Unit 7 - Data Representation
4th Grade
Unit 7 – Data Representation
Grade Level: 4
Lesson Title: Data Representation
Subject Area: Math
Unit Number:
Lesson Length: 7
Lesson Overview - This unit bundles student expectations that address multiple methods for
representing data as well as analyzing data to solve problems. According to the Texas
Education Agency, mathematical process standards including application, a problem-solving
model, tools and techniques, communication, representations, relationships, and justifications
should be integrated (when applicable) with content knowledge and skills so that students are
prepared to use mathematics in everyday life, society, and the workplace. During this unit,
students represent data on a frequency table, dot plot, or stem-and-leaf plot marked with
whole numbers and fractions. Students examine the characteristics of each data
representation, as well as compare the similarities and differences between them. Adequate
understandings of these data representations allow students to solve one- and two-step
problems using data in whole number, decimal, and fraction form in a frequency table, dot plot,
or stem-and-leaf plot.
Unit Objectives:
Students will…
 Collect, organize, represent, and summarize data using a frequency table, dot plot, tally
chart, and stem and leaf plot.
 Analyze and compare the data representations and determine which representation
most efficiently summarizes a specific aspect of the given data
 Create stem and leaf plots, frequency tables, tally charts, and dot plots
Standards addressed:
TEKS:
4.1A - Apply mathematics to problems arising in everyday life, society, and the workplace.
4.1B - Use a problem-solving model that incorporates analyzing given information, formulating
a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.
4.1C - Select tools, including real objects, manipulatives, paper and pencil, and technology as
appropriate, and techniques, including mental math, estimation, and number sense as
appropriate, to solve problems.
4.1D - Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate
4.1E - Create and use representations to organize, record, and communicate mathematical
ideas
4.1F - Analyze mathematical relationships to connect and communicate mathematical ideas
4.1G - Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
4.9A - Represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole
numbers and fractions.
4.9B - Solve one- and two-step problems using data in whole number, decimal, and fraction
form in a frequency table, dot plot, or stem-and-leaf plot
1
Unit 7 - Data Representation
4th Grade
ELPS:
ELPS.c.5B- write using newly acquired basic vocabulary and content-based grade-level
vocabulary
ELPS.c.1A- use prior knowledge and experiences to understand meanings in English
ELPS.c.2D- monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
ELPS.c.3D- speak using grade-level content area vocabulary in context to internalize new
English words and build academic language proficiency
Misconceptions:



Some students may think that categorical and numerical data can always be displayed
by the same representations rather than realizing that the appropriate representation for
a set of data depends on the type of question being asked about the data.
Some students may confuse numerical data with a count or measure of the data.
Some students may try to represent numerical data in a stem-and-leaf plot without first
arranging the leaves for each stem in order.
Underdeveloped Concepts:


Some students may not recognize that the dots on a dot plot may represent more than
one piece of data as do the symbols in a pictograph.
Although some students may be proficient at displaying data using different
representations, they may lack the experience to solve problems by analyzing the data.
Vocabulary:






Categorical data – data that represents the attributes of a group of people, events, or
objects
Data – information that is collected about people, events, or objects
Dot plot – a graphical representation to organize data that uses dots (or Xs) to show
the frequency (number of times) that each category or number occurs
Frequency table – a table to organize data that lists categories and the frequency
(number of times) that each category occurs
Numerical data – data that represents values or observations that can be measured
and placed in ascending or descending order
Stem-and-leaf plot – a graphical representation used to analyze and compare groups
or clusters of numerical data by separating one place value from another place value of
a data set. The larger of the two place values is called the stem and the smaller of the
two place values is called the leaf.
Related Vocabulary:
 Horizontal
 Interval
 Key
 Label
2




Number line
Range
Scale
Tally marks
Unit 7 - Data Representation
4th Grade


Frequency
Vertical


Title
Value
List of Materials:
Sticky Notes
Markers
Index Cards
Manila drawing paper
White boards
Handouts: Class Data- Frequency Table and Dot Plots
Day Two Riding Bikes Data Representation
Day Three Performance Assessment handout.
Mr. Jackson’s Pizza Palace (Stem and Leaf with Fractions)
Frequency Station Activity Cards
Dot Plot Activity Cards
Stem and Leal Problem Solving Cards
Snow Cone Steam and Leaf
INSTRUCTIONAL SEQUENCE
Phase - Engage
Day 1
Day 1
Materials needed: one of each- sticky notes, markers, index cards (exit tickets).
Handouts: Class Data- Frequency Table and Dot Plots
Activity:
Students collect data needed to make a frequency table and dot plots.
1. Facilitate a class discussion to assess prior knowledge of data and surveys.
Ask:



