math nation algebra 2 2017-2018 scope and sequence …€¦ · transformations of functions ......
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MATH NATION ALGEBRA 2 2017-2018 SCOPE AND SEQUENCE
Table of Contents
SECTION 1: FUNCTIONS…………………………………………………………………………………………………………………………………………………………………………………………2
SECTION 2: LINEAR FUNCTIONS, EQUATIONS, AND INEQUALITIES……………………………………………………………………………………………………………………… ..5
SECTION 3: PIECEWISE-DEFINED FUNCTIONS…………………………………………………………………………………………………………………………………………… …………9
SECTION 4: QUADRATICS ‑ PART 1…………………………………………………………………………………………………………………………………………………………………....12
SECTION 5: QUADRATICS ‑ PART 2…………………………………………………………………………………………………………………………………………………………………….15
SECTION 6: POLYNOMIAL FUNCTIONS……………………………………………………………………………………………………………………………………………………………….. 20
SECTION 8: EXPRESSIONS AND EQUATIONS WITH RADICALS AND RATIONAL
EXPONENTS……………………………………………………………………………………………………………………………………...23
SECTION 8: EXPRESSIONS AND EQUATIONS WITH RADICALS AND RATIONAL EXPONENTS………………………………………………………………………………..25
SECTION 9: EXPONENTIAL AND LOGARITHMIC FUNCTIONS……………………………………………………………………………………………………………………………….29
SECTION 10: SEQUENCES AND SERIES………………………………………………………………………………………………………………………………………………………………..33
SECTION 11: PROBABILITY………………………………………………………………………………………………………………………………………………………………………………...36
SECTION 12: STATISTICS……………………………………………………………………………………………………………………………………………………………………………………41
SECTION 13: TRIGONOMETRY – PART 1……………………………………………………………………………………………………………………………………………………………..43
SECTION 14: TRIGONOMETRY – PART 2……………………………………………………………………………………………………………………………………………………………..45
SECTION 1: FUNCTIONS 7 Days (Includes 1 Day for Baseline) August 14 – August 31
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Adding Functions
MAFS.912.A-APR.1.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
In this topic, students will add and subtract polynomial functions.
p. 399 Section 6-6 Function operations Problem 1
Day 1
(8/14 – 15)
2 Multiplying Functions
MAFS.912.A-APR.1.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
In this topic, students will multiply polynomial
functions.
p. 399 Section 6-6 Function operations Problem 2
5 Compositions of
Functions
MAFS.912.F-BF.1.1c Write a function that describes a relationship between two quantities. c. Compose functions. For Problem, if (𝑦) is the temperature in the atmosphere as a function of height and ℎ(𝑡) is the height of a weather balloon as a function of time, then 𝑇(ℎ(𝑡)) is the temperature at the location of the weather balloon as a function of time.
In this topic, students will write a function to model
a real-world context by composing functions and
the information within the context.
p.400 Section 6-6 Problems 3,4
3 Dividing Rational
Expressions
MAFS.912.A-APR.4.6 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 Problems, a computer algebra system.
In this topic, students will rewrite a rational expression as the
quotient in the form of a polynomial added to the remainder divided by the divisor. Students will use polynomial long division to divide a polynomial by
a polynomial.
p.303 Section 5-4 Dividing Polynomials Problems 1, 2
Day 2 (8/16 – 17)
4 Using Synthetic
Division to Divide Functions
MAFS.912.A-APR.4.6 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),
In this topic, students will use synthetic division as a
method of rewriting
p.303 Section 5-4 Dividing
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 Problems, a computer algebra system.
rational expressions when the divisor is in the form
𝑥 − 𝑐.
Polynomials Problems 3, 4
6 Inverse Functions –
Part 1
MAFS.912.F-BF.2.4a,c Find inverse functions. a. Solve an equation of the form (𝑥) = 𝑐 for a simple function,𝑓, that has an inverse and write an expression for the inverse. For Problem, 𝑓 𝑥 = 2×3 or (𝑥) = (𝑥 + 1)/(𝑥– 1) for 𝑥 ≠ 1. c. Read values of an inverse function from a graph or a table, given that the function has an inverse.
