be used to
compare two sets of data. The leaves for one set of
data are on one side of the stem and the leaves for
the other set of data are on the other side of the stem.
14. How many games were there in which the Tigers scored more than
75 points? the Eagles?
15. Write a few sentences comparing the points scored by each team.
Include the median, mode, and range of the points scored by each
team in your comparison.
Display each set of data in a stem-and-leaf plot. Then write a few
sentences describing each set of data.
16.
18.
17.
Quiz Scores (%)
Low Temperatures ( F)
70
96
72
91
15
13
28
32
38
80
80
79
93
30
31
13
36
35
76
95
73
93
38
32
38
24
20
90
93
77
91
Floats at Annual Parade
19.
School Play Attendance
151
158
139
103
225
227
230
229
111
134
133
154
246
243
269
269
157
142
149
159
267
278
278
278
REASONING For Exercises 20–22, use the stem-and-leaf
plot at the right which shows the number of Tour de
France titles won by eleven countries.
20. Find the range of titles won.
21. Find the median and mode of the data.
Tour de France Titles Won by
Eleven Countries
Stem
0
1
2
3
Leaf
1 1 1 2 2 4 8 9
0 8
6
0|4
4 titles
22. Which measure of central tendency is most affected by
the outlier?
23. OPEN ENDED The scores for 10 girls in a gymnastics event are 9.3,
10.0, 9.9, 8.9, 8.7, 9.0, 8.7, 8.5, 8.8, and 9.3. Analyze a stem-and-leaf
plot of the data to draw two conclusions about the scores.
24.
Display the height, in inches, of your classmates
in a stem-and-leaf plot. Then write a few sentences that analyze the data.
Stem-and-Leaf Plots 703
Select an Appropriate
Display
The displays show the maximum speed of eight animals. In
which display is it easier to find the range of the data?
MAIN IDEA
NC SCS
4.01 b) Collect,
organize, analyze,
and display data
using various
representations,
including stem-andleaf plots.
Maximum Speed
of Animals
Maximum Speed of Animals
50
Stem
1
2
3
4
45
Speed (miles per hour)
I will make and
interpret stem-and-leaf
plots.
40
35
30
25
Leaf
2 5
5
0 2 5
0 5 30
30 mi/h
20
15
10
5
0
t
t
Ca han
p
e
l
E
Elk
it
er rrel key bra
bb de
ui
ur
Ze
Ra ein
Sq ld T
R
i
W
Animal
NC Math Online
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• Extra Examples
• Personal Tutor
• Self-Check Quiz
Data can often be displayed in several different ways. The display
you choose depends on your data and what you want to show.
EXAMPLE
Choose Between Displays
1 SOCCER Which display allows you to see whether the team’s
record of wins has steadily improved since 2001?
Girls Soccer Team
Total Games Won
16
14
12
×
×
×
×
×
×
×
×
10
8
6
0
’01 ’02 ’03 ’04 ’05 ’06 ’07 ’08
Season
The line graph shows the change in games won from season
to season, revealing some declines in the number of wins.
704
You can select an appropriate display from the types of displays you
have learned: bar graph, line graph, line plot, or stem-and-leaf plot.
Real-World EXAMPLE
Select an Appropriate Display
2 MARKETING A market
Favorite Shampoo Survey
researcher conducted a survey
Brand Responses Brand Responses
to compare different brands of
A
35
D
24
hair shampoo. The table shows
B
12
E
8
the number of first-choice
C
42
F
11
responses for each brand.
Select an appropriate type of display to compare the number of
responses for each brand of shampoo.
These data show the number of responses for each brand. A bar
graph would be the best display to compare the responses.
Once you have selected an appropriate display, you can make that
display from the set of data.
EXAMPLE
Make an Appropriate Display
3 Make the appropriate display of the data from Example 2 above.
Step 2 Draw a bar to represent
the number of
responses for each
brand.
45
40
Number of Responses
Step 1 Draw and label
horizontal and vertical
axes. An interval of 0 to
45 responses can be
used along the vertical
axis. Add a title.
35
30
25
20
15
10
5
0
A
B
C
D
E
F
Brand
The Concept Summary box below summarizes the situations in
which it is most appropriate to use various types of displays.
Statistical Displays
Type of Display
Best Used to
Bar Graph
show the number of items in specific categories
Line Graph
show change over a period of time
Line Plot
Stem-and-Leaf Plot
show how many times each number occurs in the data
list all individual numerical data in a condensed form
Select an Appropriate Display 705
1. Which display makes it easier to determine the highest average price
received for a hog from 1940 to 2000? See Example 1 (p. 704)
Price per 100 Pounds ($)
Average Hog Price, 1940–2000
Stem Leaf
0 5
1 5 8
2 3
3 8
4 2
5 4 4 2 $42 per 100 lb
60
50
40
30
20
10
0
’40 ’50 ’60 ’70 ’80 ’90 ’00
Year
Select an appropriate type of display for data gathered about each
situation. See Example 2 (p. 705)
2. the favorite cafeteria lunch item of the sixth-grade students
3. the daily high temperature over the past seven days
4. Select and make an appropriate
display for the data.
