Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Grade 4
Mathematics Curriculum Unit Guide
FCPS Curriculum Indicators in these Investigations:
10.10a
30.07a
40.05
40.10a
40.10b
40.10c
40.15a
40.15c
40.16a
40.16b
50.10
60.05d
60.23a
60.23b
70.06
70.07
70.08
70.10
70.11
70.12
70.13
70.14
70.15
70.16
FCPS Curriculum Vocabulary
Represent quantities using numeric expressions with operational symbols (+, -, x, ) and whole
numbers (0 – 100) (i.e. decompose) (1.B.1.a)*
Select and use appropriate standard units and tools to estimate and determine length (to the nearest
1/4 in, ft, yd, mm, cm, m) (3.A.1.a, 3.B.1.a)*
Collect data from a math investigation to solve a problem (4.A.1.a)
Collect, organize and display data using line plots and frequency tables (4.A.1.b)*
Explore/invent displaying data using line graphs (x-axis represents time intervals), stem and leaf plots,
and double bar graphs
Use data displays to represent and communicate information
Read and interpret information taken from a display of data using line plots and line graphs (x-axis
represents time intervals) (4.B.1.a, 4.B.1.b)*
Use information taken from a data display to solve problems and make predictions
Explore, invent (using models), and determine range (4.B.2.a)*
Explore, invent (using models), and determine mode and median (measures of central tendency)
(4.B.2.a)*
Use a fraction to express the probability of a single event with equally likely outcomes (no more
than 6 outcomes) (e.g. a spinner with 4 equal sections labeled A, A, B, C: A has a probability of 2/4
or 1/2) (5.B.1.a)*
Compose/decompose whole numbers in a variety of ways
Add whole numbers (up to 3 addends of no more than 4-digits) using a variety of strategies
(6.C.1.a)*
Subtract whole numbers of no more than 4-digits using a variety of strategies (6.C.1.b)*
Select and apply problem solving strategies – Make a model/Act it out, Make a picture or diagram,
Look for patterns, Guess and check, Write an equation, Make an organized list, Make a table
(7.A.1.d, 7.A.1.e)*
Select/use appropriate tools and technology to solve problems
Identify alternate ways to find a solution (7.A.1.f)*
Apply what was learned to a new problem (7.A.1.h)*
Discuss, read, listen, observe and ask questions to obtain mathematical information (7.C.1.g)*
Represent, explain and write about mathematical ideas and solutions using objects, pictures, data
displays, mathematical language and symbols (7.C.1.a, 7.C.1.d, 7.C.1.e)*
Describe a situation mathematically by providing mathematical ideas and evidence in oral and
written form (7.C.1.b, 7.C.1.c)*
Give or use feedback to revise mathematical thinking (7.C.1.h)*
Recognize, evaluate, and explain reasonableness of answers in everyday situations
Analyze statements and provide examples which support or refute them (7.B.1.c)*
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math





Grade Level
Line plot
Median
Mode
Single event
Range
Prior/Subsequent Level
 Bar graph
 Data
 Probability
Additional Investigations Vocabulary





Conclusion
Frequency table
Landmark data
Numerical data
Outlier




Predictions
Representations
Survey
Value
Pacing Guide
1
2008-2009
Unit 2 –
70.17
Describing the Shape of the Data
Data Analysis and Probability
Grade 4
Mathematics Curriculum Unit Guide
Use proof or evidence (e.g. supporting data) to explain why a chosen method used and a solution are
mathematically correct (inductive/deductive reasoning) (7.B.1.a, 7.B.1.d, 7.C.1.f)*
Before beginning this unit, read:
1.
2.
3.
4.
Mathematics in This Unit
Ten-Minute Math in This Unit
Differentiation in This Unit
Teacher Notes
pp. 10-13
p. 16
p. 18
pp. 121-126
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
2
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Grade 4
Mathematics Curriculum Unit Guide
Teacher Notes: Addressing FCPS Essential Math Curriculum
Teacher Notes: Unit Reflections
In this unit:





