Unit of Study 1
AdvMath
Approximate Time Frame: 2 Weeks
WSH #2 – 8/2013
Domain: Build a Function that Models a Relationship Between Two Quantities
Cluster: Extend the properties of exponents to rational exponents
Standard(s):
F.BF
9-12.F.BF.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and
exponents.
Math Content Objectives
I can:
Solve logarithmic functions using exponentials as the inverse.
Solve exponential functions using logarithms as the inverse.
Vocabulary
Teacher’s Resources and Notes
function
logarithm
exponential
inverse
Solve problems using logarithms and exponents.
Graph, differentiate, and identify exponential and logarithmic
functions.
Unit of Study 1 - Additional Resources
Assessment
Unit of Study 1 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 2
AdvMath
Approximate Time Frame: 1 Weeks
WSH #2 – 8/2013
Domain: Linear and Exponential Models
Cluster: Construct and Compare Linear and Exponential Models and Solve Problems
Standard(s):
F.LE
9-12.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
 1a- Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
 1b- Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
 1c- Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
9-12.F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output
pairs (include reading these from a table).
9-12.F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more
generally) as a polynomial function.
9-12.F.LE.4 For exponential models, express as a logarithm the solution to ab = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm
using technology.
ct
Math Content Objectives
I can:
Determine whether data is linear or exponential by using a table or
graph.
Use graphing calculator regression models to determine whether linear or
exponential models best fit the data.
Determine whether a situation will produce a linear or exponential
relationship in word applications.
Construct exponential functions given geometric sequences.
Apply exponential functions to real-world applications.
Apply arithmetic and geometric sequences to real-world applications.
Compare linear, quadratic, other high order polynomial functions, and
exponential graphs and tables.
Analyze graphical representations of polynomial and exponential
functions rate of change.
Vocabulary
Teacher’s Resources and Notes
exponential function
exponential growth
exponential decay
slope
rate of change
arithmetic sequences
geometric sequences
mapping
polynomial function
Unit of Study 2 - Additional Resources
Assessment
Unit of Study 2 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 3
AdvMath
Approximate Time Frame: 1 Weeks
WSH #2 – 8/2013
Domain: Linear and Exponential Models
Cluster: Interpret Expressions for Functions in Terms of the Situation they Model
Standard(s):
F.LE
9-12.F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
Math Content Objectives
I can:
State and interpret the parameters of linear and exponential
functions in terms of the context of a given situation.
Interpret linear and exponential functions.
Vocabulary
Teacher’s Resources and Notes
function
linear function
exponential function
parameter
expression
extraneous solutions
Unit of Study 3 - Additional Resources
Assessment
Unit of Study 3 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 4
AdvMath
Approximate Time Frame: 2 Weeks
Domain: Complex Number System
Cluster: Represent Complex Numbers and Their Operations on the Complex Plane
Standard(s):
WSH #2 – 8/2013
N.CN
9-12N.CN.1 Know there is a complex number i such that i = –1, and every complex number has the form a + bi with a and b real.
9-12N.CN.2 Use the relation i2=-1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
9-12 N.CN.5 (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this
representation for computation. For example, (1 – i√3) = 8 because (1 – i√3) has modulus 2 and argument 120°.
9-12N.CN.6 (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the
numbers at its endpoints.
9-12N.CN.7 Solve quadratic equations with real coefficients that have complex solutions.
9-12N.CN.8(+) Extend polynomial identities to the complex numbers. For example, rewrite x + 4 as (x + 2i)(x – 2i).
9-12 N.CN.9 (+) Use complex numbers in polynomial identities and equations. Know the Fundamental Theorem of Algebra; show that it is true for quadratic
polynomials.
