

Unit 6 Probability
and Statistics Grade
7 Math 

Unit
Length and Description: 30
days The
initial work in Unit 6 extends students prior knowledge of statistics to
include population statistics. Students learn to draw inferences about
populations based on random samples.
Data used in this unit will be from a realworld context with an
emphasis on representative samples and their corresponding populations.
Students will utilize both measures of center and measures of variability to
compare and make inferences for two populations. After working with population statistics,
students start to explore chance events and are introduced to the concept of
probability. This is the students first experience with probability, and it
begins with the conceptual understanding that the probability of a chance
event is a rational number between 0 and 1. Students will explore simple
probability through collecting data on a chance process as well as through
developing probability models. Probability is designed to enhance the
students statistical thinking and reasoning.
The latter part of Unit 6 extends the students work with probability
to include finding probabilities of compound events. Students are not
expected to calculate the probability of a compound event arithmetically;
rather, they will be expected to find the probability of a compound event
using organized lists, tables, tree diagrams, and simulations. Students
should understand that the probability of a compound event is analogous to
the probability of a simple event in that both are ratios comparing the
number of favorable outcomes within a sample space to the entire sample
space. Students will design and use simulations to generate frequencies for
compound events. This unit should provide students with an appreciation of
how statistics and probability can be applied in a realworld context. 

Standards: 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. 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. 7.SP.B.3 Informally assess the degree of visual
overlap of two numerical data distributions with similar variability,
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.B.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 seventhgrade science book are generally longer
than the words in a chapter of a fourthgrade science book. 7.SP.C.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. o Standards Clarification:
Students use proportional reasoning and percentages when working with
probability. Students will need a strong conceptual understanding of
probability to be successful when working with compound probabilities. 7.SP.C.6 Approximate the probability of a chance
event by collecting data on the chance process that produces it and observing
its longrun 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.C.7 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. a. Develop a uniform probability model by
assigning equal probability to all outcomes, and use the model to determine
probabilities of events. For example, if a student is selected at random
from a class, find the probability that Jane will be selected and the
probability 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 openend down.
Do the outcomes for the spinning penny appear to be equally likely based on
the observed frequencies? 7.SP.C.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 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. 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?
Focus Standards of
Mathematical Practice: MP.1 Make
sense of problems and persevere in solving them. MP.2 Reason
abstractly and quantitatively. MP.3
Construct viable arguments and critique the reasoning of others. MP.4 Model
with mathematics. MP.5 Use
appropriate tools strategically. MP.6 Attend
to precision. MP.7 Look for
and make use of structure. MP.8 Look for
and express regularity in repeated reasoning. Instructional
Outcomes: Full Development of the Major Clusters,
Supporting Clusters, Additional Clusters and Mathematical Practices for this
unit could include the following instructional outcomes: 7.SP.A.1 ·
I can apply
statistics terms such as population, sample, sample size, random sampling,
generalizations, valid, biased and unbiased. ·
I can recognize sampling techniques such as convenience,
random, systematic and voluntary. ·
I can recognize that generalizations about a population
from a sample are valid only if the sample is representative of that
population. ·
I can apply statistics to gain information about a
population from a sample of the population. ·
I can generalize that random sampling tends to produce
representative samples and support valid inferences. 7.SP.A.2 ·
I can define random sample. ·
I can identify an appropriate sample size. ·
I can analyze and interpret data from a random sample to
draw inferences about a population with an unknown characteristic of
interest. ·
I can generate multiple samples (or simulated samples)
of the same size to determine the variation in estimates or predictions by
comparing and contrasting the samples. 7.SP.B.3 ·
I can identify measures of central tendency (mean,
median, and mode) in a data distribution. ·
I can identify measures of variation including upper
quartile, lower quartile, upper extrememaximum, lower extreme minimum,
range, interquartile range, and mean absolute deviation (i.e. boxandwhisker
plots, line plot, dot plots, etc.) ·
I can compare two numerical data distributions on a
graph by visually comparing data displays, and assessing the degree of visual
overlap. ·
I can compare the differences in the measure of central
tendency in two numerical data distributions by measuring the difference
between the centers and expressing it as a multiple of a measure of
variability. 7.SP.B.4 ·
I can find measures of central tendency (mean, median,
and mode) and measures of variability (range, quartile, etc.). ·
I can analyze and interpret data using measures of
central tendency and variability. ·
I can draw informal comparative inferences about two
populations from random sample. 7.SP.C.5 ·
I can understand that probability is expressed as a
number between 0 and 1. ·
I can understand that a random event with a probability
of ½ is equally likely to happen. ·
I can understand that as probability moves closer to 1
it is increasingly likely to happen. ·
I can understand that as probability moves closer to 0
it is decreasingly likely to happen. ·
I can draw conclusions to determine that a greater
likelihood occurs as the number of favorable outcomes approaches the total
number of outcomes. 7.SP.C.6 ·
I can determine relative frequency (experimental
probability) is the number of times an outcome occurs divided by the total
number of times the experiment is completed. ·
I can determine the relationship between experimental
and theoretical probabilities by using the law of large numbers. ·
I can predict the relative frequency (experimental
probability) of an event based on the (theoretical) probability. 7.SP.C.7a ·
I can use models to determine the probability of events.
·
I can recognize uniform (equally likely) probability. ·
I can develop a uniform probability model and use it to
determine the probability of each outcome/event. 7.SP.C.7b ·
I can use models to determine the probability of events.
·
I can develop a probability model (which may not be
uniform) by observing frequencies in data generated from a change process. ·
I can analyze a probability model and justify why it is
uniform or explain the discrepancy if it is not. 7.SP.C.8a ·
I can determine that the probability of a compound event
is the fraction of outcomes in the sample space for which the compound event
occurs. ·
I can identify the outcomes in the sample space for an
everyday event. 7.SP.C.8b ·
I can define and describe a compound event. ·
I can find probabilities of compound events using
organized lists, tree diagrams, etc. and analyze the outcomes. ·
I can choose the appropriate method such as organized
lists, tables and tree diagrams to represent sample spaces for compound
events. 7.SP.C.8c ·
I can define simulation. ·
I can design and use a simulation to generate
frequencies for compound events. 

Enduring Understandings: The way
that data is collected, organized and displayed influences interpretation. Measures of center and measures of variability
can be compared and used to make inferences for two populations. The probability of a chance event is a
rational number between 0 and 1. The probability of an events
occurrence can be predicted with varying degrees of confidence. The probability of a compound event can
sometimes be found using organized lists, tables, tree diagrams, and
simulations. The probability of a compound event is
similar to the probability of a simple event in that both are ratios
comparing the number of favorable outcomes within a sample space to the
entire sample space. 
Essential
Questions: ·
How can you predict the outcome of
future events? ·
Why is data collected and
analyzed? ·
How do you know which type of
graph to use when displaying data? ·
How do people use data to influence
others? ·
How can predictions be made based
on data? ·
How can the probability of an
event be determined? ·
What is the reliability of the
determination of the probability of an event? 
