Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
Unit 05: All Operations (13 days)
Possible Lesson 01 (5 days)
Possible Lesson 02 (3 days)
Possible Lesson 03 (5 days)
POSSIBLE LESSON 02 (3 days)
This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing
with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and
districts may modify the time frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your
child’s teacher. (For your convenience, please find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and
Midcycle State Adopted Instructional Materials.)
Lesson Synopsis:
Students read, create, and interpret bar graphs based on sets of unrelated and related data.
TEKS:
The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas
law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit.
The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148
4.13
Probability and statistics.. The student solves problems by collecting, organizing, displaying, and interpreting sets of data. The
student is expected to:
4.13B
Interpret bar graphs. Readiness Standard
Underlying Processes and Mathematical Tools TEKS:
4.14
Underlying processes and mathematical tools.. The student applies Grade 4 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. The student is expected to:
page 1 of 17 Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
4.14A
Identify the mathematics in everyday situations.
4.15
Underlying processes and mathematical tools.. The student communicates about Grade 4 mathematics using informal language. The
student is expected to:
4.15A
Explain and record observations using objects, words, pictures, numbers, and technology.
4.15B
Relate informal language to mathematical language and symbols.
4.16
Underlying processes and mathematical tools.. The student uses logical reasoning. The student is expected to:
4.16B
Justify why an answer is reasonable and explain the solution process.
Performance Indicator(s):
page 2 of 17 Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
Grade 04 Mathematics Unit 05 PI 02
Create a single bar graph that shows data from a class survey (e.g., favorite movie, favorite sport, etc.). According to the data in the graph, calculate and explain in words the
difference between the least popular and most popular category from the whole class survey, and write a statement that best describes the difference (e.g., 6 more students
preferred baseball than basketball, etc.). Reorganize the same class data to create a double bar graph by separating each category into boys and girls. According to the data in
the double bar graph: (1) calculate and explain in words the difference between the least popular and most popular category for the boys, and write a statement that best
describes the difference (e.g., 6 more boys preferred football than basketball, etc.) and (2) calculate and explain in words the difference between the least popular and most
popular category for the girls, and write a statement that best describes the difference (e.g., 6 more girls preferred baseball than basketball, etc.). Then, write a summary that
describes the similarities and differences between the single and double bar graphs and the purposes of each.
Sample Performance Indicator:
Survey your class to determine which type of movie is their favorite: Action, Mystery, Comedy, Family, or Other. When gathering the data, be sure
to distinguish the boys’ answers from the girls’ answers. Use the class data to create a single bar graph with appropriate labels. Use the single bar
graph to calculate and explain in words the difference between the least popular and most popular movie type for the whole class, and write a
statement that best describes the difference. Reorganize the same class data to create a double bar graph by separating each movie type into
boys and girls. According to the data in double bar graph: (1) calculate and explain in words the difference between the least popular and most
popular movie type for the boys, and write a statement that best describes the difference and (2) calculate and explain in words the difference
between the least popular and most popular type movie type for the girls, and write a statement that best describes the difference. Then, write a
summary that describes the similarities and differences between the single and double bar graphs and the purposes of each.
Standard(s): 4.13B , 4.14A , 4.15A , 4.15B , 4.16B ELPS ELPS.c.1C , ELPS.c.5G
Key Understanding(s):
Real-life problems involving a set of data in a bar graph can be interpreted and justified from the key, labels, and scale, represented with words and symbols, and
solved by applying the appropriate operation(s).
Misconceptions:
Some students may think that bar graphs have bars side by side with no space between them. Each bar in a bar graph represents a different category of no
relationship, so bars should have spaces between them. In double bar graphs, each double group of bars represent a different category of no relationship, so there
page 3 of 17 Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
should be spaces between each grouping; however, a double group of bars represent data of the same category so they are side by with no space. A graph that
has ALL bars touching is a type of bar graph known as a histogram where the consecutive bars represent consecutive equal intervals of data. Histograms are
taught in the middle school curriculum.
Vocabulary of Instruction:
bar graph
data
frequency
horizontal axis
interval
poll
survey
tally
vertical axis
Materials List:
connecting cubes (optional) (2 colors) (10 – 20 per student)
dry erase marker (1 per student)
index card (1 per student)
math journal (1 per student)
whiteboard (student-sized) (1 per student)
Attachments:
All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments
that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website.