2
3
2
Math Content Objectives
Vocabulary
Teacher’s Resources and Notes
I can:
complex number
imaginary number
Find the a+bi form of a complex number
Identify the real portion and the imaginary portion of the complex rational number
real number
number a+bi, with a and b being real
irrational number
numbers.
purely imaginary
Simplify powers of idown to ±1 or ± iusing the basic fact that
standard complex
i2=-1.
number form
Add, subtract, and multiply complex numbers using the
scalar
multiplication
commutative, associative, and distributive properties.
foil
method
Multiply a scalar value by a complex number using the
commutative, associative
distributive property.
distributive property
Addition, subtraction, multiplication, and conjugation of
complex
conjugates
complex numbers using both algebra and graphing on a
complex
plane
complex plane.
distance formula
Find the distance between two points in the complex plane.
midpoint formula
Find the midpoint of a line segment between two points in the
modulus of the difference
complex plane.
quadratic equation
Prove that the distance between two points’ z and w in the
factoring
complex plane is |z-w|.
completing the square
Write the imaginary roots as a pair of complex conjugate
quadratic formula
numbers.
polynomial identities
Use completing the square to solve a quadratic equation that
sums of squares
has no real roots.
polynomial equations
Use the quadratic formula to solve a quadratic equation that has
complex zeros
no real roots.
conjugate pairs
Use complex numbers in polynomial identities and equations
synthetic substitution
Extend polynomial identities to the complex numbers.
Rewrite a polynomial equation into a complex equations.
Determine the number of real or complex zeros in a function.
Find the number of zeros either real or complex of an equation.
Unit of Study 4 - Additional Resources
Assessment
Unit of Study 4 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 5
AdvMath
Approximate Time Frame: 1 Weeks
WSH #2 – 8/2013
Domain: Vector and Matrix Quantities
Cluster: Represent and Model with Vector Quantities & Perform Operations on Vectors
Standard(s):
N.VM
9-12N.VM.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.
9-12N.VM.4 (+) Add and subtract vectors.
a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the
magnitudes.
b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
c. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction.
Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
Math Content Objectives
Vocabulary
Teacher’s Resources and Notes
I can:
vector
magnitude
Interpret information to describe vectors used to model
direction
problems.
direction angle
Use vectors to solve problems involving vector quantities.
bearing & heading
Add vectors end-to-end, component-wise, and by the
displacement vector
parallelogram rule.
Calculate the magnitude and direction of the sum of two vectors. angle of elevation
angle of depression
Subtract vectors using an additive inverse.
resultant
horizontal component
vertical component
vector addition
& subtraction
Unit of Study 5 - Additional Resources
Assessment
Unit of Study 5 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 6
AdvMath
Approximate Time Frame: 2 Weeks
WSH #2 – 8/2013
Domain: Arithmetic with Polynomials and Rational Expressions
Cluster: Use Polynomial Identities to Solve Problems
Standard(s):
A.APR
9-12.A.APR.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x + y ) = (x – y ) +(2xy) can be used
to generate Pythagorean triples.
9-12.A.APR.5(+) Know and apply the Binomial Theorem for the expansion of (x + y) in powers of x and y for a positive integer n, where x and y are any numbers, with
coefficients determined for example by Pascal’s Triangle.
The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.
2
2 2
2
2 2
2
n
1
1
Math Content Objectives
I can:
The student can use polynomial identities to describe numerical
relationships.
The student can simplify and prove polynomial identities using
properties of algebra.
The student can demonstrate mathematical reasoning in
algebra.
Find the binomial expansion for (x+y)^n by applying Pascal’s
triangle.
Prove the binomial theorem by mathematical induction or a
combinatorial argument.
Define the Binomial theorem and compute combinations.
Vocabulary
Teacher’s Resources and Notes
polynomial identity
factor
rational polynomials
degree
zero
roots
decompose
recompose
notation
polynomial expressions
and equations
binomial theorem
Pascal’s triangle
expansion
coefficients
exponents
combinatorial argument
probability distribution
mathematical induction
Unit of Study 6 - Additional Resources
Assessment
Unit of Study 6 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 7
AdvMath
Approximate Time Frame: 1 Weeks
Domain: Rewrite Rational Expressions
Cluster: Use Polynomial Identities to Solve Problems
Standard(s):
WSH #2 – 8/2013
A.APR
9-12.A.APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the
degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
9-12.A.APR.7 (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division
by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Math Content Objectives
Vocabulary
Teacher’s Resources and Notes
I can:
polynomial
Rewrite a rational expression containing a polynomial divided by long division
degree
a monomial using inspection, long division or synthetic division.
rational expression
Demonstrate understanding by rewriting a rational expression
containing a polynomial divided by another polynomial using long common denominator
for rational expressions
division.
reciprocal
Explain and demonstrate how to add, subtract, multiply and
factor
divide rational expressions.
Find the number that will make a rational expression undefined.
