Download algebra 2, part 1

Resource Title: ALG 055 & 057: Algebra 2, Parts 1 & 2
Publisher: BYU Independent Study
Algebra II, Common Core Correlation Document
 Indicates a modeling standard linking mathematics to everyday life, work, and decision-making
(+) Indicates additional mathematics to prepare students for advanced courses.
Standard
Number and Quantity: The Complex Number System (N-CN)
-- Perform arithmetic operations with complex numbers.
1.0 Know there is a complex number i such that i 2 = −1,
and every complex number has the form a + bi with a
and b real.
2.0
Use the relation i 2 = –1 and the commutative,
associative, and distributive properties to add,
subtract, and multiply complex numbers.
Develop URL
Practice URL
Assess URL
ALG 055:
Lesson: Radical Expressions
• Section: Imaginary Numbers,
first page
• Section: Simplifying
Expressions with Complex
Numbers
ALG 055:
Lesson: Radical Expressions
Section: Simplifying
Expressions with Complex
Numbers
ALG 055:
• Self Check: Imaginary
Numbers
• Self Check: Simplifying
Expressions with Complex
Numbers
ALG 055:
Speedback Assignment:
Radical Expressions
ALG 055:
Self Check: Simplifying
Expressions with Complex
Numbers
ALG 055:
Speedback Assignment:
Radical Expressions
ALG 055:
Self Check: Solving Quadratic
Equations by Using the
Quadratic Formula
ALG 055:
Speedback Assignment:
Quadratic Equations
ALG 055:
Self Check: Solving Quadratic
Equations by Factoring
ALG 055:
Speedback Assignment:
Quadratic Equations
ALG 055:
Self Check: Solving Quadratic
Equations by Graphing
ALG 055:
Speedback Assignment:
Quadratic Graphing
-- Use complex numbers in polynomial identities and equations.
ALG 055:
7.0 Solve quadratic equations with real coefficients that
Lesson: Quadratic Equations
have complex solutions.
8.0
9.0
(+) Extend polynomial identities to the complex
numbers. For example, rewrite x2 + 4 as (x + 2i)(x –
2i).
(+) Know the Fundamental Theorem of Algebra; show
that it is true for quadratic polynomials.
Algebra: Seeing Structure in Expressions (A-SSE)
-- Interpret the structure of expressions.
Section: Solving Quadratic
Equations by Using the
Quadratic Formula, pp. 8–10
ALG 055:
Lesson: Quadratic Equations
Section: Solving Quadratic
Equations by Factoring
ALG 055:
Lesson: Quadratic Equations
Section: Solving Quadratic
Equations by Graphing
Standard
1.0
2.0
Interpret expressions that represent a quantity in
terms of its context. 
a. Interpret parts of an expression, such as terms,
factors, and coefficients.
b. Interpret complicated expressions by viewing one
or more of their parts as a single entity. For example,
interpret P(1 + r)n as the product of P and a factor not
depending on P.
Use the structure of an expression to identify ways to
rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2,
thus recognizing it as a difference of squares that can
be factored as (x2 – y2)(x2 + y2).
-- Write expressions in equivalent forms to solve problems.
4.0 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. 
Develop URL
Practice URL
Assess URL
This standard is a fundamental
idea taught throughout the
entire math portfolio, starting in
pre-algebra. It is inherent in
many of the examples and
assessments.
This standard is a fundamental
idea taught throughout the
entire math portfolio, starting in
pre-algebra. It is inherent in
many of the examples and
assessments.
This standard is a fundamental
idea taught throughout the
entire math portfolio, starting in
pre-algebra. It is inherent in
many of the examples and
assessments.