Double Data
Double Bar Graph Practice KEY
Double Bar Graph Practice
Creating Doubles
page 4 of 17 Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
GETTING READY FOR INSTRUCTION
Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to
teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using
the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested
Day
1
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Single to double bar graphs
Engage 1
Students are introduced to double bar graphs by analyzing two sets of single bar graph data.
ATTACHMENTS
Teacher Resource: Double Data (1 per
teacher)
Instructional Procedures:
1. Display teacher resource: Double Data and distribute a whiteboard and dry erase marker to each
MATERIALS
student. Facilitate a class discussion about the components of each graph displayed (e.g. the
title, the horizontal axis, vertical axis, scale, intervals, etc.) and identify where each of these graph
whiteboard (student-sized) (1 per student)
components are located.
dry erase marker (1 per student)
page 5 of 17 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
Notes for Teacher
TEACHER NOTE
Each bar in a single bar graph represents a
different category of no relationship, so bars have
spaces between them. In double bar graphs, each
double group of bars represent a different
category of no relationship, so there should be
spaces between each grouping; however, a
Ask:
double group of bars represent data of the same
category so they are side by with no space. A
What are the two sets of data displayed in these graphs? (Club memberships for boys
graph that has ALL bars touching is a type of bar
and club memberships for girls.)
graph known as a histogram, where the
How are the sets of data alike? different? Answers may vary. Both data sets show
consecutive bars represent consecutive equal
membership in the art, music, and science clubs. They are different because one set of data
show membership for girls and the other for boys.
intervals of data. Histograms are taught in the
middle school curriculum.
Is there a better way to display the two sets of data? Explain. (yes) One graph could be
used with the data combined.
If the data was combined and had both sets of bars on the same graph, what could
distinguish the boys’ data from the girls’ data? Answers may vary. Different colors could
be used for the boys’ bars and the girls’ bars; different patterns could be drawn inside the
boys’ bars and the girls’ bars; etc.
How would you know which color or pattern represented boys and which represented
girls? (A key or legend could be created to show what each color or pattern represented.)
page 6 of 17 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
Suggested Instructional Procedures
Notes for Teacher
2. Place students in pairs. Instruct student pairs to create the new double bar graph on their
whiteboard. Allow time for students to complete the activity. Monitor and assess student pairs to
check for understanding.
3. Facilitate a class discussion for students to share their graphs and to correct any misconceptions
regarding the format of a double bar graph.
Topics:
Double bar graphs
ATTACHMENTS
Teacher Resource: Double Bar Graph
Practice KEY (1 per teacher)
Explore/Explain 1
Handout: Double Bar Graph Practice (1
Students investigate interpreting data for double bar graphs.
per student)
Instructional Procedures:
MATERIALS
1. Explain to students that they will be conducting a classroom data-gathering activity in order to
gather and sort data into two categories. Instruct the students to brainstorm and select a topic to
whiteboard (student-sized) (1 per student)
be used to take a poll or survey of the class (e.g., Students could poll to determine a favorite food,
dry erase marker (1 per student)
activity, etc.).
math journal (1 per student)
2. Facilitate a class discussion to determine the subject for the survey. Gather and display student
responses to the survey for the class to see.
connecting cubes (optional) (2 colors) (10
– 20 per student)
Ask:
How could this information be used to create a single bar graph? Answers may vary.
TEACHER NOTE
Some students may benefit from building double-
page 7 of 17 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
3. Instruct students to use the displayed data from the class survey to create a single bar graph of
the data in their math journal. Allow time for students to create their graphs. Monitor and assess
students to check for understanding. Facilitate a class discussion for students to display their
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
Notes for Teacher
bar graphs with connecting cubes before drawing
the graphs on paper. Give these students cubes
in two colors, one for each set of data. Allow
graphs and determine the types of questions that could be asked from the graph.
students to construct bars for each set of data
Ask:
separately and then combine them to make a
double-bar graph. Students can then refer to their
What kinds of questions could be asked and answered using the data in this graph?
connecting cube model as they draw their graphs
Answers may vary. How many more students preferred pizza to hamburgers?; etc.
on paper. To represent large numbers, cubes
How could you determine the answers to these questions? Answers may vary. I would
could represent 10’s and 100’s.
have to subtract to find how many more students preferred pizza to hamburgers; etc.