Students focus on the overall shape of the data and then highlight the most important features of the data such as range, median, and where there is a modal
clump (see Teacher Notes p. 122 for more clarification on mode). The text series does not ask students to identify the mode, but instead asks them to identify
areas where there is a large amount of data clumped together (modal clump). For our purposes, it is important that students identify mode because it is in the
FCPS curriculum and it is MSA assessed. MA.400.40.16b Explore, invent (using models), and determine mode and median (measures of central tendency)
(4.B.2.a)*
Mode should be introduced in Investigation 1 Session 1.2 when students describe the class height data. Mode should also be determined in subsequent sessions
when students are describing data.
The time period for the End-of-Unit Assessment is 60 minutes, but students may not need the full 60 minutes to complete the assessment. After collecting the
assessment, the remaining time should be used to have a class discussion about what a good response to the BCR in the assessment would look like.
Frequency table was added to 40.10a. A frequency table shows how often each item, number, or range of numbers occurs in a set of data.
Example:
Clarification of Probability Indicator 400.50.10 Use a fraction to express the probability of a single event with equally likely outcomes (no more than 6
outcomes) (e.g. a spinner with 4 equal sections labeled A, A, B, C: A has a probability of 2/4 or 1/2) (5.B.1.a) A spinner must be divided into equal
sections. This allows each section to have an “equally likely outcome” of being landed on. However, labeling of the sections does not have to be equal.
Objects in containers must be the same shape, but the colors/patterns can be different.
Example:
Example:
not equally divided
equally divided
not equally likely
equally likely
In these 10-Minute Maths:
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
3
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Investigation 1: Landmarks in the Data
Indicator (s)
Assessment
Represent quantities using
At the end of this
investigation, students should
numeric expressions with
be able to:
operational symbols (+, -, x, )
 collect, organize, and
and whole numbers (0 – 100)
display data by creating
(i.e. decompose) (1.B.1.a)*
30.07a Select and use appropriate
line plots (Unit 2: M7)
[40.10a]
standard units and tools to
estimate and determine length
 read and describe data
(to the nearest 1/4 in, ft, yd, mm,
with a line plot (Unit 2:
cm, m) (3.A.1.a, 3.B.1.a)*
M7 and M8) [40.15a]
40.05 Collect data from a math
 describe data using range,
investigation to solve a problem
median, and mode (Unit 2:
(4.A.1.a)
M7 and M8) [40.16a,
40.10a Collect, organize and display
40.16b]
data using line plots and
frequency tables (4.A.1.b)*
40.10c Use data displays to represent and
communicate information
40.15a Read and interpret information
taken from a display of data
using line plots and line graphs
(x-axis represents time intervals)
(4.B.1.a, 4.B.1.b)*
40.15c Use information taken from a data
display to solve problems and
make predictions
40.16a Explore, invent (using models),
and determine range (4.B.2.a)*
40.16b Explore, invent (using models),
and determine mode and median
(measures of central tendency)
(4.B.2.a)*
60.05d Compose/decompose whole
numbers in a variety of ways
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
10.10a
Grade 4
Mathematics Curriculum Unit Guide
Students record, organize, and represent data, including measuring the heights of first and fourth
graders. They learn to use the median as one way to describe and compare data sets.
Session # & Name
1.1 How Many
Raisins in a
Box?