Unit of Study 7 - Additional Resources
Assessment
Unit of Study 7 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 8
AdvMath
Approximate Time Frame: 2 Weeks
WSH #2 – 8/2013
Domain: Reasoning with Equations and Inequalities
Cluster: Understand Solving Equations as a Process of Reasoning and Explain the Reasoning
Standard(s):
A.REI
9-12.A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Cluster: Represent and Solve Equations and Inequalities Graphically
Standard(s):
9-12A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x);
find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x)
and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Math Content Objectives
I can:
Solve an equation in radical form and identify the domain.
Solve an equation in rational form and identify the domain.
Examples showing how extraneous solutions may arise when
solving rational and radical equations.
Vocabulary
Teacher’s Resources and Notes
radical form (using
square roots or roots to
the nth power)
rational form (fractions)
extraneous solutions
Unit of Study 8 - Additional Resources
Assessment
Unit of Study 8 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 9
AdvMath
Approximate Time Frame: 2 Weeks
WSH #2 – 8/2013
Domain: Functions
Cluster: Analyze Functions Using Different Representation
Standard(s):
F.IF
9-12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
 9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. (Algebra I)
 9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions (Algebra I and Algebra II)
 9-12.F.IF.7c- Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. (Algebra II)
 9-12.F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. (4th course)
 9-12.F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and
amplitude (Algebra I and Algebra II)
4th course - Logarithmic and trigonometric functions.
Math Content Objectives
Vocabulary
Teacher’s Resources and Notes
I can:
maxima
minima
increasing
Identify and describe key features and characteristics of graphs. decreasing
linear function
Use features of equations and graphs to predict the behavior of a square root function
cube root function
function.
step function
Use functions to solve problems
piecewise function
step function
zeros of functions
end behavior
rational functions
asymptotes
logarithmic functions
trigonometric functions
period
midline
Graph functions.
Unit of Study 9 - Additional Resources
Assessment
Unit of Study 9 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 10
AdvMath
Approximate Time Frame: 3 Weeks
WSH #2 – 8/2013
Domain: Expressing Geometric Properties with Equations
F.IF
Cluster:
Translate Between the Geometric Description and the Equation for a Conic Section
Standard(s):
G.GPE
9-12.G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle
given by an equation.
9-12.G.GPE.2 Derive the equation of a parabola given a focus and directrix.
9-12.G.GPE.3 Derive the equations of ellipses and hyperbolas given foci and directrices.
Math Content Objectives
I can:
Describe the characteristics of a parabola given its equation.
Derive the equation for a parabola given the focus and directrix.
Explain how the Pythagorean Theorem can be used to derive
the equation of a circle.
Write the equation of a circle, given the center and radius.
Complete the square within the equation of a circle in order to
find the center and radius.
Describe the characteristics of an ellipse and hyperbola given its
equation.
Derive the equations for an ellipse and hyperbola given foci and
directrices.
Vocabulary
Teacher’s Resources and Notes
circle
radius
center of circle
Pythagorean Theorem
focus
directrix(es)
derive
equation
parabola
distance
leading coefficient
completing the square
diameter
hypotenuse
ellipses
hyperbola
Unit of Study 10 - Additional Resources
Assessment
Unit of Study 10 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 11
AdvMath
Approximate Time Frame: 1 Weeks
WSH #2 – 8/2013
Domain: Conditional Probability and the Rules of Probability
Cluster: Understand Independence and Conditional Probability and use them to Interpret Data
Standard(s):
S-CP
9-12.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”.)
9-12.S.CP.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.
9-12.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.
9-12.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 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.
9-12.S.CP.5 Understand independence and conditional probability and use them to interpret data. 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.*
Math Content Objectives
I can:
and
or
Describe events as subsets of a sample space.
subsets
Organize outcomes of an event in tree diagrams, Venn
not
diagrams, or contingency tables.
union
Analyze data and events to determine unions, intersections
intersection
and/or complements from sample sets.
notation
Calculate the probability of two (or more) independent events.
tree diagram
Determine if two events are independent when given the
probability of A, the probability of B, and the probability of A and Venn diagram
sample space
B.
events, outcomes
Determine if two events are independent or dependent.
complements
Calculate the conditional probability of an event.
contingency table
Collect data and display in a two-way frequency table of that
independent events
data.
