LESSON
8.1
Two-Way Frequency
Tables
Name
8.1
HARDBOUND SE
PAGE 279
BEGINS HERE
Summarize categorical data for two categories in two-way frequency
tables. Interpret relative frequencies in the context of the data (including
joint, marginal, and conditional relative frequencies). Recognize possible
associations and trends in the data.

Categorical Data and Frequencies
Circle the categorical data variable. Justify your choice.
temperature
weight
height
color
Temperature, weight, and height are measured on a numerical scale, so they are
Mathematical Practices
quantitative data. Color cannot be expressed numerically.
MP.7 Using Structure

Language Objective
Identify whether the given data is categorical or quantitative.
large, medium, small categorical
Distinguish between quantitative data and categorical data.
2
2
120 ft , 130 ft 2, 140 ft quantitative

ENGAGE
View the Engage section online, and then take a
quick, show-of-hands survey to determine the most
popular sports among the students in your class.
Discuss whether the survey results might have been
different had you surveyed the boys and the girls
separately. Then preview the Lesson
Performance Task.
A frequency table shows how often each item occurs in a set of categorical data. Use the
categorical data listed on the left to complete the frequency table.
© Houghton Mifflin Harcourt Publishing Company
Ways Students Get to School
bus car walk car car car bus
walk walk walk bus bus car
bus bus walk bus car bus car
Way
Frequency
bus
8
car
7
walk
5
Reflect
1.
How did you determine the numbers for each category in the frequency column?
You can determine the numbers for each category by counting the number of times each
category is listed in the data.
2.
What must be true about the sum of the frequencies in a frequency table?
The sum should equal the total number of items in the data set.
Module 8
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IN1_MNLESE389755_U4M08L1.indd 347
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Lesson 1
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© Houghto
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Reflect
347
Module 8
8L1 347
55_U4M0
ESE3897
IN1_MNL
347
Lesson 8.1
Resource
Locker
Data that can be expressed with numerical measurements are quantitative data. In this lesson you will examine
qualitative data, or categorical data, which cannot be expressed using numbers. Data describing animal type,
model of car, or favorite song are examples of categorical data.
S-ID.5
PREVIEW: LESSON
PERFORMANCE TASK
Two-Way Frequency Tables
Explore
The student is expected to:
You can summarize categorical data for two
categories in a two-way frequency table.
Date
Essential Question: How can categorical data for two categories be summarized?
Common Core Math Standards
Essential Question: How can
categorical data for two categories be
summarized?
Class
4/9/14
5:58 PM
4/2/14 9:30 AM
Explain 1
HARDBOUND SE
Constructing Two-Way Frequency Tables
PAGE 280
BEGINS HERE
If a data set has two categorical variables, you can list the frequencies of the paired values
in a two-way frequency table.
Example 1

Categorical Data and Frequencies
Complete the two-way frequency table.
A high school’s administration asked 100 randomly selected students in the 9th and 10th
grades about what fruit they like best. Complete the table.
INTEGRATE TECHNOLOGY
Preferred Fruit
Grade
Apple
Orange
Banana
9th
19
12
23
10th
22
9
15
Students have the option of completing the Explore
Activity online or in the book.
Total
Total
CONNECT VOCABULARY
Row totals:
Column totals:
Grand total:
9th: 19 + 12 + 23 = 54
Apple: 19 + 22 = 41
Sum of row totals: 54 + 46 = 100
10th: 22 + 9 + 15 = 46
Orange: 12 + 9 = 21
Sum of column totals: 41 + 21 + 38 = 100
Banana: 23 + 15 = 38
Both sums should equal the grand total.
Make sure that students understand the distinction
between quantitative and categorical data.
Quantitative data can be measured on a numbered
scale. Categorical data involves either/or choices
between two or more descriptive categories. Ask
students to provide some examples of quantitative
and categorical data.