What is data? Answers may vary. Information that is collected about people, events,
or objects.
How do you think data is collected? Answers may vary.
What is a survey? An investigation of the opinions or experience of a group of people,
based on a question or series of questions.
Have a discussion on how a survey is one way to collect data and talk about different
topics in which a survey could be conducted. Ask for students to volunteer their own
ideas including which categories could be named (Ex. What is your favorite color?
Categories could be red, blue, green, pink, and purple.) Explain that when data
represents the attributes (or characteristics) of a group of people, events, or objects, it
is called categorical data.
2. Distribute 1 sticky note and 1 marker to each student. Explain to students that you are
about to conduct a survey on the class.

3
Ask:
How many pockets do you have on everything you are wearing right now?
Unit 7 - Data Representation
4th Grade
Instruct students to count all the pockets on their clothing and write the number of
pockets they counted on their sticky note. By groups instruct students to randomly
place their sticky notes on the board in front of the room.
Activity:
Create a tally chart, frequency table, and dot plots that represent data collected in class.
1. Distribute handout: Class Data- Frequency Table and Dot Plots to each student and
display the same for the class to see. Explain to students that they will be using the
class data they just gathered to create a tally chart, frequency table, and then, dot plots.
2. Explain to students that a tally chart and frequency table is a table to organize data that
lists categories and the frequency (number of times) that each category occurs.
Ask:
 What title can be given to this frequency table so that it clarifies the meaning
of the data represented? Answer may vary. Ex. “Number of Pockets in Our Class”
 What should be the title for the first column in the table? Answers may vary. Ex.
“Number of Pockets”
 By looking at our data how can we group or classify this information? Group
them by number. Threes go with threes, fives go with fives.
 By looking at our data collected what categories should we use? Answers may
vary. Ex. 0, 1, 2, 3, 4, 5, 6
Determine the categories. If there are a large range of categories, some can be joined.
Ex. 0, 1-2, 3-4, 5-6, 7 or more.
3. Have a student go to the board where all the sticky notes are posted. The student is to
select a sticky note (it does not have to be their own) and tell the teacher what it says.
Teacher records the piece of data on the frequency table as students do the same.
Student moves sticky note to a new location to ensure it will only be recorded one time.
Teacher selects a different student to select another sticky note. Continue until all data
is recorded on frequency table.** Another option is to have student mark out number on
sticky note after it is recorded instead of moving sticky note to another location.
4. Complete frequency table by calculating frequency in last column.
5. Explain to students that a dot plot is a graphical representation to organize data that
uses dots (or Xs) to show the frequency (number of times) that each category occurs.
6. Show YouTube video, http://goo.gl/iGbmUP (This link is case sensitive) to the class.
7. Instruct students they will use the data compiled in the frequency table to make a dot
plot on the bottom of the first page of handout: Class Data- Frequency Table and Dot
Plots. Explain to students our dot plot will have a little more information than the one in
the video.
Ask guiding questions and complete each step along the way:
4






Unit 7 - Data Representation
4th Grade
What do you think we should write on the top line? A title.
What would be a good title for our dot plot? Why? Answers may vary. It should
be the same as frequency table, because they both will represent the same data.
What should we write on the very bottom line? Why? Answers may vary.
“Pockets” because that clarifies what our categories are about for the dot plot.
What is the next step in completing our dot plot? Putting tick marks on the
number line or horizontal axis and placing the category labels under the tick marks.
What do you think should be the next step? Placing the correct number of dots
above each tick mark to represent the data collected.
What does each dot represent? Each dot represents one student that has that
corresponding number of pockets.
8. Monitor to make sure students are keeping their dots vertically straight, the same size,
and evenly spaced apart. The dots need to be as congruent as possible.
9. Instruct students to look at the second dot plot on the handout: Class DataFrequency Table and Dot Plots.
Ask:
 What do you notice about this dot plot? It has a key where each dot will
represent 2 of something.
 What should be written beside the 2? Why? Students, because the dots
represents the students.
10. Instruct students to complete the second dot plot with a partner. Monitor and assess
students to check for understanding. When students are finished, model completion of
the dot plot.
Ask:
 Should the title for this dot plot be changed? Explain. No, because we are
still representing the same data we collected.
 What did you do when you had an odd number of students for a category?
How did you represent that on the dot plot? Drew half a dot, because half of 2
is 1.
11. Instruct students to complete the handout by answering the questions at the bottom.
12. Exit ticket: Pass out 1 index card to each student. Instruct students to write down one
similarity and one difference between a frequency table and a dot plot.
What’s the teacher doing?