1.2 How Tall Are
Fourth
Graders?


1.3 How Tall Are
First Graders?

1.4 Comparing the
Heights of
Fourth and
First Graders
1.5 Assessment:
Comparing
Number of
Cavities




Student Objective
Collect, organize, display, and
interpret data in order to describe
the data.
Create a line plot in order to better
represent the data
Collect, organize, display, and
interpret data using a line plot in
order to solve problems
Determine range and mode to
understand data
Collect, organize, and display data
using data displays in order to
represent and communicate
information
10-Minute Math
10.10a Represent quantities
using numeric expressions
with operational symbols
(+, -, x, ) and whole
numbers (0 – 100) (i.e.
decompose) (1.B.1.a)*
60.05d Compose/decompose whole
numbers in a variety of
Today’s
ways
Number: Broken 60.23a Add whole numbers (up
Calculator
to 3 addends of no more
than 4-digits) using a
variety of strategies
(6.C.1.a)*
60.23b Subtract whole numbers
of no more than 4-digits
using a variety of
strategies (6.C.1.b)*
Evaluate data displays to see
which one is the easiest to read
Analyze data to answer questions
Find the median data to describe
data
Show what you know about
making line plots and analyzing
data
4
DAYS 1 - 5
Math Fact Connection
40.05
Quick Survey
Collect data from a math
investigation to solve a
problem (4.A.1.a)
40.10c Use data displays to
represent and communicate
information
40.15c Use information taken from
a data display to solve
problems and make
predictions
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Grade 4
Mathematics Curriculum Unit Guide
Students record, organize, and represent data, including measuring the heights of first and fourth
graders. They learn to use the median as one way to describe and compare data sets.
Investigation 1: Landmarks in the Data
Indicator (s)
60.23a Add whole numbers (up to 3
addends of no more than 4digits) using a variety of
strategies (6.C.1.a)*
60.23b Subtract whole numbers of no
more than 4-digits using a
variety of strategies (6.C.1.b)*
70.06 Select and apply problem solving
strategies – Make a model/Act it
out, Make a picture or diagram,
Look for patterns, Guess and
check, Write an equation, Make
an organized list, Make a table
(7.A.1.d, 7.A.1.e)*
70.07 Select/use appropriate tools and
technology to solve problems
70.08 Identify alternate ways to find a
solution (7.A.1.f)*
70.10 Apply what was learned to a new
problem (7.A.1.h)*
70.11 Discuss, read, listen, observe and
ask questions to obtain
mathematical information
(7.C.1.g)*
70.12 Represent, explain and write
about mathematical ideas and
solutions using objects, pictures,
data displays, mathematical
language and symbols (7.C.1.a,
7.C.1.d, 7.C.1.e)*
Assessment
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
Session # & Name
Student Objective
5
10-Minute Math
DAYS 1 - 5
Math Fact Connection
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Grade 4
Mathematics Curriculum Unit Guide
Students record, organize, and represent data, including measuring the heights of first and fourth
graders. They learn to use the median as one way to describe and compare data sets.
Investigation 1: Landmarks in the Data
70.13
70.14
70.15
70.16
70.17
Indicator (s)
Describe a situation
mathematically by providing
mathematical ideas and evidence
in oral and written form
(7.C.1.b, 7.C.1.c)*
Give or use feedback to revise
mathematical thinking (7.C.1.h)*
Recognize, evaluate, and explain
reasonableness of answers in
everyday situations
Analyze statements and provide
examples which support or
refute them (7.B.1.c)*
Use proof or evidence (e.g.
supporting data) to explain why
a chosen method used and a
solution are mathematically
correct (inductive/deductive
reasoning) (7.B.1.a, 7.B.1.d,
7.C.1.f)*
Assessment
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
Session # & Name
Student Objective
6
10-Minute Math
DAYS 1 - 5
Math Fact Connection
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Investigation 2: Using Data to Compare
40.05
40.10a
40.10b
40.10c
40.15a
40.15c
Indicator (s)
Collect data from a math
investigation to solve a problem
(4.A.1.a)
Collect, organize and display
data using line plots and
frequency tables (4.A.1.b)*
Explore/invent displaying data
using line graphs (x-axis
represents time intervals), stem
and leaf plots, and double bar
graphs
Use data displays to represent and
communicate information
Read and interpret information
taken from a display of data
using line plots and line graphs
(x-axis represents time intervals)
(4.B.1.a, 4.B.1.b)*
Use information taken from a data
display to solve problems and
make predictions
Assessment
At the end of this
investigation, students should
be able to:
 develop a survey question
(Unit 2: M10)
 organize and display data
by creating a line plot
(Unit 2:M10) [40.10a]
 collect and accurately
organize data (Unit 2:
M10) [40.05]
 describe data using
range, mode, and median
[40.16a, 40.16b]]
 draw conclusions based
on the data display and
landmarks [40.15a]
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
Grade 4
Mathematics Curriculum Unit Guide
Students choose their own survey questions for data collection. They represent and analyze the data.
They also draw conclusions based on evidence in different sets of data.
Session # & Name
2.1 What Do We
Want to Find
Out?
2.2 Assessment:
Collecting and
Comparing
Data



Student Objective
Develop and revise a survey
question in order to compare two
groups
Collect, organize, and display data
using a data display in order to
compare groups and solve
problems
Show what you know about doing
a survey, collecting, and recording
data accurately
7
10-Minute Math
Today’s
Number: Broken
Calculator
DAYS 6 – 12
Math Fact Connection
10.10a Represent quantities
using numeric expressions
with operational symbols
(+, -, x, ) and whole
numbers (0 – 100) (i.e.
decompose) (1.B.1.a)*
60.05d Compose/decompose whole
numbers in a variety of
ways
60.23a Add whole numbers (up
to 3 addends of no more
than 4-digits) using a
variety of strategies
(6.C.1.a)*
60.23b Subtract whole numbers
of no more than 4-digits
using a variety of
strategies (6.C.1.b)*
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Grade 4
Mathematics Curriculum Unit Guide
Students choose their own survey questions for data collection. They represent and analyze the data.
They also draw conclusions based on evidence in different sets of data.
Investigation 2: Using Data to Compare
Indicator (s)
Explore, invent (using models),
and determine range (4.B.2.a)*
40.16b Explore, invent (using models),
and determine mode and median
(measures of central tendency)
(4.B.2.a)*
70.06 Select and apply problem
solving strategies – Make a
model/Act it out, Make a picture
or diagram, Look for patterns,
Guess and check, Write an
equation, Make an organized
list, Make a table (7.A.1.d,
7.A.1.e)*
70.07 Select/use appropriate tools and
technology to solve problems
70.08 Identify alternate ways to find a
solution (7.A.1.f)*
70.10 Apply what was learned to a
new problem (7.A.1.h)*
70.11 Discuss, read, listen, observe and
ask questions to obtain
mathematical information
(7.C.1.g)*
70.12 Represent, explain and write
about mathematical ideas and
solutions using objects, pictures,
data displays, mathematical
language and symbols (7.C.1.a,
7.C.1.d, 7.C.1.e)*
Assessment
40.16a
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
Session # & Name
2.3 Representing
Survey Data