Preferred Fruit

Grade
Apple
Orange
Banana
Total
9th
19
12
23
54
10th
22
9
15
46
Total
41
21
38
100
Jenna asked some randomly selected students whether they preferred dogs, cats, or other
pets. She also recorded the gender of each student. The results are shown in the two-way
frequency table below. Each entry is the frequency of students who prefer a certain pet and
are a certain gender. For instance, 8 girls prefer dogs as pets. Complete the table.
EXPLAIN 1
Gender
Dog
Cat
Other
Total
Girl
8
7
1
16
Boy
10
5
9
24
Total
18
12
10
40
HARDBOUND SE
Row totals:
Column totals:
Grand total:
Girl: 8 + 7 + 1 = 16
Dog: 8 + 10 = 18
Sum of row totals: 16 + 24 = 40
Boy: 10 + 5 + 9 = 24
Cat: 7 + 5 = 12
Sum of column totals: 18 + 12 + 10 = 40
Other: 1 + 9 = 10
Both sums should equal the grand total.
348
Constructing Two-Way
Frequency Tables
© Houghton Mifflin Harcourt Publishing Company
Preferred Pet
Module 8
EXPLORE
PAGE 281
BEGINS HERE
Lesson 1
PROFESSIONAL DEVELOPMENT
IN1_MNLESE389755_U4M08L1.indd 348
Integrate Mathematical Practices
This lesson provides an opportunity to use Mathematical Practice MP.7, which
asks students to “look for and make use of structure.” In this lesson, students use
the structure of two-way frequency tables to analyze data and understand a
problem-solving situation.
4/2/14 9:40 AM
INTEGRATE MATHEMATICAL
PRACTICES
Focus on Communication
MP.3 To check students’ understanding of the
information presented in a two-way frequency table,
have one student ask a question about the data in the
table. Have another student answer the question and
provide an explanation of how to use the table to
arrive at the answer.
QUESTIONING STRATEGIES
What is the difference between a two-way
frequency table and an ordinary frequency
table? In a two-way frequency table, each value
(other than row and column totals) indicates the
number of items that fit two data categories rather
than one, such as the number of boys who prefer
cats. In an ordinary frequency table, data values
correspond to only one data category.
Two-Way Frequency Tables 348
Reflect
EXPLAIN 2
3.
Look at the totals for each row. Was Jenna’s survey evenly distributed among boys and girls? Explain.
No, there were 24 boys and 16 girls.
Reading Two-Way Frequency Tables
4.
Look at the totals for each column. Which pet is preferred by the most students? Justify your answer.
Dogs: the total for Dog is greater than the total for Cat and the total for Other.
INTEGRATE MATHEMATICAL
PRACTICES
Focus on Reasoning
MP.2 Remind students that there may be more than
Your Turn
Complete the two-way frequency table.
5.
Antonio surveyed 60 of his classmates about their participation in school activities and whether they have a
part-time job. The results are shown in the two-way frequency table below. Complete the table.
Activities
one process for filling in a particular table. Discuss
different ways to fill cells in a table, such as using
addition to find the total for a column or row, and
working backward to find a missing value that is
not a total.
6.
Job
Clubs Only
Sports Only
Both
Neither
Total
Yes
12
13
16
4
45
No
3
5
5
2
15
Total
15
18
21
6
60
Jen surveyed 100 students about whether they like baseball or basketball. Complete the table.
Like Basketball
AVOID COMMON ERRORS
Remind students to use the row totals and column
totals to check that their work is correct. The sum of
the row totals should be the same as the sum of the
column totals. If the sums are different, students need
to review their work to look for errors.
Like Baseball
Yes
No
Total
Yes
61
13
74
No
16
10
26
Total
77
23
100
© Houghton Mifflin Harcourt Publishing Company
Explain 2
HARDBOUND SE
PAGE 282
BEGINS HERE
Reading Two-Way Frequency Tables
You can extract information about paired categorical variables by reading a two-way frequency table.
Example 2

Read and complete the two-way frequency table.
Suppose you are given the circled information in the table and instructed to complete
the table.