ALG 055:
Lesson: Quadratic Equations
• Section: Solving Quadratic
Equations by Factoring, first
few pages and examples
• Section: Solving Quadratic
Equations by Completing the
Square, first few pages
ALG 055:
• Self Check: Solving
Quadratic Equations by
Factoring
• Self Check: Solving
Quadratic Equations by
Completing the Square
ALG 055:
Speedback Assignment:
Quadratic Equations
ALG 057:
Lesson: Exponential and
Logarithmic Functions
Section: Exponential Functions,
first few pages
ALG 057:
Self Check: Exponential
Functions
ALG 057:
Speedback Assignment:
Exponential and Logarithmic
Functions
ALG 055:
Self Check: Getting to Know
the Parts of a Polynomial and
Their Properties
ALG 055:
Speedback Assignment:
Polynomials
ALG 055:
ALG 055:
Algebra: Arithmetic with Polynomials and Rational Expressions (A-APR)
-- Perform arithmetic operations on polynomials.
ALG 055:
1.0 Understand that polynomials form a system
Lesson: Polynomials
analogous to the integers, namely, they are closed
Section: Getting to Know the
under the operations of addition, subtraction, and
Parts of a Polynomial and Their
multiplication; add, subtract, and multiply
Properties, first few pages
polynomials. (revised)
-- Understand the relationship between zeros and factors of polynomials.
ALG 055:
2.0 Know and apply the Remainder Theorem: For a
Page 2
.
Standard
Develop URL
Practice URL
Assess URL
Lesson: Polynomial
Section: Dividing Polynomials
using Synthetic and Long
Division, entire section
Self Check: Dividing
Polynomials using Synthetic
and Long Division
Speedback Assignment:
Polynomials
ALG 057:
Lesson: Polynomial Functions
Section: Polynomial Factors
ALG 057:
Self Check: Polynomial
Factors
ALG 057:
Speedback Assignment:
Polynomial Functions
Identify zeros of polynomials when suitable
factorizations are available, and use the zeros to
construct a rough graph of the function defined by the
polynomial.
-- Use polynomial identities to solve problems.
4.0 Prove polynomial identities and use them to describe
numerical relationships. For example, the polynomial
identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used
to generate Pythagorean triples.
5.0 (+) Know and apply the Binomial Theorem for the
expansion of (x + y)n 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.)
-- Rewrite rational expressions.
6.0 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.
ALG 057:
Lesson: Polynomial Functions
Section: Solving Polynomials by
Graphing, and Finding the
Zeros of the Function
ALG 057:
Self Check: Solving
Polynomials by Graphing, and
Finding the Zeros of the
Function
ALG 057:
Speedback Assignment:
Polynomial Functions
ALG 055:
Lesson: Polynomials
Section: Factoring Polynomials,
before example problem 1
ALG 055:
Self Check: Polynomials
ALG 055:
Speedback Assignment:
Polynomials
ALG 055:
Lesson: Sequences and Series
Section: Pascal's Triangle and
The Binomial Theorem, after
the first Math Lab
ALG 055:
Self Check: Pascal's Triangle
and The Binomial Theorem
ALG 055:
Speedback Assignment:
Sequences and Series
ALG 055:
Lesson: Polynomials
Section: Dividing Polynomials
ALG 055:
Self Check: Dividing
Polynomials
ALG 055:
Speedback Assignment:
Polynomials
ALG 057:
Lesson: Rational Polynomial
Expressions
Section: Rational Expressions
ALG 057:
Self Check: Rational
Expressions
ALG 057:
Speedback Assignment:
Rational Polynomial
Expressions
7.0
ALG 057:
Lesson: Rational Functions
• Section: Multiplying and
Dividing Rational
Expressions
ALG 057:
Self Check: Multiplying and
Dividing Rational Expressions
Self Check: Adding and
Subtracting Rational
ALG 057:
Speedback Assignment:
Rational Functions
polynomial p(x) and a number a, the remainder on
division by x – a is p(a), so p(a) = 0 if and only if (x – a)
is a factor of p(x).
3.0
(+) 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,
Page 3
Standard
subtract, multiply, and divide rational expressions.
Algebra: Creating Equations (A-CED)
-- Create equations that describe numbers or relationships.
