Instructional Focus Unit Organizer
Course:
Pre-algebra
Instructional Focus Unit(s):
Focus 9 – Sampling, Inferences, and comparing populations
Domain(s):
Statistics and Probability
Cluster(s):
 Use random sampling to draw inferences about a population.
 Draw informal comparative inferences about two populations.
Standard(s):
7.SP.A.1. Understand that statistics can be used to gain information about a population by examining a sample of the population;
generalizations about a population from a sample are valid only if the sample is representative of that population. Understand
that random sampling tends to produce representative samples and support valid inferences.
7.SP.A.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.
Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
7.SP.B.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring
the difference between the centers by expressing it as a multiple of a measure of variability.
7.SP.B.4. Use measures of center and measures of variability for numerical data from random samples to draw informal
comparative inferences about two populations.
Verbs
Construct
Critique
Attend
Make sense
Persevere
Reason
Use
Look for
Make use of
Draw
Understand
Gain
Examine
Produce
Generalize
Recognize
Gather
Generate
Conduct
Give
Identify
Survey
Determine
Write
Revised 2/13/13
Noun (phrases)
Random sampling
Inferences
Population
Statistics
Sample
Information
Argument
Generalizations
Representative sample
Data
Reasoning
Precision
Students
Total population
Inferences
Simulated samples
Predications
Survey
Variation
Estimate
Multiple samples
Characteristic of interest
Accuracy
Sample size
Kyrene School District
Working Document
Gauge
Estimate
Random sampling
Predict
Collect
Answer
Address
Assess
Measure
Express
Research
Find
Utilize
Calculate
Connect
Decide
Compare
Include
observe
persuade
Unknown characteristics
Visual overlap
Structure
Difference
Measure of variability – range, MAD, interquartile range
Statistic functions
Measures of central tendency – mean, median,
mode
Data sets
Distribution
Comparative inferences
Numerical data
Standard deviation
Dot plot
Sense of problem
Viable argument
Tools
Graphing calculators
Spreadsheets
Computations
Student will be able to:
 Explain how statistics can be used to gain
information about a population
 Sample a population
 Make generalizations about population from a
sample
 Support valid/invalid inferences
 Identify if a sample is representative of a
population
 Explain how random samples can produce
representative samples and support valid
inferences.
 Recognize the difficulty to gather statistics on an
entire population
 Draw inferences from data
 Describe what random sampling is and how it is
used to get accurate results
 Construct viable arguments
 Critique the reasoning of others
 Attend to precision
 draw inferences about a population with
unknown characteristic of interest using data
from a random sample
 generate multiple samples of the same size
Student will understand:
 Understand the statistics can be used to gain
information about a population by
examining a sample of the population
 Understand generalizations about a
population from a sample are valid only if
the sample is representative of that
population
 Understand that random sampling tends to
produce representative samples & support
valid inferences
 Understand that a random sample
guarantees that each element of the
population has an equal opportunity to be
selected in the sample
 Understand the benefit of each method of
analyzing data with both measures of center
and measures of variability
Revised 2/13/13
Kyrene School District
Working Document


















gauge the variation in estimates or predictions
from a sample
collect & use multiple samples of data to answer
questions about a population
make sense of problems
persevere in solving them
reason abstractly & quantitatively
use appropriate tools strategically
look for & make use of structure
assess the degree of visual overlap of two
numerical data distributions with similar
variabilities
measure the difference between the centers by
expressing it as a multiple of a measure of
variability
utilize statistical functions in a graphing calculator
or spreadsheet for calculations with larger data
sets to check computations
calculate mean absolute deviations
analyze data sets to connect the mathematics to
their interests and other academic subjects
create & analyze visual representations (dot
plots, bar graphs, box & whisker, circle graphs,
stem & leaf plot, histogram) to compare multiple
measures of data
draw informal comparative inferences about two
population using measures of center and
measures of variability for numerical data.
Compare 2 sets of data using measures of center
& variability
Persuade both sides of an argument when
comparing 2 sets of data
Calculate measures of center – mean, median,
mode
Calculate measures of variability – range, mean
absolution deviation, interquartile range
Revised 2/13/13
Kyrene School District
Working Document
Revised Learning Goal(s) :
Students will be able to use random sampling to draw inferences about a population and explain how
statistics can be used to support their inferences.
Learning Scale(s):
4
In addition to level
3.0 and above and
beyond what was
taught in class,
student may:


Make
connection
with other
concepts in
math
Make
connection
with other
content areas.
3
Students will be
able to use random
sampling to draw
inferences about a
population and
explain how
statistics can be
used to support
their inferences.