Eat Cereal for Breakfast
Gender
Yes
No
Total
54
Girl
42
12
Boy
36
10
46
Total
78
22
100
Find the total number of boys by subtracting: 100 - 54 = 46
Find the number of boys who do eat cereal by subtracting: 46 - 10 = 36
Add to find the total number of students who eat cereal and the total number of students
who do not eat cereal.
Module 8
349
Lesson 1
COLLABORATIVE LEARNING
IN1_MNLESE389755_U4M08L1.indd 349
Peer-to-Peer Activity
Have students work in pairs. Challenge one in each pair to describe a data set for
which the partner must create a two-way frequency table. Students should provide
as little direct information as possible, while still making it possible to complete
the table. For example, instead of saying, “Twenty boys prefer baseball,” they
might say, “The number of boys who prefer baseball is 15 less than the number of
girls who prefer softball.” After students complete the frequency tables, have them
compare results with their partners. If the students disagree, have them discuss
and determine which is correct.
349
Lesson 8.1
2/26/16 2:14 AM
B
One hundred students were surveyed about which beverage they chose at lunch. Some of
the results are shown in the two-way frequency table below. Complete the table.
QUESTIONING STRATEGIES
To complete a two-way frequency table that is
missing information, is it necessary to know
the total of all the values in the table? Explain. No; if
there is enough other information given in the
table, the total can be determined using other
information.
Lunch Beverage
Gender
Juice
Milk
Water
Total
Girl
10
13
17
40
Boy
15
24
21
60
Total
25
37
38
100
Find the total number of girls by subtracting: 100 - 60 = 40
So, the total number of girls is 40 . The number of girls who do not choose milk is 17 + 10 = 27 .
Find the number of girls who chose milk by subtracting: 40 - 27 = 13
Reflect
7.
Which lunch beverage is the least preferred? How do you know?
Juice: the total for Juice is less than the total for Milk and the total for Water.
Your Turn
Read and complete the two-way frequency table.
8.
100 students were asked what fruit they chose at lunch. The two-way frequency table shows some of the
results of the survey. Complete the table.
Lunch Fruit
Apple
Pear
Banana
Total
Girl
21
17
11
49
Boy
25
10
16
51
Total
46
27
27
100
© Houghton Mifflin Harcourt Publishing Company
9.
Gender
200 high school teachers were asked whether they prefer to use the chalkboard or projector in class.
The two-way frequency table shows some of the results of the survey. Complete the table.
Preferred Teaching Aid
Gender
Chalkboard
Projector
Total
Female
43
56
99
Male
44
57
101
Total
87
113
200
Module 8
350
HARDBOUND SE
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BEGINS HERE
Lesson 1
DIFFERENTIATE INSTRUCTION
IN1_MNLESE389755_U4M08L1.indd 350
Cognitive Strategies
01/04/14 8:57 PM
When students are completing two-way frequency tables that are missing
information, discuss how to determine which cells in the table can be completed
first. Students should understand that in order for a value to be determined, it
must be the only missing value in either its row or its column. By completing a
row or column in which only one value is missing, students move one step closer
to completing other rows or columns.
Two-Way Frequency Tables 350
Elaborate
ELABORATE
10. You are making a two-way frequency table of 5 fruit preferences among a survey sample of girls and boys.
What are the dimensions of the table you would make? How many entries would you need to fill
the table with frequencies and totals?
You would make a 2-by-5 for the frequencies. Adding totals would increase the
INTEGRATE MATHEMATICAL
PRACTICES
Focus on Communication
MP.3 Have students discuss why the order of words
dimensions to 3-by-6. You need 3 times 6, or 18, entries to fill the table.
11. A 3 categories-by-3 categories two-way frequency table has a row with 2 numbers, and no row or column
totals. Can you fill the row?
This table would be a 4-by-4 table, including the row of totals. You cannot fill the row
is important in identifying a cell in a two-way
frequency table. For example, students should
understand that “people who watch TV but not
movies” refers to a different cell than “people who
watch movies but not TV. ”
because you need 3 numbers to figure out the last one.
12. Essential Question Check-In How can you summarize categorical data for 2 categories?
You can use a two-way frequency table.
