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Math Standards Document
Statistics
Final Draft
Hawaii School Districts
Prepared by Marzano and Associates
1
Statistics Summary
Strand
Data Analysis, Statistics,
and Probability
Data Analysis, Statistics,
and Probability
Data Analysis, Statistics,
and Probability
Total
Standard
Topic
11
Data Collection and Display
Number of
Elements
6
12
Data Interpretation
4
13
Predictions and Inferences
2
12
2
Topic: Data Collection and Display (1)
Strand: Data Analysis, Statistics, and Probability
Standard 11: FLUENCY WITH DATA: Pose questions and collect, organize, and
represent data to answer those questions.
Statistics
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 implements an experiment and lists all variables, controls, hypothesis, etc.
Level 3.5
Level 3.0
While involved in tasks regarding data collection and display the student will:
 (MA.S.11.1) develop a hypothesis for an investigation or experiment (e.g.,
develop and defend a hypothesis for an investigation)
 (MA.S.11.2) recognize the variables and controls in an experiment or
expectation (e.g., identify the variable in an investigation or experiment, set a
control, and explain the need for a control)
 (MA.S.11.3) select appropriate display for a data set (frequency table,
histogram, line graph, bar graph, stem-and-leaf plot, box-and-whisker plot,
scatter plot) (e.g., choose an appropriate display for a data set and explain
why it is an appropriate choice)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o hypothesis, variables, control, data
 performs basic processes such as:
o recognizing or recalling examples of hypotheses for given
experiments
o recognizing or recalling accurate statements about the fact that
experiments have variables and controls
o recognizing or recalling similarities and differences between
displays for data sets
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
3
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to implement an experiment and list all variables, controls,
hypothesis, etc. involved.
Level 3.0
 Ask students to develop a hypothesis for an investigation or experiment.
 Ask students to recognize the variables and controls in an experiment or
expectation.
 Ask students to select an appropriate display for a data set (frequency table,
histogram, line graph, bar graph, stem-and-leaf plot, box-and-whisker plot, scatter
plot) and explain why that is the most appropriate data set to use.
Level 2.0
 Ask students to recall the following terminology: hypothesis, variable, control, and
data.
 Ask students to recognize or recall examples of hypotheses for given experiments.
 Ask students to recognize or recall accurate statements about the fact that experiments
have variables and controls.
 Ask students to recognize or recall similarities and differences between displays for
data sets.
4
Topic: Data Collection and Display (2)
Strand: Data Analysis, Statistics, and Probability
Standard 11: FLUENCY WITH DATA: Pose questions and collect, organize, and
represent data to answer those questions.
Statistics
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 using an experiment, makes two graphs of the same piece of information, one
misleading and one fair, and talks about how the same graphs can be used to
mislead the general public
Level 3.5
Level 3.0
While involved in tasks regarding data collection and display the student will:
 (MA.S.11.4) recognize features of representations of data that can produce
misleading interpretations (e.g., explain how a data display was made to
produce misleading interpretations)
 (MA.S.11.5) recognize sampling, randomness, bias, and sampling size in data
collection and interpretation (e.g., consider possible bias and sampling errors
when interpreting data and propose options to correct the errors)
 (MA.S.11.6) describe the purpose and function of a variety of data collection
methods (census, sample surveys, experiment, observation) (e.g., explain the
differences between data collection methods)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o random, bias, skewed data, sampling
 performs basic processes such as:
o recognizing or recalling accurate statements about the fact that
data can be skewed
o recognizing or recalling examples of data collection methods
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
5
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to use an experiment to make two graphs of the same piece of
information, one misleading and one fair, and have the student talk about how the
same graphs can be used to mislead the general public.
Level 3.0
 Ask students to recognize features of representations of data that can produce
misleading interpretations.
 Ask students to recognize sampling, randomness, bias, and sampling size in data
collection and interpretation (e.g., consider possible bias and sampling errors when
interpreting data and propose options to correct the errors).
Level 2.0
 Ask students to define the following terms: random, bias, skewed data, sampling.
 Ask students to recognize or recall accurate statements about the fact that data can be
skewed.
 Ask students to recognize or recall examples of data collection methods.
6
Topic: Data Interpretation
Strand: Data Analysis, Statistics, and Probability
Standard 12: STATISTICS: Interpret data using methods of exploratory data
analysis.