Explain how
random
samples can
produce
representative
samples and
support valid
inferences.
2
Students will be
able to use random
sampling to draw
inferences about a
population.



Collect & use
multiple
samples of data
to answer
questions
about a
population
Identify if a
sample is
representative
of a population
Survey a
population to
get a sample
1
With help from
the
teacher, student
has
partial success
with the level 2.0
& 3.0
0
Even with help,
student has no
success with the
unit content.
Sequenced targets
7.SP.1 & 7.SP.2- One Population
Describe what random sampling is and how it is used to get accurate results
Draw inferences from data
Identify if a sample is representative of a population
draw inferences about a population with unknown characteristic of interest using data from a random sample
Recognize the difficulty to gather statistics on an entire population
Survey a population to get a sample
generate multiple samples of the same size
collect & use multiple samples of data to answer questions about a population
Revised 2/13/13
Kyrene School District
Working Document
Make generalizations about population from a sample
gauge the variation in estimates or predictions from a sample
Support valid/invalid inferences
Explain how statistics can be used to gain information about a population
Explain how random samples can produce representative samples and support valid inferences.
Understand the statistics can be used to gain information about a population by examining a sample of the population
Understand generalizations about a population from a sample are valid only if the sample is representative of that
population
Understand that random sampling tends to produce representative samples & support valid inferences
Understand that a random sample guarantees that each element of the population has an equal opportunity to be
selected in the sample
Revised 2/13/13
Kyrene School District
Working Document
Revised Learning Goal(s) :
Students will be able to draw comparative inferences about two populations and explain how statistics
can be used to support their inferences.
Learning Scale(s):
4
In addition to level
3.0 and above and
beyond what was
taught in class,
student may:


Make
connection
with other
concepts in
math
Make
connection
with other
content areas.
3
Students will be
able to draw
comparative
inferences about
two populations
and explain how
statistics can be
used to support
their inferences.
2
Students will be able to
draw comparative
inferences about two
populations.



Revised 2/13/13
Analyze visual
representations
(dot plots, bar
graphs, box &
whisker, circle
graphs, stem &
leaf plot,
histogram,
table) to
compare
multiple
measures of
data
Explain benefit
of analyzing
data with the
measures of
center and
measures of
variability


Calculate measures
of variability –
range, mean
absolution
deviation,
interquartile range
Compare 2 sets of
data using
measures of center
& variability
create visual
representations
(dot plots, bar
graphs, box &
whisker, circle
graphs, stem & leaf
plot, histogram) to
compare multiple
measures of data
Kyrene School District
1
With help from
the
teacher,
student has
partial success
with the level
2.0 & 3.0
0
Even with help,
student has no
success with the
unit content.
Working Document
Throughout the unit:
Construct viable arguments
Critique the reasoning of others
Attend to precision
make sense of problems
persevere in solving them
reason abstractly & quantitatively
use appropriate tools strategically
look for & make use of structure
7.SP.3 & 7.SP.4- Two Populations
Calculate measures of variability – range, mean absolution deviation, interquartile range
Calculate measures of center – mean, median, mode
Compare 2 sets of data using measures of center & variability
draw informal comparative inferences about two population using measures of center and measures of variability for
numerical data.
create visual representations (dot plots, bar graphs, box & whisker, circle graphs, stem & leaf plot, histogram) to
compare multiple measures of data
measure the difference between the centers by expressing it as a multiple of a measure of variability
Persuade both sides of an argument when comparing 2 sets of data
create & analyze visual representations (dot plots, bar graphs, box & whisker, circle graphs, stem & leaf plot,
histogram) to compare multiple measures of data
assess the degree of visual overlap of two numerical data distributions with similar variabilities
utilize statistical functions in a graphing calculator or spreadsheet for calculations with larger data sets to check
computations
Understand the benefit of each method of analyzing data with both measures of center and measures of variability
Revised 2/13/13
Kyrene School District
Working Document
Assessment(s):
Resources/Materials:
Next Steps:
What?
Revised 2/13/13
Who?
Kyrene School District
When?
Working Document