5
Ask facilitating questions.
Model how to make a frequency
table using data collected.
Show YouTube video about dot
plots.
Model how to make a dot plot.
What are the students doing?
 Participate in class discussion.
 Assist in moving data from board to
frequency table.
 Complete frequency table.
 Watch dot plot video.
 Use the data to create dot plots.
 Work cooperatively with a partner.
Monitor and assess students to check
for understanding.

Unit 7 - Data Representation
4th Grade
Complete exit ticket.
Phase – Explore/Explain
Day 2
Activity:
Materials Needed
Day Two Riding Bikes Data Representation
Manila drawing paper/construction paper.
Review with students the exit tickets from yesterday. Students were to write down one
similarity and one difference between a frequency table and a dot plot. As a whole group,
create a Venn Diagram to organize the similarities and differences. Students should create
theirs on drawing/construction paper and glue into their math journals.
Students and teachers will create a frequency table, tally chart, and dot plot using the following
hand out. – Day Two Riding Bikes Data Representation.
1. Distribute handout: Day Two Riding Bikes Data Representation and Manila paper to
each student and display the same for the class to see. Explain to students that they
will be using the class data from this hand out to create a tally chart, frequency table,
and then, dot plots.
2. Students will work with a partner to create the tally chart and frequency table on the
handout. 10 minutes for students to complete this activity. (The teacher monitors the
charts produced by the class for accuracy. Teacher also assists struggling groups.)
3. Class returns to whole group. The teacher uses the students to help fill out the handout
that is projected for all students to see. The students check their handouts for accuracy
as the “teacher handout” is filled out.
4. Using the Manila drawing paper students and the teacher will create a dot plot to
represent the data in their frequency table. Have students turn their papers
horizontally.
6

What would be a good title for our dot plot? Why? Answers may vary. It should
be the same as frequency table, because they both will represent the same data.

What is the next step in completing our dot plot? Putting tick marks on the
number line or horizontal axis and placing the category labels under the tick marks.

What should the should be the labels for the tick marks on the horizontal
axis? We should use the number of miles James rode

Why should we use the number of miles that James Rode? Because that was
Unit 7 - Data Representation
4th Grade
the information that was gathered.

What do you think should be the next step? Placing the correct number of dots
above each tick mark to represent the data collected.
Allow students a few minutes to transfer the information provided in the frequency table on to
their dot plot.

What does each dot represent? Each dot represents how many times James
rode that number of miles.

How are dot plots and frequency tables alike and different? Both the dot plot
and the frequency table collect and show data. The frequency table is more of a
numerical representation while the dot plot is a pictorial representation.

What was the fewest miles that James rode? 4.5

How many times did he ride 4.5 miles? Three times

What was the greatest number of miles that James rode? 9.5

How many times did he ride 9.5 miles? Five times
 Which number of miles did James ride more frequently? 5.5
What’s the teacher doing?
What are the student’s doing?


7
Using guiding questions to
help partners create their own
tally charts, frequency tables,
and dot plots.
Checking student work for


6
& 9.5
Working with partners to record
information into tally charts, frequency
tables, and creating a dot plot.
Participating in class discussion lead by
the teacher.
Unit 7 - Data Representation
4th Grade

accuracy
Assisting struggling groups.
Phase - Evaluate
Day 3
Activity:
Students will work independently on the Day 3 -Performance Assessment handout.
Analyze the problem situation(s) described below. Organize and record your work for each of
the following tasks. Using precise mathematical language, justify and explain each solution
process.
1) The table below shows the distances that Ellen ran on each of the twenty days while
training for a track meet.
a) Represent Ellen’s data with a frequency table and a dot plot.
b) Describe how the frequency table and dot plot you created are alike and different.
c) Explain if a frequency table or dot plot would best answer each of the following questions:

How many more days did Ellen run between 3 and 4 miles than between 2 and 3 miles?

What was the total number of miles that Ellen ran on the days that she ran 3 miles or
greater?
After students complete the performance assessment students should transition to station
time. Stations should consist of previously taught skills that have not been mastered. These
8
Unit 7 - Data Representation
4th Grade
skills should be data driven.
Stations to include:
Frequency Station Activity Cards
Dot Plot Activity Cards
What’s the teacher doing?

What are the students doing?

