Download Trig Curriculum Unit Template 2016

Teachers Preparatory High School Curriculum Map
Subject:
Teacher:
Academic Year: 2016 – 2017
Curriculum Sources NYCDOE: http://schools.nyc.gov/Academics/CIPL/default.htm
Unit Title:
Duration of the Unit
Essential Questions
Unit One
Data Analysis and Statistics
Unit Two
Sample Spaces and Probability
Unit Three
Sequences and Series
Unit Four
Trigonometric Ratios and
Functions
5 weeks
 In a normal
distribution, about what
percent of the data lies
within one, two and
three standard
deviations of the mean?
 How can you test
theoretical probability
using sample data?
 What are some
considerations when
undertaking a statistical
study?
 How can you use an
experiment to test a
conjecture?
 How can you use a
sample survey to infer a
conclusion about a
population?
 How can you test a
hypothesis about an
experiment?
5 weeks
 How can you list the
possible outcomes in
the sample space of an
experiment?
 How can you
determine whether two
events are independent
or dependent?
 How can you construct
and interpret a two
way table?
 How can you find
probabilities of
disjoint and
overlapping events?
 How can a tree
diagram help you
visualize the number
of ways in which two
or more events can
occur?
 How can you
determine the
frequency of each
outcome of an event?
5 weeks
 How can you
write a rule for the
nth term of a
sequence?
 How can you
recognize an
arithmetic
sequence from its
graph?
 How can you
recognize a
geometric
sequence from its
graph?
 How can you use
a geometric
sequence to
describe a
pattern?
 How can you find
the sum of an
infinite geometric
series?
 How can you
define a sequence
recursively?
6 - 8 weeks
Content of the Unit
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Student Objectives:
Refer to Cognitive
Rigor Matrix, DOK
&/or
Bloom’s Taxonomy
http://schools.nyc.go
v/NR/rdonlyres/39A
50715-BDF2-4C3C8180-
About 68%, about 95%
and about 99.7%
Determine how close
the experimental
probability from the
sample data is to the
theoretical probability.
Sampling Technique
and wording of survey
questions.
See if the results of the
experiment support the
conjecture.
Conduct a survey using
a random sample, and
use the survey statistics
to infer the population
parameters.
Resample the data and
evaluate the hypothesis.
SWBAT :
 Calculate probabilities
using normal
distributions.
 Use z- scores and the
standard normal table
to find probabilities.
 Recognize data sets
that are normal.
 Distinguish between
populations and

Make a table or
diagram to show all of
the possible outcomes.
 Independent; the
occurrence of one
event does not affect
the occurrence of the
other event.
Dependent; the
occurrence of one
event affects the
occurrence of the other
event.
 You can use a Venn
diagram to construct a
two -way table. Each
entry represents the
number of people in
each category.
 For Disjoint events,
add the probabilities of
each event. For
overlapping events,
add the probabilities of
each event, and
subtract the
probability that both
events occur.
 The Tree diagram
shows all the
possibilities.
 List all possible
outcomes, create a
histogram, or use
combinations.
SWBAT:
 Find sample spaces
 Find theoretical
probabilities
 Calculate
experimental
probabilities.
 Determine whether
events are
independent events.
 Determine the
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Graph the terms
and write a
function rule for
the graph.
The graph of an
Arithmetic
Sequence is
linear.
The graph of a
geometric
sequence is
exponential.
Find the common
ratio between
each consecutive
pairs of term in
geometric series.
State the first term
of a sequence and
a recursive
equation that tells
how an is related
to one or more
preceding terms.
Use the formula
S = a1/ 1- r to
sum an infinite
geometric series.
SWBAT:
 Use sequence
notation to write
terms of
sequences.
 Write a rule for
the nth term of a
sequence.
 Sum the terms of
a sequence to
obtain a series