See Example 3 (p. 705)
Number of Push-Ups Done by Each Student
15
20
8
11
6
25
32
12
14
16
21
25
18
35
40
20
25
15
10
5
18
20
31
28
5. Which display makes it easier to compare the maximum speeds of
Top Thrill Dragster and Millennium Force? See Example 1 (p. 704)
Maximum Speed of Fastest
Steel Roller Coasters
Stem
8
9
10
11
12
Maximum Speed (mi/h)
140
120
100
80
60
40
20
0
a
e
e
h
n
0
er
or
ng
np liat orc
00 Tita gst
at
a eler
do Go m F eve n 2
r
n
o
R
l D Xc
iu
Do
’s
ag
ril
nn
m
Dr
Th
ille anto eel
p
M h
To
St
P
Roller Coaster
706
Leaf
2 2 5 5
2 5
7
0 10 7
107 mi/h
See Example 1 (p. 704)
×
×
× ×
×
×
×
× ×
Gold Medal Distance (meters)
6. Which display makes it easier to see how many times the
winning distance of the javelin throw was 90 meters?
96
94
92
90
88
86
84
82
0
×
’68 ’76 ’84 ’92 ’00
Year
84 85 86 87 88 89 90 91 92 93 94 95
Select an appropriate type of display for data gathered about each
situation. See Example 2 (p. 705)
7. the amount of sales a company has for each of the past 6 months
8. the test scores each student had on a language arts test
9. the prices of five different brands of tennis shoes at an athletic store
10. Abigail’s height on her birthday over the past 10 years
16
Number of Neighbors
11. Display the data in the bar graph at the right
using another type of display. Compare the
advantages of each display.
14
12
10
8
6
4
2
0
Rep. of
Congo
Germany
China
Sudan
Country
12. Use the Internet or another source to find a set of data that is displayed in a bar graph,
line graph, stem-and-leaf plot, or line plot. Was the most appropriate type of display
used? What other ways might these same data be displayed?
13. REASONING Determine whether the following statement is true or false. If true,
explain your reasoning.
Any set of data can be displayed using a line graph.
14.
Write about a real-world situation in which you would have
to choose an appropriate display for a set of data.
Select an Appropriate Display 707
Elapsed Time
Calendars are used to represent the
length and divisions of a year. They
are separated into 12 months
MAIN IDEA
I will solve problems
involving elapsed time
on a calendar.
NC SCS
2.03 Solve problems
using the concepts
and procedures
involving elapsed
time.
NC Math Online
macmillanmh.com
• Extra Examples
• Personal Tutor
• Self-Check Quiz
1. On the calendar at the right,
what day of the week is March
12?
March
5
12
19
26
6
13
20
27
2
9
16
23
30
3
10
17
24
4
11
18
25
2. Suppose you have piano practice
on Wednesday afternoons. How
many days in March will you have piano practice?
3. What is the date of the second Friday in March?
You can use numbers on a calendar to determine elapsed time.
If you move down 1 row on a calendar, you can count 1 week, or
7 days.
Real-World EXAMPLES
Find Elapsed Time
1 Cody’s soccer season begins on
September 3 and ends on
November 8. How many weeks
and days does Cody’s soccer
season last?
First count the weeks. Start on
Wednesday, September 3, and
count the weeks until Wednesday,
November 5. This is 9 weeks.
Then count the days until you
get to November 8. This is 3 days.
September
7
14
21
28
1
8
15
22
29
2
9
16
23
30
3
10
17
24
4
11
18
25
5
12
19
26
6
13
20
27
3
10
17
24
31
4
11
18
25
October
5
12
19
26
6
13
20
27
So, Cody’s soccer season lasts
for 9 weeks and 3 days.
7
14
21
28
1
8
15
22
29
2
9
16
23
30
November
2
9
16
23
30
708
7
14
21
28
1
8
15
22
29
3
10
17
24
4
11
18
25
5
12
19
26
6
13
20
27
7
14
21
28
1
8
15
22
29
2 The Maxwell family left on a 9-day vacation on Saturday,
June 13. On what date and day of the week will they return?
Add 13 to 9 to determine the date of their return. 9
13
22
They will return on June 22.
Seven days after the date they left will be another Saturday. So,
two more days after that will be a Monday.
So, the Maxwells will return on Monday, June 22.
Real-World EXAMPLE
Patterns and Elapsed Time
3 Chen is training to run a race. The table below gives the
number of miles he will run in 6 weeks. How many miles will
he run in all during his training?
Make a table to show the number of miles Chen runs each week.
Week
1
2
3
4
5
6
Miles
2
4
6
8
10
12
Add the number of miles from each week.
2
4
6
8
10
12
42
So, Chen will run a total of 42 miles during his training.
