Content Area
Standard
Math
4.7 Grade 7
Strand
Statistics and Probability
Content Statement
CPI#
Cumulative Progress Indicator (CPI)
ACSSSD
Objectives
4.7.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
representative of that population.
Understand that random sampling tends
to produce representative samples and
support valid inferences.
4.7.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 randomly
sampled survey data. Gauge how far off
the estimate or prediction might be.
1. List the uses of statistics.
2. Define statistical sampling.
3. Identify types of statistical
samples.
4. Define random sampling in
statistics.
5. List reasons for using a random
sample to examine a population.
6. Define validity.
7. Define inference.
1. Demonstrate the ability to draw
inferences from data.
2. Define random sampling in
statistics.
3. List reasons for using a random
sample to examine a population.
4. Create a sample or a simulated
sample based off of data from a
random sample.
5. Use multiple samples to make
predictions.
6. Evaluate predictions and
estimates for accuracy.
Use random sampling to draw inferences about a population.
Draw informal comparative inferences about two populations.
4.7.SP.3
Informally assess the degree of visual
overlap of two numerical data
distributions with similar variabilities,
measuring the difference between the
1. Demonstrate the ability to find
the mean in a given set of data
points.
2. Demonstrate the ability to find
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.
4.7.SP.4
the distance of each data point
from the mean.
3. Demonstrate the ability to find
the mean absolute deviation of a
data set by finding the mean of
the distances of the data points
from the mean.
4. Demonstrate the ability to read
and create dot plots.
Use measures of center and measures of
1. Demonstrate the ability to find
variability for numerical data from
the measures of central tendency
random samples to draw informal
(mean, median and mode) of a
comparative inferences about two
given data set.
populations. For example, decide whether 2. Demonstrate the ability to find
the words in a chapter of a seventh-grade
the measures of variability
science book are generally longer than the
(range, interquartile range and
words in a chapter of a fourth-grade
mean absolute deviation) of a
science book.
given data set.
Investigate chance processes and develop, use, and evaluate probability models.
4.7.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 1/2 indicates an event that is
neither unlikely nor likely, and a
probability near 1 indicates a likely event.
1. Define probability.
2. Demonstrate an understanding
that probability ranges from 0 to
1.
3. Recognize that a probability
closer to 1 indicates that an event
is more likely to occur.
4. Recognize that a probability
closer to 0 indicates that an event
is less likely to occur.
5. Recognize that a probability
around ½ indicates that an event
is neither unlikely nor likely to
occur.
6. Recognize that if an event is a
certainty, then the probability is
4.7.SP.6
4.7.SP.7
a.
b.
1.
7. Recognize that if an event is
impossible, then the probability
is 0.
Approximate the probability of a chance
1. Find the experimental probability
event by collecting data on the chance
of a chance event.
process that produces it and observing its 2. Demonstrate the ability to
long-run relative frequency, and predict
approximate probabilities.
the approximate relative frequency given 3. Demonstrate the ability to collect
the probability. For example, when
data.
rolling a number cube 600 times, predict 4. Define long-run relative
that a 3 or 6 would be rolled roughly 200
frequency.
times, but probably not exactly 200 times. 5. Given data from experimental
probability, make a prediction.
6. Make a prediction based on
theoretical probability.
7. Compare experimental and
theoretical probabilities.
Develop a probability model and use it to find probabilities of events. Compare
probabilities from a model to observed frequencies; if the agreement is not good,
explain possible sources of the discrepancy.
Develop a uniform probability model by
1. Define uniform probability
assigning equal probability to all
model.
outcomes, and use the model to determine 2. Demonstrate an understanding of
probabilities of events. For example, if a
equal probability.
student is selected at random from a
3. Complete a chart to find
class, find the probability that Jane will
experimental probability.
be selected and the probability that a girl 4. Create a uniform probability
will be selected.
model.
5. Use a model to determine
probability.
6. Identify independent outcomes in
probability.
Develop a probability model (which may 1. Define probability model.
not be uniform) by observing frequencies 2. Distinguish between a
in data generated from a chance process.
probability model and a uniform
For example, find the approximate
probability model.
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?
4.7.SP.8
3. Determine if a situation has equal
probability or unequal
probability.
4. Create a probability model.
5. Demonstrate the ability to make
observations from data.
6. Identify situations that would
cause biased results or random
results.
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 sample spaces 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.
1. Demonstrate the ability to create
a table that displays possible
outcomes of a compound event.
2. Demonstrate the ability to count
possible outcomes of a
compound event displayed in a
table.
3. Demonstrate the ability to
express the probability of a
compound event as a fraction
where the possible outcome
described is represented by the
numerator and the total of all
possible outcomes is represented
by the denominator.
1. Demonstrate the ability to create
an organized list that displays
possible outcomes of a
compound event.
2. Demonstrate the ability to create
a table that displays possible
outcomes of a compound event.
3. Demonstrate the ability to create
a tree diagram that displays
possible outcomes of a
compound event.
c.
Design and use a simulation to generate
frequencies for compound events. For
example, use random digits as a
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?
1. Refer to the ACSSSD Objectives
of 4.7.SP.8.ba and 4.7.SP.8.b for
the prerequisite skills needed to
complete this CPI.
2. Demonstrate the ability to use
multiple means (coin toss, die
roll, color wheel or computer) to
generate random numbers for
data set.
3. Demonstrate the ability to assign
random numbers generated to
each of possible outcomes in a
simulation.
4. Demonstrate the ability to record
outcomes of simulation in a
table.
5. Demonstrate the ability to
express the experimental
probability of a simulation as a
fraction where the possible
outcome described is represented
by the numerator and the total of
all possible outcomes generated
is represented by the
denominator.