The teacher is evaluating the
student’s knowledge of frequency
tables and dot plots.
Phase - Engage
Demonstrating their knowledge of frequency
tables and dot plots.
Day 4
Activity: Stem and Leaf with whole numbers
Materials needed:
Construction paper or white cardstock
White board
Markers
Sticky Notes
Manila Drawing Paper
Explain to students that we will gather information and create a stem and leaf plot to represent
data.
Ask Students:
Can you name something that has both a stem and a leaf? Flowers and Plants
How many stems does a flower normally have? - answers may vary, but lead the kids to 1
stem
How many leaves does a flower normally have? – many or more than one
Pass out a sticky note to each student and have them write down their favorite WHOLE
number between 30-70.
By gathering this information, what am I conducting? A survey
Collect the sticky notes and read the results to the class.
How should this information be classified? 30s 40s 50s 60s 70s
Students fold their manila drawing paper in half (remind the students that when we fold,
9
Unit 7 - Data Representation
4th Grade
cut, or separate items in half, we are dividing by 2)
Instruct students to use the top half of their paper to separate the numbers from the class into
categories.
Have a student come to the board and sort the sticky note numbers into categories, seated
students will do this on their manila paper.
Numbers may vary
35
32
33
33
42
48
48
48
50
57
65
61
61
60
70
A stem and left plot contain both a vertical and horizontal axis.
Explain to students that the “STEM” is the place value that is common. For the numbers
grouped by 30s 3 is the common stem.
Add 3 to the stem column.
One by one break down each number in the 30s categories and place the appropriate
numbers in the leaf column. Have students cross out the numbers when they move the data
from groups to the stem and leaf plot. (This is to ensure that students get all of their data onto
their stem and leaf plot.)
10
Unit 7 - Data Representation
4th Grade
For the numbers grouped by 40s
Ask
What is the common stem for the numbers group in to the 40s category? 4 is the
common stem.
Add 4 to the stem column.
One by one break down each number in the 40s categories and place the appropriate
numbers in the leaf column. Have students cross out the numbers when they move the data
from groups to the stem and leaf plot. (This is to ensure that students get all of their data onto
their stem and leaf plot.)
For the numbers grouped by 50s
Ask
What is the common stem for the numbers group in to the 50s category? 5 is the
common stem.
Add 5 to the stem column.
What are the number/numbers that would belong in the leaf column? zero
One by one break down each number in the 50s categories and place the appropriate
11
Unit 7 - Data Representation
4th Grade
numbers in the leaf column. Have students cross out the numbers when they move the data
from groups to the stem and leaf plot. (This is to ensure that students get all of their data onto
their stem and leaf plot.)
For the numbers grouped by 60s
Ask
What is the common stem for the numbers group in to the 60s category? 6 is the
common stem.
Add 6 to the stem column.
What are the number/numbers that would belong in the leaf column? 0 1 1 5
Why does two 1s belong in the leaf column? Because there are two 61s
One by one break down each number in the 60s categories and place the appropriate
numbers in the leaf column. Have students cross out the numbers when they move the data
from groups to the stem and leaf plot. (This is to ensure that students get all of their data onto
their stem and leaf plot.)
For the numbers grouped by 70s
12
Unit 7 - Data Representation
4th Grade
Ask
What is the common stem for the numbers group in to the 70s category? 7 is the
common stem.
Add 7 to the stem column.
What are the number/numbers that would belong in the leaf column? 0
One by one break down each number in the 70s categories and place the appropriate
numbers in the leaf column. Have students cross out the numbers when they move the data
from groups to the stem and leaf plot. (This is to ensure that students get all of their data onto
their stem and leaf plot)
After the Stem and Leaf plot is created, ask the following questions.
What is the value of this number? That number has a value of 48. (repeat this process with
several numbers from the plot) This is to ensure that students are reading the plot correctly.
Stem
13
Leaf
3
2
3
3
5
4
2
8
8
8
5
0
7
6
0
1
1
5
7
0
Unit 7 - Data Representation
4th Grade
Math journal: Create a foldable to define Stem and leaf. Students will create this foldable
using a piece of construction paper or white cardstock for durability and glue inside Math
Journal.
What’s the teacher doing?

The teacher is facilitating
discussion on stem and leaf
plots.

Showing students how to
organize data into the new
representation

Creating a Stem and Leaf Plot
Phase - elaborate
14
What are the students doing?

Participating in discussion lead by the
teacher.