Statistics
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 using baseball statistics, predicts how a certain player will perform by using
best fit curves (opportunity to talk about sabermetrics)
Level 3.5
Level 3.0
While engaged in tasks involving data interpretation the student will:
 (MA.S.12.1) use measures of central tendency and spread to interpret data
(e.g., interpret a data set based on the mean and standard deviation)
 (MA.S.12.2) interpret data based on the correlation coefficient of two
variables (e.g., identify a data set that has a positive correlation and makes an
interpretation based on that trend)
 (MA.S.12.3) describe the effect of sample size and transformation on the
shape, center, and spread of data (e.g., explain the effect on shape, center, and
spread of data, if the unit of measure is changed)
 (MA.S.12.4) use the line or curve of best fit to interpret data (e.g., draw the
line (or curve) of best fit on a graph and use it to describe any trends that
exist)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o sample size, central tendency
 performs basic processes such as:
o recognizing or recalling examples of measure of central tendency
o recognizing or recalling examples of the correlation coefficient of
two variables
o recognizing or recalling accurate statements about the fact that
sample size and transformation can affect shape, center, and
spread of data
o recognizing or recalling examples of the line or curve of best fit
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
7
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Ask students to use baseball statistics to try to predict how a certain player will
perform by using best fit curves (opportunity to talk about sabermetrics).
Level 3.0
 Ask students to use measures of central tendency and spread to interpret data
(e.g., interpret a data set based on the mean and standard deviation).
 Ask students to interpret data based on the correlation coefficient of two variables
(e.g., identify a data set that has a positive correlation and makes an interpretation
based on that trend).
 Ask students to use the line or curve of best fit to interpret data (e.g., draw the line
(or curve) of best fit on a graph and uses it to describe any trends that exist).
Level 2.0
 Ask students to define the following terms: random, bias, skewed data.
 Ask students to recognize or recall examples of measure of central tendency.
 Ask students to recognize or recall examples of the correlation coefficient of two
variables.
 Ask students to recognize or recall accurate statements about the fact that sample size
and transformation can affect shape, center, and spread of data.
 Ask students to recognize or recall examples of the line or curve of best fit.
8
Topic: Predictions and Inferences
Strand: Data Analysis, Statistics, and Probability
Standard 13: DATA ANALYSIS: Develop and evaluate inferences, predictions, and
arguments that are based on data.
Statistics
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught such as:
 given a random set of data, interprets the results and explains the results
statistically to the class
Level 3.5
Level 3.0
While engaged in tasks involving predictions and inferences the student will:
 (MA.S.13.1) describe the ways data can be represented (linear, quadratic,
exponential, sinusoidal) (e.g., identify data that is linear (sales tax), quadratic,
(height of a bouncing ball), exponential (growth of certificate of deposit), or
sinusoidal (number of daylight hours throughout the year)
 (MA.S.13.2) use interpolation and extrapolation to make predictions and
inferences about data (e.g., analyze the trend in a data set and make
interpolations and extrapolations based on the trend)
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o linear, quadratic, exponential, sinusoidal, interpolation,
extrapolation
 performs basic processes such as:
o recognizing or recalling examples of the ways data can be
represented (linear, quadratic, exponential and sinusoidal)
o recognizing or recalling accurate statements about using
interpolation and extrapolation to make predictions an inferences
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
9
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0
 Given a random set of data, ask students to interpret the results and explain the
results statistically to the class.
Level 3.0
 Ask students to recognize that some data can be represented algebraically (linear,
quadratic, exponential, sinusoidal) (e.g., identify data that is linear (sales tax),
quadratic, (height of a bouncing ball), exponential (growth of certificate of
deposit), or sinusoidal (number of daylight hours throughout the year).
 Ask students to use interpolation and extrapolation to make predictions and
inferences about data (e.g., analyze the trend in a data set and make interpolations
and extrapolations based on the trend).
Level 2.0
 Ask students to define linear, quadratic, exponential, sinusoidal, interpolation, and
extrapolation.
 Ask students to recognize or recall examples of the ways data can be represented
(linear, quadratic, exponential and sinusoidal).
 Ask students to recognize or recall accurate statements about using interpolation and
extrapolation to make predictions and inferences.
10