Interpret the data to determine if it is independent or dependent. dependent events
Determine conditional probability from the data.
conditional probability
Identify real world situations in which conditional probability can bivariate data
be found.
two-way frequency table
Find a real world situation involving conditional probability and
independence
make conjectures based on the situation.
Calculate conditional probability given a real world situation.
Vocabulary
Teacher’s Resources and Notes
Unit of Study 11 - Additional Resources
Assessment
Unit of Study 11 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 12
AdvMath
Approximate Time Frame: 1 Weeks
WSH #2 – 8/2013
Domain: Conditional Probability and the Rules of Probability
S.CP
F.IF
Cluster:
Use the Rules of Probability to Compute Probabilities of Compound Events in a Uniform Probability Model
Standard(s):
9-12.S.CP.6 Use the rules of probability to compute probabilities of compound events in a uniform probability model. 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.*
9-12.S.CP.7 Use the rules of probability to compute probabilities of compound events in a uniform probability 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.
9-12.S.CP.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.
S.CP.9 (+) Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use permutations and combinations to compute
probabilities of compound events and solve problems.
Math Content Objectives
I can:
Determine the type of probability that exists in a real world
situation and calculate probabilities of the events.
Recognize situations that have compound events and calculate
probabilities of events determined by the situation.
Use probability rules to calculate a probability which has more
than one event affecting the results.
Determine if compound events are mutually exclusive or
inclusive.
Calculate the probability of compound events that are inclusive
using the addition rule and interpret the result in context of the
situation.
Calculate the probability of the intersection of two events using
the multiplication rule and interpret the result in context of the
situation.
Determine if permutations or combinations should be used to
find the probability of a given situation.
Use permutations to compute probabilities of compound events
and solve real world problems.
Use combinations to compute probabilities of compound events
and solve real world problems.
Vocabulary
compound events
conditional probability
uniform probability model
compound events
mutually exclusive events
inclusive events
addition rule of probability
inspection
multiplication rule
of probability
permutations
combinations
ordered list
Teacher’s Resources and Notes
Unit of Study 12- Additional Resources
Assessment
Unit of Study 12 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 13
AdvMath
Approximate Time Frame: 2 Weeks
Domain: Using Probability to Make Decisions
Cluster: Calculate Expected Values and use Them to Solve Problems
Standard(s):
WSH #2 – 8/2013
S.MD
9-12.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.
9-12.S.MD.2 (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
9-12.S.MD.3. (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the
expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiplechoice test where each question has four choices, and find the expected grade under various grading schemes.
9-12.S.SMD.4 (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected
value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per
household. How many TV sets would you expect to find in 100 randomly selected households?
Math Content Objectives
I can:
Identify the numerical values of events in a sample space that
define the random variable.
Determine a the probabilities associated with the events in the
sample space (probability distribution).
Graphically display probability distributions using methods such
as frequency distributions, grouped frequency distributions,
histograms, frequency polygons, stem-and-leaf plots, bar charts,
and normal probability distributions.
Calculate the expected value of the random variable by finding
the mean of the probability distribution.
Find the mean of the probability distribution by using weighted
averages.
Create a probability distribution of theoretical probabilities of an
experiment.
Use a probability distribution model to find the probability and
expected values of a specific outcome.
Make a table of values to show how the probabilities of an
experiment are distributed.
Make a histogram to describe the theoretical probabilities an
experiment.
Find the expected value of an occurrence using the distribution
probabilities.
Vocabulary
event
sample space
probability
frequency distribution
grouped frequency
distribution
histogram
frequency polygon
stem-and-leaf plot
bar chart
normal probability
distribution
mean
probability distribution
random variable
theoretical probability
probability histogram
expected value
empirically assigned
probabilities
Teacher’s Resources and Notes
Unit of Study 13 - Additional Resources
Assessment
Unit of Study 13 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 14
AdvMath
Approximate Time Frame: 2 Weeks
WSH #2 – 8/2013
Domain: Using Probability to Make Decisions
Cluster: Using Probability to Evaluate Outcomes of Decisions
Standard(s):
S.MD
9-12.S.MD.6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
9-12. S.MD.7. (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
9-12.SMD.5(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
a. Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.
b. Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy
using various, but reasonable, chances of having a minor or a major accident.
Math Content Objectives
I can:
Use a random number generator to make fair decisions.
