Download Inferences and Conclusions From Data

Grade
Montclair Public Schools
CCSS Algebra 2 High Honors Unit: Marshall A.b.
9 or 11 Unit # 4
Pacing
Subject
Algebra 2 High
Honors
Unit
Name
Overview
Inferences and Conclusions From Data
Marking Period 4
In this unit, students see how the visual displays and summary statistics they learned in earlier grades relate to different types of data and to probability distributions.
They identify and evaluate different ways of collecting data—including sample surveys, experiments, and simulations—and the role that randomness and careful
design play in the conclusions that can be drawn. Students also investigate arithmetic and geometric sequences both recursively and with an explicit formula, use
them to model situations, and translate between the two forms.
Standard #
MC,
SC,
or
AC
SLO
#
Describe events as subsets of a sample space (the
set of outcomes) using characteristics (or categories)
of the outcomes, or as unions, intersections, or
complements of other events (“or,” “and, ”not”).
Understand that two events A and B are
independent if the probability of A and B occurring
together is the product of their probabilities, and
use this characterization to determine if they are
independent.
AC
1
AC
2
3
S.CP.3
Understand the conditional probability of A given B
as P(A and B)/P(B), and interpret independence of A
and B as saying that the conditional probability of A
given B is the same as the probability of A, and the
conditional probability of B given A is the same as
the probability of B.
AC
S.CP.4
Construct and interpret two-way frequency tables of
data when two categories are associated with each
object being classified. Use the two-way table as a
AC
S.CP.1
S.CP.2
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Standard
Student Learning Objectives
Depth of
Knowledge
Define a sample space and events within a sample space.
Identify subsets from the sample space given defined
events, including unions, intersections, or complements of
events.
Identify two events as independent or not.
Explain Properties of Independence and Conditional
Probabilities in context and in simple English.
1
4
5
Define and calculate conditional probabilities.
Use the Multiplication Principle to decide if two events are
independent and to calculate conditional probabilities.
2
3
6
Construct and interpret two-way frequency tables of data
for two categorical variables. Calculate probabilities from
the table.
3
1
2
sample space to decide if events are independent
and to approximate conditional probabilities. For
example, collect data from a random sample of
students in your school on their favorite subject
among math, science, and English. Estimate the
probability that a randomly selected student from
your school will favor science given that the student
is in tenth grade. Do the same for other subjects and
compare the results.
Recognize and explain the concepts of
conditional probability and independence in
everyday language and everyday situations. For
example, compare the chance of having lung
cancer if you are a smoker with the chance of
being a smoker if you have lung cancer.
Find the conditional probability of A given B as the
fraction of B’s outcomes that also belong to A, and
interpret the answer in terms of the model.
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A
and B), and interpret the answer in terms of the
model.
S.CP.5
S.CP.6
S.CP.7
S.IC.1
S.IC.2
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7
Use probabilities from a two-way frequency table to
evaluate independence of two variables.
AC
8
Use everyday language to explain independence and
conditional probability in real-world situations.
3
AC
9
Find the conditional probability of A given B as the fraction
of B’s outcomes that also belong to A
2
AC
10
Apply the addition [P(A or B) = P(A) + P(B) – P(A and B)] rule
of probability in a uniform probability model; interpret the
results in terms of the model.
2
11
Explore the difference and similarity of addition rule when A
and B are not conditional events
Describe the difference between a population and a sample
2
Make inferences about population parameters based on a
random sample from that population. For example: if 70%
of all students voted for Joe Mama, then approximately how
many in a class of 25 students voted for Joe Mama?
Explain how well and why a sample represents the variable
of interest from a population.
2
15
Demonstrate understanding of the different kinds of
sampling methods.
2
16
Design simulations of random sampling: assign digits in
4
Understand statistics as a process for making
inferences about population parameters based on a
random sample from that population. ★
SC
Decide if a specified model is consistent with results
from a given data-generating process, e.g., using
simulation. For example, a model says a spinning
coin falls heads up with probability 0. 5. Would a
result of 5 tails in a row cause you to question the
model?
SC
12
13
14
1
3
appropriate proportions for events, carry out the
simulation using random number generators and random
number tables and explain the outcomes in context of the
population and the known proportions.
S.IC.3
Recognize the purposes of and differences among
sample surveys, experiments, and observational
studies; explain how randomization relates to each.
S.IC.4
Use data from a sample survey to estimate a
population mean or proportion; develop a margin of
error through the use of simulation models for
random sampling.
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MC
MC
17
Calculate chi-squared values and degrees of freedom;
compare to statistics tables at 95% confidence to determine
if a given model is appropriate
2
18
Understand reasonable doubt in the context of probability
19
Identify different methods and purposes for conducting
sample surveys, experiments, and observational studies.
4
20
Explain how randomization relates to each. Example of
random events are reaching into a bag to draw a colored
marble or taking from a hat a folded piece of paper with a
number .
2
21
Use data from a sample survey to estimate a population
mean or proportion; develop a margin of error through the
use of simulation models for random sampling.
3
22
Using collected data, calculate the estimated population
proportion and estimated population mean.
2
23
Calculate a margin of error for a given confidence interval.
2