SWBAT:
 Evaluate
trigonometric
functions of acute
angles.
 Find unknown side
lengths and angle
measures of right
triangles.
 Use trigonometric
functions to solve
D5075FFD36BE/0/C
ognitiveRigorMatri
xReadingWriting.do
c
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samples
Analyze hypotheses.
Identify types of
sampling methods in
statistical studies.
Recognize bias in
sampling.
Analyze methods of
collecting data.
Recognize bias in
survey questions.
Describe experiments
Recognize how
randomization applies
to experiments and
observational studies.
Analyze experimental
designs.
Estimate population
parameters.
Analyze estimated
population
parameters.
Find margin of error
for surveys.
Organize data from
an experiment with
two samples.
Resample data using a
simulation to analyze
a hypothesis.
Make inferences
about a treatment.
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probabilities of
independent and
dependent events.
Find conditional
probabilities.
Make two-way
tables.
Evaluate relative and
conditional relative
frequencies.
Use conditional
relative frequencies
to find conditional
probabilities.
Calculate
probabilities of
compound events.
Use more than one
probability rule to
solve real-life
problems.
Use the formula for
the number of
permutations and the
number of
combinations.
Use combinations
and the Binomial
Theorem to expand
binomials.
Construct and
interpret probability
distributions.
Construct and
interpret binomial
distributions.
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and use
summation
notation.
Identify
arithmetic
sequences.
Write rules for
arithmetic
sequences.
Find the sum of
finite sequences.
Identify
geometric
sequences.
Write rules for
geometric
sequences.
Find sums of
finite geometric
series.
Find partial
sums of infinite
geometric series.
Find sums of
infinite
geometric series.
Evaluate
recursive rules
for sequences.
Write recursive
rules for
sequences.
Translate
between
recursive and
explicit rules for
sequences.
Use recursive
rules to solve
real-life
problems.
real-life problems.
 Draw angles in
standard position.
 Find co-terminal
angles.
 Use radian measure.
 Evaluate
trigonometric
functions of any
angle.
 Find and use
reference angles to
evaluate
trigonometric
functions.
 Explore
characteristics of
sine and cosine
functions.
 Stretch and shrink
graphs of sine and
cosine functions.
 Translate graphs of
sine and cosine
functions.
 Reflect graphs of
sine and cosine
functions.
 Explore
characteristics of
tangent and
cotangent functions.
 Graph tangent and
cotangent functions.
 Graph secant and
cosecant functions.
Essential
Vocabulary
Probability distribution, mean ,
skewed, standard deviation,
median, population, sample,
hypothesis, random sample,
systemic sample, stratified
sample, cluster sample, selfselected sample, convenience
sample, bias, unbiased sample,
experiment, observational study,
survey, simulation, controlled
experiment, control group,
treatment group, randomization,
replication, randomized
comparative experiment,
placebo, descriptive statistics,
inferential statistics, margin of
error, dot plot, outlier,
Probability distributions, event,
binomial distributions, sample
space, theoretical probabilities,
experimental probabilities,
geometric probabilities,
outcome, independent events,
dependent events, conditional
probabilities. Two way table,
relative frequency , compound
event, overlapping events,
disjoint or mutually exclusive
events, permutation,
combination, Binomial
Theorem, n factorial
Assessments
Aligned to
Standards & Skills
Assessments
Assessments
Formative assessment daily
during each class.
Summative assessment
weeklyin the form of
Assessments
Assessments
Rubrics
Aligned to
Standards & Skills
Rubrics (Source)
Rubrics (Source)
Rubrics (Source)
Rubrics (Source)
Materials &
Resources
New Visions work sheets
Jmap.org review sheet
Strategies/
Differentiated
Instruction
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Small group
instructions for low
performers and
special needs students.
Pair Ells with dual
language students to
complete daily tasks
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
Small group
instructions for low
performers and
special needs
students.
Pair Ells with dual
language students to

Mixed ability groups
to help special needs
students.