Use lots to make impartial decisions
Determine experimental probability of an event and compare it to
the theoretical.
Analyze a situation and determine the various outcomes.
Use probability to assignment values to the various outcomes.
Assign probabilities to outcomes of a game or lottery and
compare the chance of success to loss.
Determine payoff of an event.
Vocabulary
Teacher’s Resources and Notes
random number
lots
probability
theoretical probability
contingency table
outcome
odds
chance
observed or experimental
probability
Unit of Study 14 - Additional Resources
Assessment
Unit of Study 14 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 15
AdvMath
Approximate Time Frame: 1 Weeks
WSH #2 – 8/2013
Domain: Interpreting Categorical and Quantitative Data
Cluster: Summarize, Represent, and Interpret Data on a Single Count or Measurement Variable
Standard(s):
S.ID
9-12.S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of
two or more different data sets.*
9-12.S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).*
9-12.S.ID.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
sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
Math Content Objectives
I can:
Compare center and spread of two data sets.
Analyze the shapes of two or more data distributions to choose
the appropriate statistical measurements to compare data sets.
Explain the reasoning for choosing appropriate measurements.
Identify the measures of central tendency.
Identify the measures of spread.
Interpret the meaning of the measures of central tendency in
context of the graph.
Describe how the changes of data affect the shape of the data
set.
Explain the context of the given set of data.
Vocabulary
Teacher’s Resources and Notes
center
mean
median
spread
interquartile range
upper quartile
lower quartile
standard deviation
outliers
box and whiskers
central tendency
mode
range
bell shaped curve
u-shaped
right & left skewed
symmetrical
normal distribution
Unit of Study 15 - Additional Resources
Assessment
Unit of Study 15 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 16
AdvMath
Approximate Time Frame: 1 Weeks
WSH #2 – 8/2013
Domain: Making Inferences and Justifying Conclusions
Cluster: Understanding and Evaluate Random Processes Underlying Statistical Experiments
Standard(s):
S.IC
9-12.S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
9-12.S.IC.2 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?
Math Content Objectives
I can:
Determine the type of collection, what is being measured, and
the bias that may be associated with a given scenario.
Design a study, choose a collection method, and explain
potential issues behind the study.
Find the probability of a randomly chosen value from a given
graph.
Determine the median, mean, mode from a given frequency
graph.
Compare experimental probability to the theoretical probability to
determine if the data-generating process was likely accurate or
flawed.
Create accurate data-generating processes.
Evaluate the validity of existing models by using data-generating
processes.
Vocabulary
Teacher’s Resources and Notes
population
inference
population parameter
random
fair
simulation
outcome
probability
trial
Unit of Study 16 - Additional Resources
Assessment
Unit of Study 16 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 17
AdvMath
Approximate Time Frame: 1 Weeks
WSH #2 – 8/2013
Domain: Making Inferences and Justifying Conclusions
Cluster: Make Inferences and Justify Conclusions from Sample Surveys, Experiments, and Observational Studies
S.IC
9-12.S.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
9-12.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.
9-12.S.IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
9-12.S.IC.6 Evaluate reports based on data
Math Content Objectives
I can:
sample survey
experiment
Explain why a sample survey, an experiment, or an
observational study
observational study is most appropriate for a situation.
randomization
Distinguish between sample surveys, experiments, and
margin of error
observational studies.
Recognize and explain whether a sample survey, experiment, or confidence interval
randomized experiment
observational study is random or if it has bias.
treatment
Estimate a population mean or proportion using data from a
statistically significant
sample survey.
Type I and II error
Determine the margins of error for population estimates.
Determine confidence intervals for a sample survey.
Use a randomization test to decide if an experiment provides
statistically significant (outer 5%) evidence that one treatment is
more effective than another.
Compare two treatments, using data from a randomized
experiment.
Recognize when a Type I or Type II error may be occurring.
Define the characteristics of experimental design (control,
randomization, and replication).
Evaluate the experimental study design, how the data was
gathered, and what analysis (numerical or graphical) was used
(ex: use of randomization, control, and replication).
Draw conclusions based on graphical and numerical summaries.
