Download Find the mean, variance, standard deviation, and

Curriculum and Instruction – Office of Mathematics
Statistics
2nd Nine Weeks
Introduction
In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student
performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,



80% of our students will graduate from high school college or career ready
90% of students will graduate on time
100% of our students who graduate college or career ready will enroll in a post-secondary opportunity
In order to achieve these ambitious goals, we must collectively work to provide our students with high-quality, College and
Career Ready standards-aligned instruction. Acknowledging the need to develop competence in literacy and language as the
foundation for all learning, Shelby County Schools developed the Comprehensive Literacy Improvement Plan (CLIP). The CLIP
ensures a quality balanced literacy approach to instruction that results in high levels of literacy learning for all students across
content areas. Destination 2025 and the CLIP establish common goals and expectations for student learning across schools.
CLIP connections are evident throughout the mathematics curriculum maps.
The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end
of a grade. College and Career Ready Standards are rooted in the knowledge and skills students need to succeed in postsecondary study or careers. While the academic standards establish desired learning outcomes, the curriculum provides
instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a
roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational
skills are spiraled in order to facilitate student mastery of the standards.
These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond
multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints
(http://www.tn.gov/education/article/tnready-blueprints ) have been designed to show educators a summary of what will be
assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail
which standards will be assessed on Part I of TNReady and which will be assessed on Part II.
Curriculum and Instruction – Office of Mathematics
Statistics
Our collective goal is to ensure our students graduate ready
for college and career. The Standards for Mathematical
Practice describe varieties of expertise that mathematics
educators at all levels should seek to develop in their
students. These practices rest on important “processes and
proficiencies” with longstanding importance in
mathematics education. The first of these are the NCTM
process standards of problem solving, reasoning and proof,
communication, representation and connections.
2nd Nine Weeks
Problem Solving
Connecton
Representation
Look for and
express
regularity in
repeated
reasoning
Look for and
make use of
structure
Make sense of
problems and
persevere in
solving them
Reason
abstractly and
quatitatively
Mathematical
Practices
Attend to
precision
Construct viable
arguments and
crituqe the
reasoning of
others
Model with
mathematics
Use appropriate
tools
strategically
Reasoning and
Proof
Communication
The second are the strands of mathematical proficiency
specified in the National Research Council’s report Adding
It Up: adaptive reasoning, strategic competence, conceptual
understanding (comprehension of mathematical concepts,
operations and relations) procedural fluency (skill in
carrying out procedures flexibly, accurately, efficiently and
appropriately), and productive disposition (habitual
inclination to see mathematics and sensible, useful and
worthwhile, coupled with a belief in diligence and one’s
own efficacy). Throughout the year, students should
continue to develop proficiency with the eight Standards
for Mathematical Practice.
Curriculum and Instruction – Office of Mathematics
How to Use the Mathematic Curriculum Maps
This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that ultimately our
students can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their
instructional practice in alignment with the three College and Career Ready shifts in instruction for Mathematics. We should see these shifts
in all classrooms:
1) Focus
2) Coherence
3) Rigor
Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to
reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage
The TNCore Mathematics Standards
The Tennessee Mathematics Standards:
Teachers can access the Tennessee State standards, which
https://www.tn.gov/education/article/mathematics- are featured throughout this curriculum map and
standards
represent college and career ready learning at reach
respective grade level.
Mathematical Shifts
Focus
The standards are focused on fewer topics so students can
http://achievethecore.org/shifts-mathematics
learn more
Coherence
http://achievethecore.org/shifts-mathematics
Topics within a grade are connected to support focus, and
learning is built on understandings from previous grades
Rigor
http://achievethecore.org/shifts-mathematics
The standards set expectations for a balanced approach to
pursuing conceptual understanding, procedural fluency,
and application and modeling
resources around each of the three shifts that teachers should consistently access:
Subject to revision
TN Statistics Standards
Shelby County Schools2015/2016
Revised 9/23/15
3 of 10
Curriculum and Instruction – Office of Mathematics
Curriculum Maps:







Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to a learning target in
the second column.
Consult your Elementary Statistics: A Step by Step Approach, 7th edition by Bluman Teachers’ Edition (TE) and other cited references to
map out your week(s) of instruction.
Plan your weekly and daily objectives, using the standards' explanations provided in the second column. Best practices tell us that
making objectives measureable increases student mastery.
Carefully review the web-based resources provided in the 'Content and Tasks' column and use them as you introduce or assess a
particular standard or set of standards.
Review the CLIP Connections found in the right column. Make plans to address the content vocabulary, utilizing the suggested
literacy strategies, in your instruction.
Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard.
Using your TE and other resources cited in the curriculum map, plan your week using the SCS lesson plan template. Remember to
include differentiated activities for small-group instruction and math stations.
Subject to revision
TN Statistics Standards
Shelby County Schools2015/2016
Revised 9/23/15
4 of 10
Curriculum and Instruction – Office of Mathematics
2nd Nine Weeks
TN State Standards
Statistics
Essential Understandings
Content & Tasks
CLIP Connections
Chapter 4
(4 weeks for instruction, review, and assessment)
S-CP
1. 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").
3. Demonstrate an understanding of the
Law of Large Numbers (Strong and
Weak).
S.IC.A.2 Decide if a specified model is
consistent with results from a given datagenerating process, e.g., using simulation.
S-CP (See 4-1 above)
S-CP
4. Demonstrate an understanding of the
addition rule, the multiplication rule,
conditional probability, and
independence.
4-1 Sample Spaces and Probability
 Determine sample spaces and find the
probability of an event.
Explain what is meant by the Law of Large
Numbers.
Elementary Statistics Textbook
Elementary Statistics 7th edition Bluman
Elementary Statistics PowerPoint for Chapter 4
Q2_statstask_Lof LN (see Math Tasks on C &
I page)
Law of Large Numbers Applet
4-2 The Addition Rules for Probability
Find the probability of compound events
using the addition rule of probability.
Elementary Statistics Textbook
Elementary Statistics PowerPoint for Chapter 4
4-3 The Multiplication Rules and Conditional
Probability
Elementary Statistics Textbook
Elementary Statistics PowerPoint for Chapter 4
Statistics Today
Critical Thinking Challenges
Speaking of Statistics
Applying the Concepts
Extending the Concepts
Data Projects
S.CP.B.7 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. Demonstrate an understanding of the
addition rule, the multiplication rule,
conditional probability, and
independence.
Subject to revision
 Find the probability of compound events
using the multiplication rule of probability.
 Find the conditional probability of an event.
Q2_statstask_Independence (see Math Tasks
on C & I page)
TN Statistics Standards
Shelby County Schools2015/2016
Revised 9/23/15
5 of 10
Curriculum and Instruction – Office of Mathematics
2nd Nine Weeks
TN State Standards
Statistics
Essential Understandings
Content & Tasks
CLIP Connections
 Discuss the concept of independence
S.CP.A.2 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.
S.CP.A.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.
S.CP.A.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 sample
space to decide if events are independent and
to approximate conditional probabilities.
S.CP.A.5 Recognize and explain the concepts
of conditional probability and independence in
everyday language and everyday situations.
S.CP.B.6
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.
S-CP
5. Apply the general Multiplication Rule in a
uniform probability model, P(A and B) =
P(A)P(B|A) = P(B)P(A|B), and interpret
Subject to revision
Elementary Statistics Textbook
Elementary Statistics 7th edition Bluman
4-4 Counting rules
 Find the total number of outcomes in a
sequence of events using the fundamental
counting rule.
 Find the number of ways that r objects can
be selected from n objects, using the
permutation rule.
Find the number of ways that r objects can be
selected from n objects, without regard to
order, using the combination rule.
Elementary Statistics PowerPoint for Chapter 4
Q2_statsactivity_TooManyChoices (see Math
Tasks on C & I page)
TN Statistics Standards
Statistics Today
Critical Thinking Challenges
Speaking of Statistics
Applying the Concepts
Extending the Concepts
Data Projects
Shelby County Schools2015/2016
Revised 9/23/15
6 of 10
Curriculum and Instruction – Office of Mathematics
2nd Nine Weeks
TN State Standards
Statistics
Essential Understandings
Content & Tasks
CLIP Connections
the answer in terms of the model.
S-CP
2. Use permutations and combinations to
compute probabilities of compound
events and solve problems.
4-5 Probability and Counting Rules
Find the probability of an event using the
counting rules.
Elementary Statistics Textbook
Elementary Statistics 7th edition Bluman
Elementary Statistics PowerPoint for Chapter 4
Q2_statstask_M&Ms6 (see Math Tasks on C
& I page)
Chapter 5
(3 weeks for instruction, review, and assessment)
S-MD
1. Define a random variable for a quantity of
interest by assigning a numerical value to
each event in a sample space; graph the
corresponding probability distribution
using the same graphical displays as for
data distributions.
5-1 Probability Distributions
Construct a probability distribution for a
random variable.
S-MD
2. Calculate the expected value of a random
variable; interpret it as the mean of the
probability distribution.
S-MD
6. Develop a probability distribution for a
random variable defined for a sample
space in which theoretical probabilities
can be calculated; find the expected
value.
5-2 Mean, Variance, Standard Deviation, and
Expected Value
Find the mean, variance, standard
deviation, and expected value for a
discrete random variable.
Subject to revision
Elementary Statistics Textbook
Elementary Statistics PowerPoint for Chapter 5
Q2_statsactivity_GOFISH (see Math Tasks
on C & I page)
Elementary Statistics Textbook
Elementary Statistics PowerPoint for Chapter 5
Q2_statsactivity_Its To Be Expected (see
Math Tasks on C & I page)
Q2_statstask_CollectingPens
TN Statistics Standards
Statistics Today
Critical Thinking Challenges
Speaking of Statistics
Applying the Concepts
Shelby County Schools2015/2016
Revised 9/23/15
7 of 10
Curriculum and Instruction – Office of Mathematics
2nd Nine Weeks
TN State Standards
7.
8.
Statistics
Essential Understandings
Content & Tasks
Weigh the possible outcomes of a
decision by assigning probabilities to
payoff values and finding expected
values.
Use probabilities to make fair decisions
Extending the Concepts
Data Projects
S-MD
6. Develop a probability distribution for a
random variable defined for a sample
space in which theoretical probabilities
can be calculated; find the expected
value.
8. Use probabilities to make fair decisions
14-3 Simulation Techniques and Expected
Value
S-MD
2. Calculate the expected value of a random
variable; interpret it as the mean of the
probability distribution.
S-MD
6. Develop a probability distribution for a
random variable defined for a sample
space in which theoretical probabilities
can be calculated; find the expected
value.
8. Use probabilities to make fair decisions
5-3 The Binomial Distribution
S-MD (see 5-3 above)
5-4 Other Types of Distributions -OPTIONAL
Find the probabilities for outcomes of
variables, using Geometric, Poisson,
hypergeometric, and multinomial
distributions.
Subject to revision
CLIP Connections
 Construct a probability distribution for a
random variable using a simulation.