Student Objective
Represent data to compare groups
and solve problems
Show what you know about
representing data accurately
Quick Surveys
2.4 What Did You
Learn from
Your Survey?

2.5 Mystery Data


2.6 Comparing
WNBA
Players’
Points Per
Game

Analyze data in order to make
conclusions
Interpret data using line plots in
order to solve problems
Use range, median, and number of
data pieces to create a line plot
Organize, display, and interpret
data using line plots in order to
answer questions
8
Today’s
Number: Broken
Calculator
10-Minute Math
40.05 Collect data from a math
investigation to solve a
problem (4.A.1.a)
40.10c Use data displays to
represent and communicate
information
40.15c Use information taken
from a data display to
solve problems and make
predictions
DAYS 6 – 12
Math Fact Connection
10.10a Represent quantities
using numeric expressions
with operational symbols
(+, -, x, ) and whole
numbers (0 – 100) (i.e.
decompose) (1.B.1.a)*
60.05d Compose/decompose whole
numbers in a variety of
ways
60.23a Add whole numbers (up
to 3 addends of no more
than 4-digits) using a
variety of strategies
(6.C.1.a)*
60.23b Subtract whole numbers
of no more than 4-digits
using a variety of
strategies (6.C.1.b)*
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Grade 4
Mathematics Curriculum Unit Guide
Students choose their own survey questions for data collection. They represent and analyze the data.
They also draw conclusions based on evidence in different sets of data.
Investigation 2: Using Data to Compare
70.13
70.14
70.15
70.16
70.17
Indicator (s)
Describe a situation
mathematically by providing
mathematical ideas and evidence
in oral and written form
(7.C.1.b, 7.C.1.c)*
Give or use feedback to revise
mathematical thinking
(7.C.1.h)*
Recognize, evaluate, and explain
reasonableness of answers in
everyday situations
Analyze statements and provide
examples which support or
refute them (7.B.1.c)*
Use proof or evidence (e.g.
supporting data) to explain why
a chosen method used and a
solution are mathematically
correct (inductive/deductive
reasoning) (7.B.1.a, 7.B.1.d,
7.C.1.f)*
Assessment
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
Session # & Name
2.7 Is This a Good
Game?

Student Objective
Interpret data using line plots in
order to answer questions
10-Minute Math
DAYS 6 – 12
Math Fact Connection
40.05
Quick Surveys
9
Collect data from a math
investigation to solve a
problem (4.A.1.a)
40.10c Use data displays to
represent and communicate
information
40.15c Use information taken from
a data display to solve
problems and make
predictions
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Investigation 3: Finding and Comparing Probabilities
40.05
40.10a
40.15c
50.10
70.06
70.07
70.08
70.10
Indicator (s)
Collect data from a math
investigation to solve a problem
(4.A.1.a)
Collect, organize and display
data using line plots and
frequency tables (4.A.1.b)*
Use information taken from a data
display to solve problems and
make predictions
Use a fraction to express the
probability of a single event with
equally likely outcomes (no more
than 6 outcomes) (e.g. a spinner
with 4 equal sections labeled A,
A, B, C: A has a probability of
2/4 or 1/2) (5.B.1.a)*
Select and apply problem
solving strategies – Make a
model/Act it out, Make a picture
or diagram, Look for patterns,
Guess and check, Write an
equation, Make an organized
list, Make a table (7.A.1.d,
7.A.1.e)*
Select/use appropriate tools and
technology to solve problems
Identify alternate ways to find a
solution (7.A.1.f)*
Apply what was learned to a
new problem (7.A.1.h)*
Assessment
At the end of this
investigation, students should
be able to:
 collect, organize, and
display data using line
plots [40.10a]
 use fractions to express the
probability of an event
[50.10]
 compare the probabilities
of an event
REQUIRED
ASSESSMENT: End of
Unit Assessment (EOUA 2)
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
Grade 4
Mathematics Curriculum Unit Guide
Students learn to describe probability using words such as impossible and certain, and the numbers 0
to 1. They conduct probability experiments and describe and compare results.
Session # & Name
SL 1 Probability
Experiments