complete daily tasks
Mixed ability groups
to help special needs
students.
UDL/SWD
Accommodations
ELLS
Accommodations
Pair Ells with bilingual
students to assist with
translation of daily activities.
Translate given work sheet
Standards/Skills
Common Core Standards
Addressed
HSS-ID.A.4
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 set
for which such a procedure is
not appropriate. Use calculators
to estimate areas under the
normal curve.
Common Core
http://www.corestand
ards.org/thestandards
TPS Foci:
College and Career
Readiness Anchor
Standards for:
Reading
1. Read closely to
determine what the
text says explicitly
and to make logical
inferences from it;
cite specific textual
evidence when
writing or speaking to
support conclusions
drawn from the text.
Writing
1. Write arguments to
support claims in an
analysis of
substantive topics or
texts, using valid
reasoning and
HSS-IC.A.2
Decide if a specified model is
consistent with results from a
given data- generating process,
e.g...using simulation.
HSS-IC.A.1
Understand statistics as a
process for making inferences
about population parameters
based on a random sample from
that population.
HSS-IC.B.3
Recognizing the purposes of and
differences among sample
surveys, experiments, and
observational studies; explain
how randomization relates to
each.
Common Core Standards
Addressed
HSS-CP.A.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” )
HSS-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.
HSS-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 .
HSS-CP.A.5
Common Core Standards
Addressed
HSF-IF.A.3
Recognize that sequences
are functions…whose
domain is a subset of the
integers..
HSB-BF.A.2
Write arithmetic sequences
& geometric sequences…
with an explicit formula,
use them to model
situations.
HSF-LE. A.2
Construct Linear
…functions, including
arithmetic …sequences,
given a graph, a
description of a
relationship…
HSA-SSE.B.4
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.
HSF-BF.A.1a
Determine an explicit
expression, a recursive
process, or steps for
Common Core Standards
Addressed
relevant and
sufficient evidence.
Speaking and
Listening
1. Prepare for and
participate effectively
in a range of
conversations and
collaborations with
diverse
partners, building on
others’ ideas and
expressing their own
clearly and
persuasively.
HSS-IC.B.6
Evaluate reports based on data.
HSS-IC.B.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.
HSS-IC.B.5
Use data from a randomized
experiment to compare two
treatments; use simulations to
decide if differences between
parameters are significant.
Recognize and explain the
concepts of conditional
probability and independence in
everyday language and
everyday situations.
HSS-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.
HSS-CP.B.8
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 the
answer in terms of the model.
HSS-CP.A.4
Construct and interpret twoway frequency tables of data
when two categories are
associated with each object
being classified. Use the twoway table as a sample space to
decide if events are
independent and to approximate
conditional probabilities.
HSS-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.
HSS-CP.B.9
Use permutations and
combinations to compute
probabilities of compound
events and solve problems
HSA-APR.C.5
Know and apply the Binomial
Theorem for the expansion of
(x + y )n in powers of x and y
calculation from a context.
for a positive integer n, where x
and y are any numbers, with
coefficients determined for
example by Pascal’s Triangle.
New York
NY State Standard, Key Idea
NY State Standard, Key Idea
http://www.emsc.nys
ed.gov/nysatl/standar
ds.html
Performance Indicators-Students will:
 Calculate probabilities
using normal
distributions.
 Use z- scores and the
standard normal table to
find probabilities.
 Recognize data sets that
are normal.
 Distinguish between
populations and
samples
 Analyze hypotheses.
 Identify types of
sampling methods in
statistical studies.
 Recognize bias in
sampling.
 Analyze methods of
collecting data.
 Recognize bias in
survey questions.
 Describe experiments
 Recognize how
randomization applies
to experiments and
observational studies.
 Analyze experimental
designs.
 Estimate population
parameters.
 Analyze estimated
population parameters.
 Find margin of error for
surveys.
 Organize data from an
experiment with two
samples.
Performance Indicators-Students will:
 Find sample spaces
 Find theoretical
probabilities
 Calculate experimental
probabilities.
 Determine whether
events are independent
events.
 Determine the
probabilities of
independent and
dependent events.
 Find conditional
probabilities.
 Make two-way tables.
 Evaluate relative and
conditional relative
frequencies.
 Use conditional
relative frequencies to
find conditional
probabilities.
 Calculate probabilities
of compound events.
 Use more than one
probability rule to
solve real-life
problems.
 Use the formula for
the number of
permutations and the
number of
combinations.
 Use combinations and
the Binomial Theorem
to expand binomials.
 Construct and interpret
NY State Standard, Key
Idea
NY State Standard, Key
Idea
Performance Indicators-Students will:
 Use sequence
notation to write
terms of
sequences.
 Write a rule for
the nth term of a
sequence.
 Sum the terms of
a sequence to
obtain a series and
use summation
notation.
 Identify arithmetic
sequences.
 Write rules for
arithmetic
sequences.
 Find the sum of
finite sequences.
 Identify geometric
sequences.
 Write rules for
geometric
sequences.
 Find sums of
finite geometric
series.
 Find partial sums
of infinite
geometric series.
 Find sums of
infinite geometric
series.
 Evaluate recursive
rules for
sequences.
Performance Indicators-Students will:


Resample data using a
simulation to analyze a
hypothesis.
Make inferences about
a treatment.

probability
distributions.
Construct and interpret
binomial distributions.



Write recursive
rules for
sequences.
Translate between
recursive and
explicit rules for
sequences.
Use recursive
rules to solve reallife problems.