Download math 7 core curriculum document unit 4 statistics and probability

CURRICULUM MAP
Content Area:
Grade Level:
Duration: (30-35 days) *Accelerated (25-30 days)
Essential Question/Understandings:
Standards for Mathematical
Practice:
Focus Area:
Date:
1) Use random sampling to draw inferences about a population. (supporting)
2) Draw informal comparative inferences about two populations. (additional)
3) Investigate chance processes and develop, use, and evaluate probability models.
(supporting)
4) Investigate patterns of association in bivariate data.* (supporting)
* Accelerated
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Unit 4: Statistics and Probability (7.SP)
Common Core Standard
Performance Indicator
7.SP.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 a representative
of that population. Understand that
random sampling tends to produce
representative samples and support
valid inferences.
7.SP.1 Students recognize that
is difficult to gather statistics
on an entire population.
Instead a random sample
can be representative of the
total population and will
generate valid results.
Students use this information
to draw inferences from data.
A random sample must be
used in conjunction with the
population to get accuracy.
For example, a random
sample of elementary
students cannot be used to
give a survey about the prom.
Vocabulary
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Biased
Convenience
Sample
Inference
Invalid
Population
Sample
Simple
Random
Sample
Systematic
Random
Sample
Valid
Voluntary
Sample
Assessments
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5 Week Tests
(Including Midterm
and Final Exams)
Quizzes/Buddy
Quizzes
Homework
Checks for
Understanding
Tickets Out The
Door
Problems of the
Week Journals
Group Work
Resources
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Common Core
Modules
Glencoe Course
2/Course 3 Textbook
Series
Teacher Created
/Workshop Materials
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7.SP.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.
For example, estimate the mean
word length in a book by randomly
sampling words from the book;
predict the winner of a school
election based on a randomly
sampled survey data. Gauge how
far off the estimate or prediction
might be.
7.SP.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.
For example, the mean height of
players on the basketball team is 10
cm greater than the mean height of
players on the soccer team, about
twice the variability (mean absolute
deviation) on either team; on a dot
plot, the separation between the two
distributions of heights is noticeable.
7.SP.2
Students collect and use
multiple samples of data to
answer question(s) about a
population. Issues of
variation in the samples
should be addressed.
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7.SP.3
This is the student’s first
experience with comparing
two data sets. Students build
on their understanding of
graphs, mean, median, Mean
Absolute Deviation, and
interquartile range from 6th
grade.
Students understand that
1. A full understanding of the
data requires
consideration of the
measures of variability as
well as mean or median.
2. Variability is responsible
for the overlap of the two
data sets and that an
increase in variability can
increase the overlap.
3. Median is paired with the
interquartile range and
mean is paired with the
mean absolute deviation.
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Compound
Event
Dependent
Event
Event
Independent
Event
Probability
Probability
Model
Random
Sample
Sample Space
Simulation
Uniform
Probability
Model
Bivariate
Box-Plot (Boxand-Whisker
Plot)
Clustering
Data Set
Dot Plot
Histogram
Interquartile
Range
Median
Mode
Range
Scatter Plot
Shape
Skew
Spread
Statistics
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Edited by: lvs 4/30/2017
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7.SP.4 Use measures of center and
measures of variability for numerical
data from random samples to draw
informal comparative inferences
about two populations. For example,
decide whether the words in a
chapter of a seventh-grade science
book are generally longer than the
words in a chapter of a fourth-grade
science book.
7.SP. 5 Understand that the
probability of a chance event is a
number between 0 and 1 that
expresses the likelihood of the event
occurring. Larger numbers indicate
greater likelihood. A probability near
0 indicates an unlikely event, a
probability around ½ indicates an
even that is neither unlikely nor likely,
and a probability near 1 indicated a
likely event.
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Mean
Mean
Absolute
Deviation
(MAD)
Measures of
Variability
(Central
Tendency)
Median
Mode
Observation
Quantitative
7.SP. 5
This is students’s first formal
introduction to probability.