Vocabulary
Teacher’s Resources and Notes
Unit of Study 17 - Additional Resources
Assessment
Unit of Study 17 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 18
AdvMath
Approximate Time Frame: 2 Weeks
WSH #2 – 8/2013
Domain: Seeing Structure in Expressions
Cluster: Write Expressions in Equivalent Forms to Solve Problems
A.SSE
9-12.A.SSE.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. For example,
calculate mortgage payments.
Math Content Objectives
I can:
Derive the formula for a finite geometric series and explain what
each component of the formula represents.
Apply the formula to calculate the value of a real world finite
geometric series.
Vocabulary
Teacher’s Resources and Notes
infinite
finite
recursive formula
explicit formula
common ratio; r
number of terms; N
A1; first term
sequence
series
geometric series
Unit of Study 18 - Additional Resources
Assessment
Unit of Study 18 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 19
AdvMath
Approximate Time Frame: 2 Weeks
WSH #2 – 8/2013
Domain: Building Functions
Cluster: Build a Function that Models a Relationship Between Two Quantities
F.BF
9-12.F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Math Content Objectives
I can:
Calculate the common difference in an arithmetic sequence.
Calculate the common ratio in a geometric sequence.
Calculate an indicated term in an arithmetic or geometric
sequence.
Write an explicit formula of an arithmetic or geometric sequence
that models a situation.
Write a recursive formula of an arithmetic or geometric sequence
that models a situation.
Convert an explicit formula to its corresponding recursive
formula.
Convert a recursive formula to its corresponding explicit formula,
if possible.
Vocabulary
Teacher’s Resources and Notes
arithmetic sequence
common difference
geometric sequence
recursive formula
explicit formula
Unit of Study 19 - Additional Resources
Assessment
Unit of Study 19 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 20
AdvMath
Approximate Time Frame: 1 Weeks
WSH #2 – 8/2013
Domain: Linear and Exponential Models
Cluster: Build a Function that Models a Relationship Between Two Quantities
F.LE
9-12.F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output
pairs (include reading these from a table).*
Math Content Objectives
Vocabulary
Teacher’s Resources and Notes
I can:
linear function
exponential function
Construct linear functions given arithmetic sequences.
arithmetic sequence
Construct exponential functions given geometric sequences.
geometric sequence
Develop arithmetic and geometric sequences given multiple
graph
representation of data (table, graph, input-output pairs, or
table
description).
Apply linear and exponential functions to real-world applications. input-output pair
mapping
Apply arithmetic and geometric sequences to real-world
relationship
applications.
Unit of Study 20 - Additional Resources
Assessment
Unit of Study 20 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 21
AdvMath
Approximate Time Frame: 2 Weeks
WSH #2 – 8/2013
Domain: Arithmetic with Polynomials and Rational Expressions
Cluster: Use Polynomial Identities to Solve Problems
A.APR
9-12.A.APR.5(+) Know and apply the Binomial Theorem for the expansion of (x + y) in powers of x and y for a positive integer n, where x and y are any numbers, with
coefficients determined for example by Pascal’s Triangle.
The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.
n
1
1
Math Content Objectives
I can:
Find the binomial expansion for (x+y)^n by applying Pascal’s
triangle.
Solve applications to find the number of possible ways of a
situation
Prove the binomial theorem by mathematical induction or a
combinatorial argument.
Vocabulary
Teacher’s Resources and Notes
binomial theorem
Pascal’s triangle
expansion
coefficients
mathematical induction
combinatorial argument
exponents
probability distribution
Unit of Study 21 - Additional Resources
Assessment
Unit of Study 21 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments
Unit of Study 22
AdvMath
Approximate Time Frame: 2 Weeks
WSH #2 – 8/2013
Domain: Limits
Cluster: Use Polynomial Identities to Solve Problems
Math Content Objectives
Vocabulary
Teacher’s Resources and Notes
I can:
derivative
antiderivative
Find the limit of a function.
limits
Discover the techniques of evaluating a limit of a quotient.
Sketch the graph of a rational function through various medians. integrals
rational function
Determine what makes a series converge or diverge.
converge
Use derivatives to sketch the curve of functions.
diverge
Define and find the derivatives of functions.
Use the power series of a function to find the infinite series of a power series
functional value.
Unit of Study 22 - Additional Resources
Assessment
Unit of Study 22 Formative Assessment.
Possible Daily/Weekly Formative Assessments: Exit Slips, Observation, Daily Work, Homework, Summative Assessments