For Exercises 1 and 2, use the calendars below. See Examples 1–3 (pp. 708–709)
June
Sun
6
13
20
27
July
Mon
Tue
Wed
Thu
Fri
Sat
7
14
21
28
1
8
15
22
29
2
9
16
23
30
3
10
17
24
4
11
18
25
5
12
19
26
Sun
4
11
18
25
Mon
5
12
19
26
Tue
6
13
20
27
August
Wed
Thu
Fri
Sat
7
14
21
28
1
8
15
22
29
2
9
16
23
30
3
10
17
24
Sun
2
9
16
23
30
Mon
3
10
17
24
31
Tue
4
11
18
25
Wed
5
12
19
26
Thu
6
13
20
27
Fri
Sat
7
14
21
28
1
8
15
22
29
1. Sun-Li joined the swim team over the summer. The swim season starts
on June 14 and ends on August 6. How many weeks and days does the
swim season last?
2. Mateo is working at an ice cream parlor ever Saturday and Sunday
over the summer. His first day of work is Saturday, June 5. His last
day of work is Sunday, August 23. How many weekends did Mateo
work at the ice cream parlor over the summer?
Elapsed Time 709
3. Carlos turned 11 years old on Tuesday, February 8. Ten days later,
his sister turned 8 years old. What is the date of Carlos’ sister’s
birthday? What day of the week is this?
4. Caroline spends 2 minutes reading on Sunday, 4 minutes reading on
Monday, and 8 minutes reading on Tuesday. She continues to double
the amount of time she spends reading for the next four days of the
week. How many minutes will Caroline spend reading during the week?
For Exercises 5–9, use the calendars below. See Examples 1–3 (pp. 708–709)
5. The ski club goes to the local ski slopes
every Thursday afternoon from January 8
to March 4. How many times does the ski
club go to the slopes?
6. Opening night of the school musical is
March 19. Rehearsal begins on January 19.
How many weeks and days will the performers
have to practice?
7. Adriana’s grandparents left for vacation on
January 4. They will be on vacation for 12 days.
When will Adriana’s grandparents return from
their vacation?
8. Mr. Rollins has to go to physical therapy once
a week for 6 weeks. His first appointment is on
January 9. What will be the date of his last
appointment?
9. The school cookie dough sale starts on March 2
and ends on March 27. How many weeks and days
does the cookie dough sale last?
10. The sign at the right shows the dates the school
cafeteria will have pizza from a local pizzeria for
lunch this quarter. How many weeks pass by between
the second and third pizza days of the quarter?
11. In 1927, Babe Ruth hit 60 home runs as a New
York Yankee. He hit his first home run of the season
on April 15. He hit his second home run of the
season 8 days later. What was the date of his
second home run of the 1927 season?
710
January
4
11
18
25
5
12
19
26
6
13
20
27
7
14
21
28
1
8
15
22
29
2
9
16
23
30
3
10
17
24
31
5
12
19
26
6
13
20
27
7
14
21
28
5
12
19
26
6
13
20
27
7
14
21
28
February
1
8
15
22
2
9
16
23
3
10
17
24
4
11
18
25
March
1
8
15
22
29
2
9
16
23
30
3
10
17
24
31
4
11
18
25
September 12
October 6
October 27
November 19
12. Alexis was eleven years old on November 13. Her friend was eleven
years old on November 27. How many days older is Alexis than her
friend? How many weeks older is Alexis?
Real-World PROBLEM SOLVING
Tomato plants can be started
from a seed indoors and then transferred to an
outside garden when the weather is appropriate.
13. Sonya planted tomato seeds inside on April 1.
Ten days later seedlings emerged. What was the
date when the seedlings emerged?
14. Sonya transferred the tomato plants to her
outdoor garden 6 weeks after she first planted
them inside. What was the date when Sonya
transferred the plants?
15. The first tomato was ready to eat on June 29.
How many weeks and days was this after Sonya
planted the seeds?
16. If Sonya wanted the first tomato to be ready to
eat by June 23, when should she have planted
the seeds inside?
April
7
14
21
28
1
8
15
22
29
2
9
16
23
30
3
10
17
24
4
11
18
25
5
12
19
26
6
13
20
27
2
9
16
23
30
3
10
17
24
31
4
11
18
25
6
13
20
27
7
14
21
28
May
5
12
19
26
6
13
20
27
1
8
15
22
29
7
14
21
28
June
2
9
16
23
30
3
10
17
24
31
4
11
18
25
5
12
19
26
1
8
15
22
29
17. OPEN ENDED Write a beginning date and an ending date so that
the elapsed time is 3 weeks 5 days.
18. CHALLENGE Jonah is saving money to buy a new video game. The
first week he saves $1, the next week he saves $3, and the following
week he saves $5. He is going to continue to save $2 more than he
saved the previous week. If the video game he wants to buy costs
$50, after how many weeks will Jonah have enough money saved?
19.
Use the calendars in Exercises 5-9. Write a
problem that can be solved by finding elapsed time on the calendars.
Elapsed Time 711