Students recognize that all
probabilities are between 0
and 1, inclusive, the sum of all
possible outcomes is 1. For
example, there are three
choices of jellybeans –
grape, cherry, and orange. If
the probability of getting
grape is 3/10 and the
probability of getting cherry is
1/5, what is the probability of
getting oranges? The
probability of any single
event can be recognized as
a fraction. The closer the
fraction is to 1, the greater the
probability the event will
occur. Larger numbers
indicate greater likelihood.
For example, if you have 10
oranges and 3 apples, you
have a greater likelihood of
getting an orange.
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7.SP. 6 Approximate the probability
of a chance event by collecting data
on the chance process that produces
it and observing its long-run relative
frequency, and predict the
approximate relative frequency
given the probability.
For example, when rolling a number
cube 600 times, predict that a 3 or 6
would be rolled roughly 200 times,
but probably not exactly 200 times.
7.SP.6
Students collect data from a
probability experiment,
recognizing that as the
number of trials increase, the
experimental probability
approaches the theoretical
probability. The focus of this
standard is relative
frequency—The relative
frequency is the observed
number of successful events
for a finite sample of trials.
Relative frequency is the
observed proportion of
successful events.
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Relative
Frequency
7.SP. 7 Develop a probability model
and use it to find probabilities of
event. Compare probabilities from a
model to observed frequencies. If
the agreement is not good, explain
possible sources of the discrepancy.
a. Develop a uniform probability
model by assigning equal probability
to all outcomes, and use the model
to determine probabilities of events.
For examples, is a student is selected
at random from a class, find the
probability that Jane will be selected
that a girl will be selected.
b. Develop a probability model
(which may not be uniform) by
observing frequencies in data
generated from a chance process.
For example, find the approximate
probability that a spinning penny will
land heads up or that a tossed paper
cup will land open-end down. Do
the outcomes for the spinning penny
appear to be equally likely based on
the observed frequencies?
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7.SP.8
Find probabilities of compound
events using organized lists, tables,
tree diagrams, and simulation.
a. Understand that just as with
simple events, the probability of a
compound event is the fraction of
outcomes in the sample space
for which the compound event
occurs.
b. Represent for compound events
using methods such as organized
lists, tables, and tree diagrams.
For an event described in
everyday language (e.g., “rolling
double sixes”), identify the
outcomes in the sample space
which compose the event.
c. Design and use a simulation to
generate frequencies for
compound events. For example,
use random digits as simulation
tool to approximate the answer to
the question: If 40% of donors
have type A blood, what is the
probability that it will take at least
4 donors to find one with type A
blood?
Linear
Association
Positive and
Negative
Correlation
7.SP.8
Students use tree diagrams,
frequency tables, and
organized lists, and
simulations to determine the
probability of compounding
events.
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Probabilities are useful for
predicting what will happen
over the long run. Using
theoretical probability,
students predict frequencies
of outcomes. Students
recognize an appropriate
design to conduct an
experiment with simple
probability events,
understanding that the
experimental data give
realistic estimates of the
probability of an event but
are affected by sample size.
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Independent
Probability
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Tree Diagram
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Dependent
Probability
Dot Plots
Histograms
Accelerated
8.SP.1
Construct and interpret scatter plots
for bivariate measurement data to
investigate patterns of association
between two quantities. Describe
patterns such as clustering, outliers,
positive or negative association,
linear association, and nonlinear
association.
8.SP.2
Know that straight lines are widely
used to model relationships between
two quantitative variables. For scatter
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plots that suggest a linear
association, informally fit a straight
line, and informally assess the model
fit by judging the closeness of the
data points to the line.
8.SP.3
Use the equation of a linear model to
solve problems in the context of
bivariate measurement data,
interpreting the slope and intercept.
8.SP.4
Understand that patterns of
association can also be seen in
bivariate categorical data by
displaying frequencies and relative
frequencies in a two-way table.
Construct and interpret a two-way
table summarizing data on two
categorical variables collected from
the same subjects. Use relative
frequencies calculated
for rows or columns to describe
possible association between the two
variables.
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Edited by: lvs 4/30/2017