In this topic, students
will investigate inverse
functions. will use a
graph or a table of a
function to determine
values of the function’s
inverse.
Students will find the inverse of a function.
one-to-one: p.408 Section 6-6 notes vertical line test: p.62-63 Section 2-1 Problem 4 p.405 Section 6-7 Problems 1, 2, 3
Day 3 (8/18 – 21)
7 Inverse Functions –
Part 2
MAFS.912.F-BF.2.4a,b,c,d Find inverse functions. a. Solve an equation of the form (𝑥) = 𝑐 for a simple function,𝑓, that has an inverse and write an expression for the inverse. For Problem, 𝑓 𝑥 = 2×3 or (𝑥) = (𝑥 + 1)/(𝑥– 1) for 𝑥 ≠ 1. b. Verify by composition that one function is the inverse of another. c. Read values of an inverse function from a graph or a table, given that the function has an inverse. d. Produce an invertible function from a non-invertible function by restricting the domain.
In this topic, students will continue to work with inverses. Students will use compositions to
determine if two functions are inverses. Students will restrict
domains to create invertible functions.
p.405 Section 6-7 Problems 1, 2, 3, 4
8 Recognizing Even
and Odd Functions
MAFS.912.F-BF.2.3 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.
In this topic, students will investigate features of
even and odd functions. Students will determine if
functions are even or odd by examining
equations, tables, and graphs.
p.283 Section 5-1 problems 2, 3
Day 4 (8/22-23)
9 Key Features of
Graphs of Functions
MAFS.912.F-IF.3.7a Graph functions expressed
symbolically and show key features of the
graph, by hand in simple cases and using
In this topic, students will review key features of
graphs of functions.
Domain/Range p.61-62 Section 2-1 note/Problems 2, 3
technology in more complicated cases. A.
Graph linear and quadratic functions and show
intercepts, maxima, and minima. This section
focuses on linear functions.
MAFS.912.F-IF.2.4 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.
(solutions, y-intercepts, positive/negative,
increasing/decreasing, maximum, minimum,).
Solutions, Zeros or Roots: p.76 Section 2-3 notes. p.266 Section 4-5 Intro p.299 Section 5-3 Problem 3 Beat the Test – Introduction to Piece-wise Functions p.90 – 91 Concept Byte 2-4
10 Transformations of Functions – Part 1
MAFS.912.F-BF.2.3 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.
In this topic,
students will
review
transformations of
functions.
Students will investigate horizontal shifts of
functions. Students will also consider multiple transformations on a
function.
p.99 Section 2-6 Problems 1 – 4
Day 5 (8/24-25)
11 Transformations of Functions – Part 2
MAFS.912.F-BF.2.3 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.
In this topic,
students will
review
transformations of
functions.
Students will investigate horizontal shifts of
functions. Students will also consider multiple transformations on a
function.
Linear: p.99 Section 2-6 Problems 1 – 4 Exponential: p.442 Section 7-2 Problems 1, 2 Quadratic: p.144 Section 4-1 Problems 1,2
12 Comparing Functions
MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For Problem, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
In this video, students will compare the features of
all the functions previously studied.
Not in current video list
A Review and
Assessments
Day 6/7 (8/28-29)
Baseline 1 Day
SECTION 2: Linear Functions, Equations and Inequalities 7 Days September 1 – September 21
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Linear Equations in
One Variable – Part 1
MAFS.912.A-CED.1.1 Create equations and
inequalities in one variable and use them to
solve problems.
MAFS.912.A-REI.1.1 Explain each step in solving
a simple equation as following from the equality
of numbers asserted at the previous step,
starting from the assumption that the original
equation has a solution.
MAFS.912.A-REI.1.2 Solve simple rational and
radical equations in one variable, and give
examples showing how extraneous solutions
may arise.