SUMMARIZE THE LESSON
Evaluate: Homework and Practice
What information is provided by a two-way
frequency table, and how is that information
organized? A two-way frequency table provides
categorical data for two categorical variables, such
as color and size or gender and job. Data for one
variable is organized in rows, and data for the other
variable is organized in columns. The value in each
cell of the table identifies the number of items that
fit the intersection of the two categories.
1.
100 m, 200 m, 400 m quantitative
2.
A theater company asked its members to bring in canned food for a food drive.
Use the categorical data to complete the frequency table.
BEGINS HERE
© Houghton Mifflin Harcourt Publishing Company
Cans Donated to Food Drive
HARDBOUND SE
PAGE 284
• Online Homework
• Hints and Help
• Extra Practice
Identify whether the given data is categorical or quantitative.
gold medal, silver medal, bronze medal categorical
peas corn peas soup corn
corn soup soup corn peas
peas corn soup peas corn
peas corn peas corn soup
corn peas soup corn corn
Cans
Frequency
soup
6
peas
8
corn
11
Complete the two-way frequency table.
3.
James surveyed some of his classmates about what vegetable they like best.
Complete the table.
Preferred Vegetable
Grade
Carrots
Green Beans
Celery
Total
9th
30
15
24
69
10th
32
9
20
61
Total
62
24
44
130
Module 8
351
Lesson 1
LANGUAGE SUPPORT
IN1_MNLESE389755_U4M08L1 351
Connect Vocabulary
The word quantitative in the phrase quantitative data shares a root with the word
quantity, meaning an amount. The word categorical in the phrase categorical data
shares a root with the word category, meaning a descriptive grouping. Categorical
data can also be referred to as qualitative data because these data describe qualities
or characteristics. The word frequency in the phrase frequency table shares a root
with the word frequent, meaning often. Each value in a frequency table shows how
often that value falls into a given category.
351
Lesson 8.1
7/25/14 7:44 AM
4.
A high school’s extracurricular committee surveyed a randomly selected group of
students about whether they like tennis and soccer. Complete the table.
EVALUATE
Like Tennis
5.
Like Soccer
Yes
No
Total
Yes
37
20
57
No
16
15
31
Total
53
35
88
ASSIGNMENT GUIDE
After a school field trip, Ben surveyed some students about which animals they liked
from the zoo. Complete the table.
Preferred Animal at a Zoo
6.
Grade
Lion
Zebra
Monkey
Total
11th
9
15
14
38
12th
4
17
15
36
Total
13
32
29
74
Jill asked some randomly selected students whether they preferred blue, green, or
other colors. She also recorded the gender of each student. The results are shown in
the two-way frequency table below. Complete the table.
Blue
Other
Total
15
3
10
28
Boy
3
16
6
25
Total
18
19
16
53
Kevin surveyed some students about whether they preferred soccer, baseball, or
another sport. He also recorded their gender. Complete the table.
HARDBOUND SE
PAGE 285
BEGINS HERE
Preferred Sport
Gender
Soccer
Baseball
Other
Total
Girl
33
7
10
50
Boy
15
27
7
49
Total
48
34
17
99
Module 8
Exercise
Depth of Knowledge (D.O.K.)
Mathematical Practices
1–12
1 Recall of Information
MP.7 Using Structure
13–14
2 Skills/Concepts
MP.3 Logic
15–22
2 Skills/Concepts
MP.4 Modeling
23
1 Recall of Information
MP.7 Using Structure
24
2 Skills/Concepts
MP.3 Logic
3 Strategic Thinking
MP.3 Logic
25–26
Exercises 1–2, 23
Example 1
Constructing Two-Way
Frequency Tables
Exercises 3–12
Example 2
Reading Two-Way Frequency Tables
Exercises 13–22,
24–26
Lesson 1
352
IN1_MNLESE389755_U4M08L1.indd 352
Explore
Categorical Data and Frequencies
of filled cells in a two-way frequency table that makes
it possible to complete the table. Work backward from
a completed frequency table by removing values one
at a time, making sure it is possible to do so while
leaving a row or column with only one missing value.