Find the expected value of the
simulation.
 Find the exact probability for X successes in
n trials of a binomial experiment.

Find the mean, variance, and
standard deviation for the variable of
a binomial distribution.
Elementary Statistics Textbook
Elementary Statistics 7th edition Bluman
Elementary Statistics PowerPoint for Chapter 14
Q2_statstask_DistractedDriving (see Math
Tasks on C & I page)
Elementary Statistics Textbook
Elementary Statistics PowerPoint for Chapter 5
Q2_statstask_MakinItThroughWinter
Elementary Statistics Textbook
Elementary Statistics PowerPoint for Chapter 5
TN Statistics Standards
Shelby County Schools2015/2016
Revised 9/23/15
8 of 10
Curriculum and Instruction – Office of Mathematics
2nd Nine Weeks
TN State Standards
Statistics
Essential Understandings
Content & Tasks
CLIP Connections
Chapter 6/Sections 1 & 2
(2 weeks for instruction, review, and assessment)
S-MD
11. Use the mean and standard deviation of a
data set to fit it to a normal distribution
and to estimate population percentages.
Recognize that there are data sets for
which such a procedure is not
appropriate. Use calculators,
spreadsheets, and tables to estimate
areas under the normal curve.
6-1 Normal Distributions
 Identify the properties of a normal
distribution.
Find the area under the standard normal
distribution, given various z values.
Elementary Statistics PowerPoint for Chapter 6
S-MD
(See 6-1 above)
6-2 Applications of the Normal Distribution
Find probabilities for a normally
distributed variable by transforming it
into a standard normal variable.
Elementary Statistics Textbook
Elementary Statistics PowerPoint for Chapter 6
Subject to revision
 Identify distributions as symmetric or
skewed.
Elementary Statistics Textbook
Elementary Statistics 7th edition Bluman
TN Statistics Standards
Statistics Today
Critical Thinking Challenges
Speaking of Statistics
Applying the Concepts
Extending the Concepts
Data Projects
Shelby County Schools2015/2016
Revised 9/23/15
9 of 10
Curriculum and Instruction – Office of Mathematics
RESOURCE TOOLBOX
Textbook Resources
Elementary Statistics 7th edition Bluman
http://interactmath.com/
Calculator
Texas Instruments Education
http://www.casioeducation.com/educators
Standards
Common Core Standards - Mathematics
Common Core Standards - Mathematics Appendix A
State Academic Standards (Statistics)
TN Core
The Mathematics Common Core Toolbox
Link to common core glossary
Tennessee’s State Mathematics Standards
Videos
Khan Academy
Interactive Manipulatives
Stat Trek
AmStat.org
Applet Collection
Shodor.org
Rossmanchance.com
Additional Sites
The Data and Story Library
Fed Stats
Bureau of Labor Statistics
Educational Statistics
NCTM Math Illuminations
United States Census Bureau
Core Math Tools
Math is Fun
Gapminder
STatistics Education Web
SCS Math Tasks (Statistics)
CLIP
Literacy Skills and Strategies for Content Area Teachers
(Math, p. 22)
Glencoe Reading & Writing in the Mathematics Classroom
Graphic Organizers (9-12)
Subject to revision
TN Statistics Standards
Shelby County Schools2015/2016
Revised 9/23/15
10 of 10