Student Objective
Conduct probability experiments
to compare the predicted
probability of an event with the
actual results
Collect, organize, and display data
using line plots in order to answer
a question
10-Minute Math
40.05
40.10a
3.4 Comparing
Probability
Experiments


Conduct probability experiments
to compare the predicted
probability of an event with the
actual results
Collect, organize, display, and
interpret data using line plots in
order to answer questions
10
Quick Survey
40.15c
40.15c
DAYS 13-17
Math Fact Connection
Collect data from a
math investigation to
solve a problem
(4.A.1.a)
Collect, organize and
display data using line
plots and frequency
tables (4.A.1.b)*
Use information taken
from a data display to
solve problems and make
predictions
Use information taken
from a data display to
solve problems and make
predictions
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Grade 4
Mathematics Curriculum Unit Guide
Investigation 3: Finding and Comparing Probabilities
70.11
70.12
70.13
70.14
70.15
70.16
70.17
Indicator (s)
Discuss, read, listen, observe and
ask questions to obtain
mathematical information
(7.C.1.g)*
Represent, explain and write
about mathematical ideas and
solutions using objects, pictures,
data displays, mathematical
language and symbols (7.C.1.a,
7.C.1.d, 7.C.1.e)*
Describe a situation
mathematically by providing
mathematical ideas and evidence
in oral and written form
(7.C.1.b, 7.C.1.c)*
Give or use feedback to revise
mathematical thinking
(7.C.1.h)*
Recognize, evaluate, and explain
reasonableness of answers in
everyday situations
Analyze statements and provide
examples which support or
refute them (7.B.1.c)*
Use proof or evidence (e.g.
supporting data) to explain why
a chosen method used and a
solution are mathematically
correct (inductive/deductive
reasoning) (7.B.1.a, 7.B.1.d,
7.C.1.f)*
Assessment
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
Students learn to describe probability using words such as impossible and certain, and the numbers 0
to 1. They conduct probability experiments and describe and compare results.
Session # & Name
SL 2a Fractional
Probability


Student Objective
Collect, organize, and display data
in a frequency table in order to
answer a question
Use fractions to express the
probability of an event
10-Minute Math
30.24a
S 1a: Elapsed
Time
SL 2b
Fractional
Probability
continued


Collect, organize, and display data
in a frequency table in order to
answer a question
Use fractions to express the
probability of an event
30.24a
S 1b: Elapsed
Time
11
30.24b
30.24b
DAYS 13-17
Math Fact Connection
Estimate and find start
time, elapsed, and end
time to the hour and half
hour (3.C.1.c)*
Compose/decompose time
using hours and minutes
(3.C.2.b)
Estimate and find start
time, elapsed, and end
time to the hour and half
hour (3.C.1.c)*
Compose/decompose time
using hours and minutes
(3.C.2.b)
2008-2009
Unit 2 –
Describing the Shape of the Data
Data Analysis and Probability
Grade 4
Mathematics Curriculum Unit Guide
Investigation 3: Finding and Comparing Probabilities
Indicator (s)
Assessment
Students learn to describe probability using words such as impossible and certain, and the numbers 0
to 1. They conduct probability experiments and describe and compare results.
Session # & Name
3.5 End-of-Unit
Assessment
(EOUA 2)

Student Objective
Show what you know about
making line plots, analyzing data,
and probability
10-Minute Math
Today’s
Number: Broken
Calculator
Unit #: M# - Investigations Master
FCPS Unit #: M# - Master modified for use in FCPS
SL # or S # - Supplemental lesson or supplemental 10-minute Math
12
DAYS 13-17
Math Fact Connection
10.10a Represent quantities
using numeric expressions
with operational symbols
(+, -, x, ) and whole
numbers (0 – 100) (i.e.
decompose) (1.B.1.a)*
60.05d Compose/decompose
whole numbers in a variety
of ways
60.23a Add whole numbers (up
to 3 addends of no more
than 4-digits) using a
variety of strategies
(6.C.1.a)*
60.23b Subtract whole numbers
of no more than 4-digits
using a variety of
strategies (6.C.1.b)*
2008-2009