Students may discover that completing a frequency
table requires that the table have at least as many
filled cells as the number of interior cells.
© Houghton Mifflin Harcourt Publishing Company
7.
Green
Girl
Practice
INTEGRATE MATHEMATICAL
PRACTICES
Focus on Patterns
MP.8 Have students try to find the smallest number
Preferred Color
Gender
Concepts and Skills
01/04/14 8:57 PM
Two-Way Frequency Tables 352
8.
MULTIPLE REPRESENTATIONS
Have students create a two-question survey whose
results can be summarized in a two-way frequency
table. Students should understand that the questions
they choose for their surveys should not allow for
open-ended answers.
A school surveyed a group of students about whether they like backgammon and
chess. They will use this data to determine whether there is enough interest for the
school to compete in these games. Complete the table.
Like Backgammon
Like Chess
Yes
No
Total
Yes
10
61
71
No
5
3
8
15
64
79
Total
AVOID COMMON ERRORS
9.
Remind students that in a two-way frequency table,
the total of the values in each row and the total of the
values in each column must add up to the same
number. Students can check their work for errors by
comparing the sum of the row totals to the sum of the
column totals.
Hugo surveyed some 9th and 10th graders in regard to whether they preferred math,
English, or another subject. The results of the survey are in the following table.
Complete the table.
Preferred Subject
Grade
Math
English
Other
9th
40
35
20
Total
95
10th
41
32
17
90
Total
81
67
37
185
HARDBOUND SE
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BEGINS HERE
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Dragon
Images/Shutterstock
10. Luis surveyed some middle school and high school students
about the type of music they prefer. Complete the table.
Preferred Music
School Level
Country
Pop
Other
Total
Middle School
18
13
23
54
High School
7
32
15
54
Total
25
45
38
108
11. Natalie surveyed some teenagers and adults on whether they prefer standard cars,
vans, or convertibles. Her results are in the following table. Complete the table.
Preferred Car Type
Age
Standard
Van
Convertible
Total
Adults
10
25
9
44
Teenagers
11
7
24
42
Total
21
32
33
86
Module 8
IN1_MNLESE389755_U4M08L1 353
353
Lesson 8.1
353
Lesson 1
7/25/14 7:44 AM
12. Eli surveyed some teenagers and adults on whether they prefer apples, oranges, or
bananas. His results are in the following table. Complete the table.
Preferred Fruit
Age
Apple
Orange
Banana
Total
Adults
22
12
10
44
Teenagers
24
9
9
42
Total
46
21
19
86
200 students were asked to name their favorite science class. The results are shown
in the two-way frequency table. Use the table for the following questions.
Favorite Science Class
Gender
Biology
Chemistry
Physics
Total
Girl
42
39
23
104
Boy
19
45
32
96
Total
61
84
55
200
13. How many boys were surveyed? Explain how you found your answer.
96 boys: 104 of the 200 students were girls, so 200 − 104 = 96 of them were boys.
14. Complete the table. How many more girls than boys chose biology as their favorite
science class? Explain how you found your answer.
42 − 19 = 23, so 23 more girls than boys chose biology.
The results of a survey of 150 students about whether they
own an electronic tablet or a laptop are shown in the two-way
frequency table.
Gender
Electronic tablet
Laptop
Both
Neither
Total
Girl
15
54
10
9
88
Boy
14
35
8
5
62
Total
29
89
18
14
150
15. Complete the table. Do the surveyed students own more laptops or more
electronic tablets?
The number of boys is 150 − 88 = 62.
HARDBOUND SE
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BEGINS HERE
© Houghton Mifflin Harcourt Publishing Company
Device
Girls who own both electronic devices: 88 − 9 − 54 − 15 = 10
Boys who own an electronic tablet: 62 − 5 − 8 − 35 = 14; Students own more laptops.
16. Which group had more people answer the survey, boys or students who own an
electronic tablet only? Explain.