S.IC.5
S.IC.6

Use data from a randomized experiment to
compare two treatments; use simulations to
decide if differences between parameters are
significant.
Evaluate reports based on data.
MC
24
Use data from a randomized experiment to compare two
treatments and use simulations to decide if differences
between parameters are significant; evaluate reports based
on data.
3
25
As the saying goes, “Statistics don’t lie, but liars use
statistics.” Discuss results of experiment by initiating
questions such as:
3








F.BF.2
A.SSE.4
Write arithmetic and geometric sequences both
recursively and with an explicit formula, use them to
model situations, and translate between the two
forms.
Derive the formula for the sum of a finite geometric
series (when the common ratio is not 1), and use the
formula to solve problems. For example, calculate
mortgage payments.
Use statistics appropriate to the shape of the
data distribution to compare center (median,
mean) and spread (interquartile range,
S.ID.2
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MC
MC
26
What is the purpose of the study?
Were the collection methods appropriate for this
particular study?
Were they randomized?
What was the null hypothesis?
Were the correct statistical tests used for the data?
Was the data fully presented?
Who were the study participants?
Who funded the study? Can bias arise from that?
Write arithmetic and geometric sequences both recursively
and with an explicit formula, use them to model situations,
and translate between the two forms.
3
27
Derive the formula for the sum of a finite geometric series
(when the common ratio is not 1), and use the formula to
solve problems.
4
28
Use finite geometric series to calculate a car loan or
mortgage payment.
3
29
Extend the content of finite geometric series to infinite
geometric series to understand how repeating decimals are
representations of infinite geometric series.
30
Calculate mean and standard deviation of a set of data
31
Use percentages in the context of standard deviation to
AC
2
1
standard deviation) of two or more different
data sets.
Mathematical
Practice #
determine how many in a sample will fall within certain
parameters. For example: If a set of data has a mean of 10
and standard deviation of 3, then out of a 500 sample, how
many will have a value between 7 and 16?
3
Selected Opportunities for Connections to Mathematical Practices
1
2
SLOs 3, 11
SLOs 14, 15, 24, 25
3
5, 18, 24
4
5
6
7
8
16, 24
13, 25, 31
4, 17, 28, 30
10, 11, 27
27, 29
Big Ideas
1.
2.
3.
Statistics are a useful tool for describing data; they can also be easily misinterpreted
Certain statistics do not paint the full picture when it comes to a set of data
Critical decisions are often made based upon the collection of data
Essential Questions



How to we become ‘statistically literate’ Americans so that we are not fooled into believing false or misleading data? What questions should we ask
ourselves when presented with data preceded with the statement ‘Studies show that….’?
At what point do we say ‘unusual’ data is due to chance versus due to a faulty model?
In what ways can we construct an experiment in order to achieve true results as opposed to biased ones?
Assessments


Formal and informal formative and summative assessments as determined by the teacher
Algebra 2 High Honors Unit 4 Model Assessment is a 90-minute, double-class-period assessment that should be administered at the end of the
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year, allowing enough time for grading and subsequent reviewing of material.
Key Vocabulary
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
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Standard deviation
Degrees of freedom
Chi-squared
Experiment vs. observation
Randomization
Margin of error
Suggested Resources (list specific chapters and or page numbers from existing text that correspond to the SLOs and Standards)
SLOs 1-5, 8-11 see Glencoe Algebra 2 Ch 12-4 thru 12-6
SLOs 14-16 see Glencoe Algebra 2 Ch 12-7
SLO 23 see Glencoe Algebra 2 Ch 12-8
SLOs 26-28 see Glencoe Algebra 2 Ch 11-3 & 11-4
SLOs 29-30 see Glencoe Algebra 2 Ch 6-8 & 6-9
All other SLOs see www.shmoop.com and type in corresponding standard
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