4. Place students in pairs. Instruct student pairs to generate at least one question from the class
data and to find the solution. Allow time for student pairs to develop a question and determine the
solution(s). Monitor and assess students to check for understanding. Facilitate a class discussion
for students to share their questions and solutions.
Ask:
How could this same information be used to create a double bar graph? Answers may
vary.
5. Instruct students to use the displayed data from the class survey to create a double bar graph of
the data in their math journal. Allow time for students to create their graphs. Monitor and assess
students to check for understanding. Facilitate a class discussion for students to display their
graphs and determine the types of questions that can be asked from the graph.
Ask:
page 8 of 17 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
Suggested Instructional Procedures
Notes for Teacher
What kinds of questions could be asked and answered using the data in this graph?
Answers may vary. How many more girls preferred pizza than boys?; etc.
How could you determine the answers to these questions? Answers may vary. I would
have to subtract to find how many more girls preferred pizza than boys; etc.
6. Instruct student pairs to generate at least one question from the class data and to find a solution.
Allow time for student pairs to develop a question and determine the solution. Monitor and assess
students to check for understanding. Facilitate a class discussion for students to share their
questions and solutions.
7. Distribute handout: Double Bar Graph Practice to each student. Instruct student pairs to
complete the graph. Allow time for students to complete the activity. Monitor and assess student
pairs to check for understanding. Facilitate a class discussion to debrief student answers.
2
Topics:
Spiraling Review
Double bar graphs
Elaborate 1
Students investigate creating and interpreting data for double bar graphs.
ATTACHMENTS
Teacher Resource: Creating Doubles (1
per student)
Instructional Procedures:
1. Place students in pairs. Distribute an index card and handout: Creating Doubles to each student.
Handout: Creating Doubles (1 per
student)
2. Display teacher resource: Creating Doubles. Remind students of the previous activity where they
conducted a classroom poll to gather and display data. Instruct student pairs to create a situation
MATERIALS
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Suggested
Day
Suggested Instructional Procedures
in which a double bar graph could be used to display data. Explain to students that although they
will be working with a partner to create the situation, they will each be responsible for completing
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
Notes for Teacher
index card (1 per student)
their own handout: Creating Doubles, as well as individually generating 3 (different) questions
that could be answered using the information in their graph, and recording the solutions to each
created question on an index card. Allow time for students to complete the activity. Monitor and
assess students to check for understanding.
3. Instruct students to exchange their completed handout: Creating Doubles with their partner and
answer the 3 questions created by the other student. Allow time for students to complete the
activity.
4. Instruct students to return the completed handout: Creating Doubles to the original owner and
verify their partner’s solutions with the solutions recorded on their index card. Allow time for
students to complete the activity. Monitor and assess students to check for understanding.
Facilitate a class discussion regarding the student created data, questions, and solutions.
3
Evaluate 1
Instructional Procedures:
1. Assess student understanding of related concepts and processes by using the Performance
Indicator(s) aligned to this lesson.
Performance Indicator(s):
Grade 04 Mathematics Unit 05 PI 02
Create a single bar graph that shows data from a class survey (e.g., favorite movie, favorite sport, etc.).
page 10 of 17 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
Notes for Teacher
According to the data in the graph, calculate and explain in words the difference between the least
popular and most popular category from the whole class survey, and write a statement that best
describes the difference (e.g., 6 more students preferred baseball than basketball, etc.). Reorganize the
same class data to create a double bar graph by separating each category into boys and girls. According
to the data in the double bar graph: (1) calculate and explain in words the difference between the least
popular and most popular category for the boys, and write a statement that best describes the difference
(e.g., 6 more boys preferred football than basketball, etc.) and (2) calculate and explain in words the
difference between the least popular and most popular category for the girls, and write a statement that
best describes the difference (e.g., 6 more girls preferred baseball than basketball, etc.). Then, write a
summary that describes the similarities and differences between the single and double bar graphs and
the purposes of each.