Boys: 62 boys answered the survey, which is more than the 29 people
who own an electronic tablet only.
Module 8
IN1_MNLESE389755_U4M08L1 354
354
Lesson 1
7/25/14 7:44 AM
Two-Way Frequency Tables 354
17. The table shows the results of a survey about students’ preferred frozen yogurt flavor.
Complete the table, and state the flavors that students preferred the most and the least.
Preferred Flavor
Gender
Girl
Boy
Total
Vanilla
12
Mint
Strawberry
15
18
Total
45
17
25
55
29
40
13
31
100
Students preferred mint the most and vanilla the least.
18. Teresa surveyed 100 students about whether they like pop music or country music. Out
of the 100 students surveyed, 42 like only pop, 34 like only country, 15 like both pop and
country, and 9 do not like either pop or country. Complete the two-way frequency table.
Like Pop
Like Country
Yes
No
Total
Yes
15
42
57
No
34
9
Total
49
51
100
43
19. Forty students in a class at an international high school were surveyed about which
non-English language they can speak. Complete the table.
Foreign Language
Gender
Girl
Boy
Total
Chinese
Spanish
7
8
French
7
Total
22
5
12
6
7
18
14
14
40
HARDBOUND SE
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BEGINS HERE
© Houghton Mifflin Harcourt Publishing Company
Luis surveyed 100 students about whether they like soccer. The number of girls and
the number of boys completing the survey are equal.
20. Complete the table.
Likes Soccer
Gender
Girl
Boy
Total
35
Total
50
50
45
55
100
20
Likes Tennis
IN1_MNLESE389755_U4M08L1 355
Lesson 8.1
No
21. Twice as many girls like soccer as the number that like tennis. The same number of
students like soccer as like tennis. Construct a table containing the tennis data.
Module 8
355
Yes
30
15
Gender
Yes
No
Total
Girl
15
35
50
Boy
30
20
50
Total
45
55
100
355
Lesson 1
7/25/14 7:44 AM
22. A group of 200 high school students were asked about their use of email and text
messages. The results are shown in the two-way frequency table. Complete the table.
Text Messages
Email
Yes
No
Total
Yes
72
18
90
65
45
110
137
63
200
No
Total
23. Circle the letter of each data set that is categorical. Select all that apply.
A. 75°, 79°, 77°, 85°
B. apples, oranges, pears
C. male, female
D. blue, green, red
E. 2 feet, 5 feet, 12 feet
F. classical music, country music
G. 1 centimeter, 3 centimeters, 9 centimeters
24. Explain the Error Find the mistake in completing the two-way frequency table for
a survey involving 50 students. Then complete the table correctly.
Favorite Foreign Language Class
Russian
German
Italian
Total
Girl
8
8
8
24
Boy
42
9
7
58
Total
50
© Houghton Mifflin Harcourt Publishing Company
Gender
Possible answer: 50 was used as the total whose favorite is Russian
instead of as the grand total.
Total boys: 50 - 24 = 26
Boys who prefer Russian: 26 - 9 - 7 = 10
Correct table:
Favorite Foreign Language Class
Gender
Russian
German
Italian
Total
Girl
8
8
8
24
Boy
10
9
7
26
Total
18
17
15
50
Module 8
IN1_MNLESE389755_U4M08L1 356
356
Lesson 1
7/25/14 7:44 AM
Two-Way Frequency Tables 356
JOURNAL
Have students explain the steps they take to complete
a two-way frequency table that has missing values.
Students should be sure to include descriptions of
how to determine column totals and row totals.
HARDBOUND SE
H.O.T. Focus on Higher Order Thinking
PAGE 289
BEGINS HERE
25. Justify Reasoning Charles surveyed 100 boys about their favorite color. Of the
100 boys surveyed, 44 preferred blue, 25 preferred green, and 31 preferred red.
a. Explain why it is not possible to make a two-way frequency table from the given
data.
Charles only surveyed boys, so there is only one categorical variable:
color. You need two categorical variables to make a two-way
frequency table.
b. Suppose Charles also surveyed some girls. Of the girls surveyed, 30 preferred blue
and 43 preferred green. Can Charles make a two-way frequency table now? Can
he complete it?