1.0 Create equations and inequalities in one variable
including ones with absolute value and use them to
solve problems. Include equations arising from linear
and quadratic functions, and simple rational and
exponential functions. (revised) 
2.0 Create equations in two or more variables to
represent relationships between quantities; graph
equations on coordinate axes with labels and scales. 
Develop URL
• Section: Adding and
Subtracting Rational
Expressions
Page 4
Expressions
ALG 055:
Self Check: Inequalities
ALG 055:
Speedback Assignment:
Equations and Inequalities
This is taught throughout the
courses. The most evident
lesson is Quadratic Equations
(ALG 055), where nearly every
concept is taught in relation to
graphs of equations in two
variables.
ALG 055:
Self Check: all in the Quadratic
Equations lesson
ALG 055:
Speedback Assignment:
Quadratic Equations
ALG 055:
Self Check: Inequalities
Self Check: Compound
Sentences and Absolute Value
Inequalities
ALG 055:
Speedback Assignment:
Equations and Inequalities
ALG 057:
Self Check: More Formulas to
Apply
ALG 057:
Speedback Assignment:
Rational Functions
ALG 057:
Self Check: Graphing to Solve
a Rational Equation
ALG 057:
Speedback Assignment:
Rational Functions
ALG 055:
Self Check: Compound
Sentences and Absolute Value
Inequalities
ALG 055:
Speedback Assignment:
Equations and Inequalities
ALG 055:
Represent constraints by equations or inequalities,
Lesson: Equations and
and by systems of equations and/or inequalities, and
Inequalities
interpret solutions as viable or non-viable options in a • Section: Inequalities
modeling context. For example, represent inequalities
• Section: Compound
Sentences and Absolute
describing nutritional and cost constraints on
Value Inequalities
combinations of different foods. 
ALG
057:
4.0 Rearrange formulas to highlight a quantity of interest,
Lesson: Rational Functions
using the same reasoning as in solving equations. For
Section: More Formulas to
example, rearrange Ohm’s law V = IR to highlight
Apply
resistance R. 
Algebra: Reasoning with Equations and Inequalities (A-REI)
-- Understand solving equations as a process of reasoning and explain the reasoning.
ALG 057:
2.0 Solve simple rational and radical equations in one
Lesson: Rational Functions.
variable, and give examples showing how extraneous
Section: Graphing to Solve a
solutions may arise.
Rational Equation
Solve one-variable equations and inequalities
involving absolute value, graphing the solutions and
interpreting them in context. (revised)
Assess URL
ALG 055:
Lesson: Equations and
Inequalities
Section: Inequalities
3.0
3.1
Practice URL
ALG 055:
Lesson: Equations and
Inequalities
Section: Compound Sentences
Standard
Develop URL
Practice URL
Assess URL
ALG 055:
a. Lesson: Systems of
Equations and Inequalities
Section: Solving Systems,
starting on p. 1 (and
especially example
problems)
b. Lesson: Equations and
Inequalities
• Section: Compound
Sentences and Absolute
Value Inequalities
• Section: Absolute Values
ALG 055:
a. Self Check: Solving
Systems
b.
• Self Check: Compound
Sentences and Absolute
Value Inequalities
• Self Check: Absolute
Values
ALG 055:
a. Speedback Assignment:
Systems of Equations and
Inequalities
b. Speedback Assignment:
Equations and Inequalities
ALG 057:
Lesson: Exponential and
Logarithmic Functions, entire
lesson
ALG 057:
Self Check: all in the
“Exponential and Logarithmic
Functions” lesson
ALG 057:
Speedback Assignment:
Exponential and Logarithmic
Functions
and Absolute Value Inequalities
-- Represent and solve equations and inequalities graphically.
11.0 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. 
Functions: Interpreting Functions (F-IF)
-- Interpret functions that arise in applications in terms of the context.