Sample Performance Indicator:
Survey your class to determine which type of movie is their favorite: Action, Mystery,
Comedy, Family, or Other. When gathering the data, be sure to distinguish the
boys’ answers from the girls’ answers. Use the class data to create a single bar
graph with appropriate labels. Use the single bar graph to calculate and explain in
words the difference between the least popular and most popular movie type for the
whole class, and write a statement that best describes the difference. Reorganize
the same class data to create a double bar graph by separating each movie type
into boys and girls. According to the data in double bar graph: (1) calculate and
explain in words the difference between the least popular and most popular movie
type for the boys, and write a statement that best describes the difference and (2)
calculate and explain in words the difference between the least popular and most
popular type movie type for the girls, and write a statement that best describes the
page 11 of 17 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 4/Mathematics
Unit 05:
Suggested Duration: 3 days
Notes for Teacher
difference. Then, write a summary that describes the similarities and differences
between the single and double bar graphs and the purposes of each.
Standard(s): 4.13B , 4.14A , 4.15A , 4.15B , 4.16B ELPS ELPS.c.1C , ELPS.c.5G
04/15/13
page 12 of 17 Grade 4
Mathematics
Unit: 05 Lesson: 02
Double Data
Use these graphs to answer the questions below. Be prepared to discuss your
answers.
Club Memberships
14
14
12
12
Number of Girls
Number of Boys
Club Memberships
10
8
6
4
10
2
8
6
4
2
Art
Music
Science
Art
Music
Science
(1)
What are the two sets of data displayed in these graphs?
(2)
Is there a better way to display the two sets of data? Explain.
©2012, TESCCC
09/17/12
page 1 of 1
Grade 4
Mathematics
Unit: 05 Lesson: 02
Double Bar Graph Practice KEY
Use this table of data to create a double bar graph on the grid below. Be sure to include: title, axes
labels, scale, and intervals.
Movie Tickets Sold
Friday
Saturday
Sunday
Adults
130
120
95
Students
85
90
145
Graph scales may vary
Movie Tickets Sold
Key
Adults
Students
Number of Tickets
140
120
100
80
60
40
20
0
Friday
Saturday
Sunday
Use the data from your double bar graph to answer the following questions.
(1)
(2)
How did you decide on the scale for the axis of your graph?
Answers may vary.
The scale was determined from the minimum and maximum amounts of tickets sold—
minimum of 85, maximum of 145; etc.
What does the graph’s vertical axis show?
The number of tickets sold
(3)
What does the graph’s horizontal axis show?
The days when the tickets were sold
(4)
How many tickets were sold on all three days? How do you know? 665 tickets; because
when you add all of the bar amounts together you get 665.
©2012, TESCCC
04/02/12
page 1 of 1
Grade 4
Mathematics
Unit: 05 Lesson: 02
Double Bar Graph Practice
Use this table of data to create a double bar graph on the grid below. Be sure to include: title, axes
labels, scale, and intervals.
Movie Tickets Sold
Friday
Saturday
Sunday
Adults
130
120
95
Students
85
90
145
Key
Adults
Students
Use the data from your double bar graph to answer the following questions.
(1)
How did you decide on the scale for the axis of your graph?
(2)
What does the graph’s vertical axis show?
(3)
What does the graph’s horizontal axis show?
(4)
How many tickets were sold on all three days? How do you know?
©2012, TESCCC
09/17/12
page 1 of 1
Grade 4
Mathematics
Unit: 05 Lesson: 02
Creating Doubles
(1)
Describe a situation in which a double-bar graph could be used to display data. Write it
below.
(2)
Create a table of data in the box based on your situation described in problem 1.
(3)
Use the grid below to draw the double-bar graph of your data. Be sure to include: title, axes,
labels, scale, and key.
©2012, TESCCC
09/17/12
page 1 of 2
Grade 4
Mathematics
Unit: 05 Lesson: 02
Creating Doubles
Use the data from your bar graph to answer the following questions.
(4)
What does the vertical axis show?
(5)
What does the horizontal axis show?
(6)
Create 3 questions that could be answered using the data in your graph. List them below.
(a)___________________________________________________________________
(b)___________________________________________________________________
(c)___________________________________________________________________
Write these same questions on an index card and create an answer key for each. Be sure to show
how you got each answer. Keep the card until your teacher gives you further directions.
©2012, TESCCC
09/17/12
page 2 of 2