Creating a Stem and Leaf Plot
Day 5
Unit 7 - Data Representation
4th Grade
Activity: Stem and leaf with fractions
Handouts: Mr. Jackson’s Pizza Palace (Stem and Leaf with Fractions)
Refresh from yesterday and discuss how we made Stem and leaf with whole numbers.
What were the different components of a stem and leaf plot? Whole numbers were
divided by place value. The common number equaled the steam and the uncommon numbers
were the leaves.
What did the stem represent? The common numbers according to place value. Yesterday’s
example: the stems were the 10s place
What did the leaf represent? The uncommon numbers. Yesterday’s example: The leaves
were the ONEs place.
Ask students:
Can we use a Stem and leaf plot with fractions? Answers may vary.
What would that look like? Answers may vary. Whole numbers would be the stems and the
proper fractions would be the leaves.
Propose the following problem and data to the students.

Mr. Jackson was tracking how many pizzas were being eaten at Pizza Palace each day
over the course of a month. The table below shows the data Mr. Jackson collected in
30 days:
5½
4¼
3¼
6¼
4¼
2½
6¼
5½
2½
5½
7½
4¼
3½
8½
3½
3½
7¾
3¼
7½
7½
5¼
8½
8¼
5¼
3½
8½
6½
7¾
5¼
8½
Ask students:
By looking at the data Mr. Jackson collected, which numbers would be the Stems?
Students may say “2 through 8” or “the whole number”.
If the whole numbers are the Stems, then what would the fractions be? Students will say
“leaves”.
Handout- Mr. Jackson’s Pizza Palace (Stem and Leaf with Fractions)
Do handout together with students leading the process of stem and leaf with fractions.
Stem
2
3
15
Leaves
½ ½
¼ ¼ ½ ½ ½ ½
Unit 7 - Data Representation
4th Grade
4
¼ ¼ ¼
5
¼ ¼ ¼ ½ ½ ½
6
¼ ¼ ½
7
¾ ¾ ½ ½ ½
8
¼ ½ ½ ½ ½
Homework Handout- Mrs. Booker’s Travels (Stem and Leaf with Fractions Homework)
What’s the teacher doing?
What are the students doing?
Monitoring students, asking questions,
checking for understanding.
Students are engaged in discussion of fractional
parts in a stem and leaf plot. Students are actively
working on handout to practice with fractions.
Phase: explore/elaborate
Day 6
Activity – Stem and Leaf with Decimals.
Materials: chart paper, markers, stopwatches
Ask students: “When making a stem and leaf plot with decimals, what would the whole
number be?”
Students may say “the number before the decimal…the number in the ones place”
Teacher will give each table (this works if you have tables into groups) a piece of chart paper.
 If you do not have tables separated into groups, then split your students into groups of 4
or 5 in each group.
Handout: Jumping Jacks
Students will be filling out a frequency table to record how long it takes to do 5 jumping jacks,
twenty different times. Explain to students that each person in the group will be doing jumping
16
Unit 7 - Data Representation
4th Grade
jacks. (example: if there are 5 people in a group, they will each do 5 jumping jacks, 4 different
times)
After students have recorded their data on the frequency table, they will use the chart paper to
create their stem and leaf plot as a group.
Example of chart below:
*NOTE: Student chart should have twenty recordings.
What’s the teacher doing?
What are the students doing?
Monitoring student collaboration and
data collection. Asking higher level
thinking questions.
Working with peers to gather data, record data and
create a stem and leaf. Using mathematical terms
such as frequency table, decimal, place value,
hundredths, tenths, stem and leaf.
Ex: How would you recognize the time
on the stopwatch?
How would you identify where to place
the whole numbers on the stem and
leaf?
Phase - Evaluate
17
Day 7
Unit 7 - Data Representation
4th Grade
Activity:
Students will work independently on the Day 7 -Performance Assessment handout
Analyze the problem situation(s) described below. Organize and record your work for each of
the following tasks. Using precise mathematical language, justify and explain each solution
process.
The table below shows the distances that Ellen ran on each of the twenty days while training
for a track meet
Create a stem-and-leaf plot using Ellen’s data.
Create a question that can be answered using the data represented in the stem-and-leaf plot
and has an answer of “15 days”.
Describe how the stem-and-leaf plot would change if Ellen trained for five additional days and
ran 3 miles or greater each day.
After students complete the performance assessment students should transition to station
time. Stations should consist of previously taught skills that have not been mastered. These
skills should be data driven.
Stations to include:
Frequency Station Activity Cards
Dot Plot Activity Cards
Stem and Leal Problem Solving Cards
Snow Cone Steam and Leaf
What’s the teacher doing?
What are the students doing?
The teacher is evaluating students
understanding of stem and leaf plots.
The student is demonstrating knowledge of stem
and leaf plots.
18
Unit 7 - Data Representation
4th Grade
19