Page 5
Standard
Develop URL
Practice URL
Assess URL
4.0
For a function that models a relationship between two
quantities, interpret key features of graphs and tables
in terms of the quantities, and sketch graphs showing
key features given a verbal description of the
relationship. Key features include: intercepts;
intervals where the function is increasing, decreasing,
positive, or negative; relative maximums and
minimums; symmetries; end behavior; and
periodicity. 
ALG 055:
Lesson: Linear Relations and
Functions
Section: Slope-Intercept and
Standard Forms of Equations
ALG 055:
Self Check: Slope-Intercept
and Standard Forms of
Equations
ALG 055:
Speedback Assignment: Linear
Relations and Functions
ALG 057:
• Lesson: Polynomial
Functions
Section: Solving Polynomials
by Graphing, and Finding the
Zeros of the Function
• Lesson: Rational Functions
Section: Graphing to Solve a
Rational Equation
ALG 057:
• Self Check: Solving
Polynomials by Graphing,
and Finding the Zeros of
the Function
• Self Check: Graphing to
Solve a Rational Equation
ALG 057:
• Speedback Assignment:
Polynomial Functions
• Speedback Assignment:
Rational Functions
Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it
describes. For example, if the function h gives the
number of person-hours it takes to assemble n
engines in a factory, then the positive integers would
be an appropriate domain for the function. 
ALG 055:
• Lesson: Quadratic Equations
Section: Graphing Quadratic
Equations
• Lesson: Linear Relations
and Functions
Section: Graphing a
Function
ALG 055:
Lesson: Linear Relations and
Functions
Section: Slope-Intercept and
Standard Forms of Equations
ALG 055:
• Self Check: Graphing
Quadratic Equations
• Self Check: Graphing a
Function
ALG 055:
• Speedback Assignment:
Quadratic Equations
• Speedback Assignment:
Linear Relations and
Functions
ALG 055:
Self Check: Slope-Intercept
and Standard Forms of
Equations
ALG 055:
Speedback Assignment: Linear
Relations and Functions
ALG 055:
Lesson: Linear Relations and
Functions
Section: Special Functions
ALG 055:
Self Check: Special Functions
ALG 055:
Speedback Assignment: Linear
Relations and Functions
ALG 057:
a. Lesson: Exponential and
Logarithmic Functions
Section: Exponential
Functions
b. Lesson: Polynomial
Functions
Section: Graphing
Polynomials
ALG 057:
a. Self Check: Exponential
Functions
b. Self Check: Graphing
Polynomials
c. Self Check: Inverse
Trigonometric Functions
ALG 057:
a. Speedback Assignment:
Exponential and
Logarithmic Functions
b. Speedback Assignment:
Polynomial Functions
c. Speedback Assignment:
Trigonometric Functions
5.0
6.0
Calculate and interpret the average rate of change of a
function (presented symbolically or as a table) over a
specified interval. Estimate the rate of change from a
graph. 
-- Analyze functions using different representations.
7.0 Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and
using technology for more complicated cases. 
b. Graph square root, cube root, and piecewise-defined
functions, including step functions and absolute value
functions. 
c. Graph polynomial functions, identifying zeros when
suitable factorizations are available, and showing end
behavior. 
e. Graph exponential and logarithmic functions,
showing intercepts and end behavior, and
Page 6
Standard
trigonometric functions, showing period, midline, and
amplitude. 
8.0
Write a function defined by an expression in different
but equivalent forms to reveal and explain different
properties of the function.