He can make a table, but he cannot complete it. There are now two
categorical variables, color and gender, but there is not enough
information about the girls’ preferences. In addition to the information
provided, you need to know how many girls were surveyed or how many
prefer red to complete the table.
26. Persevere in Problem Solving Shown are two different tables about a survey
involving students. Each survey had a few questions about musical preferences.
All students answered all questions. Complete the tables. What type of music do
the students prefer?
Likes Classical Music
© Houghton Mifflin Harcourt Publishing Company
Gender
Total
Girl
21
28
49
Boy
29
22
51
Total
50
50
100
Gender
Yes
No
Girl
34
15
49
Total
Boy
36
15
51
Total
70
30
100
All students answered all the questions, so total girls in both is 49, and the total
students in both is 100.
Overall, the students prefer blues music: 70 students like blues, 50 like classical.
IN1_MNLESE389755_U4M08L1.indd 357
Lesson 8.1
No
Likes Blues Music
Module 8
357
Yes
357
Lesson 1
01/04/14 8:57 PM
Lesson Performance Task
HARDBOUND SE
PAGE 290
BEGINS HERE
Two hundred students were asked about their favorite sport. Of the 200 students surveyed,
98 were female. Some of the results are shown in the following two-way frequency table.
Favorite Sport
Gender
Football
Baseball
Basketball
Soccer
Female
26
Male
38
Total
64
Total
24
36
12
98
19
21
24
102
43
57
36
200
a. Complete the table.
Total number of males: 200 - 98 = 102
Females who chose football: 64 - 38 = 26
Females who chose baseball: 98 - 26 - 36 - 12 = 24
Males who chose soccer: 36 - 12 = 24
QUESTIONING STRATEGIES
In what order would you fill in the empty
spaces in the table? Explain why. Possible
answer: I would first fill in the numbers given in the
text of the problem (200 students in total, and 98
female students). Then I would look for a row or
column with only one empty cell, and find the
missing number (such as the total number of males,
the number of females who chose football, or the
number of males who chose soccer). After I fill in
those numbers, there would still be other rows and
columns with only one empty cell, so I would repeat
the process until the table is completed.
Males who chose basketball: 102 - 38 - 19 - 24 = 21
Total baseball: 24 + 19 = 43
INTEGRATE MATHEMATICAL
PRACTICES
Focus on Reasoning
MP.2 Discuss with students how the sample of
Total basketball: 36 + 21 = 57
b. Which sport is the most popular among the students? Which is the least popular?
Explain.
Most popular is football; 64 is the greatest total.
Least popular is soccer; 36 is the least total.
c.
students chosen for the survey could have influenced
the survey results. For example, consider whether
age, country of origin, participation in sports, or
other characteristics of survey participants might
influence the results. Have students describe a target
population for which soccer is likely to be the most
popular sport among those surveyed.
Which sport is most popular among the females? Which sport is most popular
among the males? Explain.
© Houghton Mifflin Harcourt Publishing Company
Most popular among females is basketball; 36 is the greatest number
of choices.
Most popular among males is football; 38 is the greatest number
of choices.
Module 8
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Lesson 1
EXTENSION ACTIVITY
IN1_MNLESE389755_U4M08L1 358
Have students create and conduct a survey of 20 students and then record the
results in a two-way frequency table. Students should begin by selecting two
categorical variables to record, such as gender and favorite subject, or grade level
and music preference. Remind them that quantitative and free-response answers
are not appropriate for recording in a frequency table. Encourage students to
select a sample of students that is not expected to skew the survey results. Have
students share their frequency tables and discuss their findings.
7/25/14 7:44 AM
Scoring Rubric
2 points: Student correctly solves the problem and explains his/her reasoning.
1 point: Student shows good understanding of the problem but does not fully
solve or explain his/her reasoning.
0 points: Student does not demonstrate understanding of the problem.
Two-Way Frequency Tables 358