Develop URL
Practice URL
Assess URL
ALG 057:
Lesson: Polynomial Functions
Section: Solving Polynomials by
Graphing, and Finding the
Zeros of the Function
ALG 057:
Self Check: Solving
Polynomials by Graphing, and
Finding the Zeros of the
Function
ALG 057:
Speedback Assignment:
Polynomial Functions
ALG 055:
• Lesson: Quadratic Equations
Section: Graphing Quadratic
Equations
• Lesson: Linear Relations
and Functions
Section: Special Functions
ALG 055:
• Self Check: Graphing
Quadratic Equations
• Self Check: Special
Functions
ALG 055:
• Speedback Assignment:
Quadratic Equations
• Speedback Assignment:
Linear Relations and
Functions
ALG 057:
Lesson: Polynomial Functions
Section: Positive, Negative, and
Real Zeros
ALG 057:
Self Check: Positive, Negative,
and Real Zeros
ALG 057:
Speedback Assignment:
Polynomial Functions
ALG 055:
Self Check: Solving Problems
with Quadratics
ALG 055:
Speedback Assignment:
Quadratic Equations
ALG 055:
Self Check: Composition of
Functions
ALG 055:
Speedback Assignment:
Polynomial Functions
c. Lesson: Trigonometric
Functions
Section: Inverse
Trigonometric Functions,
pp. 4 and 5
ALG 055:
Compare properties of two functions each
Lesson: Quadratic Equations
represented in a different way (algebraically,
Section: Solving Problems with
graphically, numerically in tables, or by verbal
Quadratics
descriptions). For example, given a graph of one
quadratic function and an algebraic expression for
another, say which has the larger maximum.
Functions: Building Functions (F-BF)
-- Build a function that models a relationship between two quantities.
1.0 Write a function that describes a relationship between ALG 055:
Lesson: Polynomial Functions
two quantities.
Section: Composition of
b. Combine standard function types using arithmetic
Functions
operations. For example, build a function that models
the temperature of a cooling body by adding a
constant function to a decaying exponential, and
relate these functions to the model. 
9.0
Page 7
Standard
-- Build new functions from existing functions.
3.0 Identify the effect on the graph of replacing f(x) by f(x)
+ k, kf(x), f(kx), and f(x + k) for specific values of k
(both positive and negative); find the value of k given
the graphs. Experiment with cases and illustrate an
explanation of the effects on the graph using
technology. Include recognizing even and odd
functions from their graphs and algebraic expressions
for them.
4.0
Find inverse functions.
a. Solve an equation of the form f(x) = c for a simple
function f that has an inverse and write an expression
for the inverse. For example, f(x) =2x3 or f(x) = (x +
1)/(x − 1) for x ≠ 1.
Functions: Linear, Quadratic, and Exponential Models (F-LE)
Develop URL
Practice URL
Assess URL
ALG 055:
• Lesson: Linear Relations
and Functions
Section: Special Functions
• Lesson: Quadratic Equations
Section: Solving Quadratic
Equations by Graphing
ALG 055:
• Self Check: Special
Functions
• Self Check: Solving
Quadratic Equations by
Graphing
ALG 055:
• Speedback Assignment:
Linear Relations and
Functions
• Speedback Assignment:
Quadratic Equations
ALG 057:
Lesson: Polynomial Functions
Section: Graphing Polynomials
ALG 057:
Lesson: Polynomial Functions,
Section: Inverses of Functions
ALG 057:
Self Check: Graphing
Polynomials
ALG 057:
Self Check: Inverses of
Functions
ALG 057:
Speedback Assignment:
Polynomial Functions
ALG 057:
Speedback Assignment:
Polynomial Functions
ALG 057:
• Self Check: Solving
Equations with Logarithms
• Self Check: Logarithms
ALG 057:
Speedback Assignment:
Exponential and Logarithmic
Functions
ALG 057:
Self Check: Logarithms
ALG 057:
Speedback Assignment:
Exponential and Logarithmic
Functions
ALG 057:
Speedback Assignment:
Exponential and Logarithmic
Functions
-- Construct and compare linear, quadratic, and exponential models and solve problems.
ALG 057:
4.0 For exponential models, express as a logarithm the
solution to abct = d where a, c, and d are numbers and Lesson: Exponential and
Logarithmic Functions
the base b is 2, 10, or e; evaluate the logarithm using
• Section: Solving Equations
technology. 
with Logarithms
4.1
Prove simple laws of logarithms.  (Formerly ASSE.3.d) (CA Standard Algebra II – 11.0)
4.2
Use the definition of logarithms to translate between
logarithms in any base.  (Formerly A-SSE.3.e.) (CA
Standard Algebra II – 13.0)
4.3
Understand and use the properties of logarithms to
simplify logarithmic numeric expressions and to
identify their approximate values.  (Formerly A-SSE.3.f)
(CA Standard Algebra II – 14.0)
Page 8
• Section: Logarithms
ALG 057:
Lesson: Exponential and
Logarithmic Functions
Section: Logarithms
ALG 057:
Lesson: Exponential and
Logarithmic Functions
• Section: Solving Equations
with Logarithms
• Section: Logarithms
ALG 057:
Lesson: Exponential and
Logarithmic Functions
Section: Logarithms
ALG 057:
• Self Check: Solving
Equations with Logarithms
• Self Check: Logarithms
ALG 057:
Self Check: Logarithms
ALG 057:
Speedback Assignment:
Exponential and Logarithmic
Functions
Standard
Develop URL
Functions: Trigonometric Functions (F-TF)
-- Extend the domain of trigonometric functions using the unit circle.
ALG 057:
1.0 Understand radian measure of an angle as the length
Lesson: Trigonometric
of the arc on the unit circle subtended by the angle.
2.0
2.1
Explain how the unit circle in the coordinate plane
enables the extension of trigonometric functions to all
real numbers, interpreted as radian measures of
angles traversed counterclockwise around the unit
circle. [includes all 6 trigonometric functions]
Graph all 6 basic trigonometric functions. (Formerly FTF.6.1., F-TF.6.2. revised).
Functions,
Section: Unit Circles, before
Example Problem 1
ALG 057:
Lesson: Trigonometric
Functions
Section: Unit Circles, entire
section
ALG 057:
Lesson: Trigonometric
Functions
Section: Inverse Trigonometric
Functions, pp. 4 and 5
Practice URL
Assess URL
ALG 057:
Self Check: Unit Circles
ALG 057:
Speedback Assignment:
Trigonometric Functions
ALG 057:
Self Check: Unit Circles
ALG 057:
Speedback Assignment:
Trigonometric Functions
ALG 057:
Self Check: Inverse
Trigonometric Functions
ALG 057:
Speedback Assignment:
Trigonometric Functions
-- Model periodic phenomena with trigonometric functions. [In Algebra II, these standards address sine and cosine functions]
ALG 057:
ALG 057:
ALG 057:
5.0 Choose trigonometric functions to model periodic
Lesson: Trigonometric
Self Check: Inverse
Speedback Assignment:
phenomena with specified amplitude, frequency, and
Functions
Trigonometric Functions
Trigonometric Functions
midline. 
Section: Inverse Trigonometric
Functions, pp. 4 and 5
-- Prove and apply trigonometric identities.
8.0 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1
and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ),
cos(θ), or tan(θ) and the quadrant.
ALG 057:
Lesson: Trigonometric
Functions
Section: Prove and Use the
Pythagorean Identity
ALG 057:
Self Check: Prove and Use the
Pythagorean Identity
ALG 057:
Speedback Assignment:
Trigonometric Functions
ALG 057:
Self Check: Conic Sections
ALG 057:
Speedback Assignment: Conics
Geometry: Expressing Geometric Properties with Equations (G-GPE)
-- Translate between the geometric description and the equation for a conic section
ALG 057:
3.1 Given a quadratic equation of the form ax2 + by2 + cx
+ dy + e = 0, use the method for completing the square Lesson: Conics
Section: Conic Sections
to put the equation into standard form; identify
whether the graph of the equation is a circle or a
parabola, and graph the equation (ellipse or
hyperbola +) (revised)
Statistics and Probability: Interpreting Categorical and Quantitative Data (S-ID)
Page 9
Standard
Develop URL
-- Summarize, represent, and interpret data on a single count or measurement variable.
ALG 057:
4.0 Use the mean and standard deviation of a data set to
Lesson: Probability and
fit it to a normal distribution and to estimate
Statistics
population percentages. Recognize that there are data
• Section: Normal Distribution
sets for which such a procedure is not appropriate.
• Section: Mean, Median, and
Mode
Use calculators, spreadsheets, and tables to estimate
areas under the normal curve. 
Statistics and Probability: Making Inferences and Justifying Conclusions (S-IC)
-- Understand and evaluate random processes underlying statistical experiments.
ALG 057:
1.0 Understand statistics as a process for making
Lesson: Probability and
inferences to be made about population parameters
Statistics
based on a random sample from that population. 
• Section: Normal Distribution
2.0
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? 
• Section: Making Inferences
and Justifying Conclusions
ALG 057:
Lesson: Probability and
Statistics
• Section: Making Inferences
and Justifying Conclusions
• Section: Using Probability to
Make Decisions
Practice URL
Assess URL
ALG 057:
• Self Check: Normal
Distribution
• Self Check: Mean, Median,
and Mode
ALG 057:
Speedback Assignment:
Probability and Statistics
ALG 057:
• Self Check: Normal
Distribution
• Self Check: Making
Inferences and Justifying
Conclusions
ALG 057:
• Self Check: Making
Inferences and Justifying
Conclusions
• Self Check: Using
Probability to Make
Decisions
ALG 057:
Speedback Assignment:
Probability and Statistics
-- Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
ALG 057:
ALG 057:
3.0 Recognize the purposes of and differences among
Lesson: Probability and
Self Check: Mean, Median and
sample surveys, experiments, and observational
Statistics
Mode
studies; explain how randomization relates to each.  Section: Mean, Median and
4.0
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. 
5.0
Use data from a randomized experiment to compare
two treatments; use simulations to decide if
differences between parameters are significant. 
Page 10
Mode
ALG 057:
Lesson: Probability and
Statistics
• Section: Normal Distribution
• Section: Making Inferences
and Justifying Conclusions
ALG 057:
Lesson: Probability and
Statistics
• Section: Making Inferences
and Justifying Conclusions
• Section: Mean, Median and
Mode
ALG 057:
• Self Check: Normal
Distribution
• Self Check: Making
Inferences and Justifying
Conclusions
ALG 057:
• Self Check: Making
Inferences and Justifying
Conclusions
• Self Check: Mean, Median
and Mode
ALG 057:
Speedback Assignment:
Probability and Statistics
ALG 057:
Speedback Assignment:
Probability and Statistics
ALG 057:
Speedback Assignment:
Probability and Statistics
ALG 057:
Speedback Assignment:
Probability and Statistics
Standard
Develop URL
Practice URL
Assess URL
6.0
ALG 057:
Lesson: Probability and
Statistics
Section: Making Inferences and
Justifying Conclusions
ALG 057:
Self Check: Making Inferences
and Justifying Conclusions
ALG 057:
Speedback Assignment:
Probability and Statistics
ALG 057:
Self Check: Probability
ALG 057:
Speedback Assignment:
Probability and Statistics
ALG 057:
Self Check: Using Probability
to Make Decisions
ALG 057:
Speedback Assignment:
Probability and Statistics
Evaluate reports based on data. 
Statistics and Probability: Using Probability to Make Decisions (S-MD)
-- Use probability to evaluate outcomes of decisions.
ALG 057:
6.0 (+) Use probabilities to make fair decisions (e.g.,
drawing by lots, using a random number generator).  Lesson: Probability and
7.0
(+) Analyze decisions and strategies using probability
concepts (e.g., product testing, medical testing, pulling
a hockey goalie at the end of a game). 
Page 11
Statistics
Section: Probability
ALG 057:
Lesson: Probability and
Statistics
Section: Using Probability to
Make Decisions