MAFS.912.A-SSE.1.1a Interpret
expressions that represent a quantity in
terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
In this topic, students will justify the steps to solve equations. Students will
create and solve equations representing
real-world situations. Additionally, students will
interpret expressions and what the terms
represent.
p.26 Section 1-4 Problems 1-4
Day 1 (9/1-5)
2 Linear Equations in
One Variable – Part 2
MAFS.912.A-CED.1.4 Rearrange formulas to
highlight a quantity of interest using the same
reasoning as in solving equations.
MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems.
In this topic, students will solve equations with
multiple variables for a specific variable.
p.26 Section 1-4 Problem 5
3 Linear Equations
and Inequalities in Two Variables
MAFS.912.A-CED.1.2 Create equations in two or
more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
I In this topic, students will represent real-world
situations with linear functions. Students will graph the functions and
p.60 Section 2-1 Problem 6 p.74 Section 2-3 Problems 1 – 4
MAFS.912.A-CED.1.3 Represent constraints by
equations or inequalities and by systems of
equations and/or inequalities, and interpret
solutions as viable or nonviable options in a
modeling context.
MAFS.912.F-LE.2.5 Interpret the
parameters in a linear or an exponential
function in terms of a context.
MAFS.912.A-SSE.1.1a Interpret
expressions that represent a quantity in
terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
interpret key features of the graph.
p.114 Section 2-8 Problems 1, 2
4 Key Features of Linear Functions
MAFS.912.F-IF.2.4 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.
In this topic, students will review the key features
of linear functions.
p.81 Section 2-4 Problem 4
Day 2
(9/6 – 7)
5 Classifying Linear
Functions and Finding Inverses
MAFS.912.F-BF.2.4 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.
b. Verify by composition that one function is
the inverse of another.
c. Read values of an inverse function from a
graph or a table, given that the function has
an inverse.
d. Produce an invertible function from a
non-invertible function by restricting the
In this topic, students will classify linear functions as even, odd, or neither.
Additionally, students will find the inverse of a linear function, if it
exists.
p.407 Section 6-7 Problem 1
domain.
6
Solving Linear Systems -
Investigating Graphing,
Substitution, and Elimination
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in
two variables.
MAFS.912.A-REI.4.11 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).
In this topic, students investigate solutions to
systems of linear equations. Students will
solve systems by graphing and
substitution. Additionally, students will explore equivalent systems of
equations.
Solve Systems by graphing: p.134 Section 3-1 Problems 1,2,4 Intro to Substitution: p.142 Section 3-2 Problem 1 Intro to Elimination: P.142 Section 3-2 Problem 3
Days 3 and 4 (9/8 - 13)
7
Solving Linear Systems Using
Elimination
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in
two variables.
MAFS.912.A-CED.1.2 Create equations in two or
more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
MAFS.912.A-SSE.1.1a Interpret
expressions that represent a quantity in
terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
In this topic, students will solve systems using the
elimination method. Additionally, student will interpret different terms in a system of equations.
P.142 Section 3-2 Problem 3, 4,5
8 Solving Linear Systems Using Substitution
MAFS.912.A-CED.1.2 Create equations in two or
more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in
In the topic, students
will solve systems of
equations by
substitution. They will
explore why the x-
coordinates of the
points where the
p.142 Section 3-2 Problems 1,2
two variables.
MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
graphs of the
equations
𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥)
intersect are the
solutions of the equation
𝑓(𝑥) = 𝑔(𝑥).
9 Systems of Linear
Equations in Three Variables -Part 1
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in
two variables.
MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
In this topic, students will write and solve systems
of linear equations in three variables that
represent real- world situations.
p.166 Section 3-5 Problems 1 - 4
Day 5
(9/14 – 15)
10 Systems of Linear
Equations in Three Variables -Part 2
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in
two variables.
MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
In this topic, students will write and solve systems
of linear equations in three variables that
represent real- world situations.
11 Systems of Linear
Inequalities
MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
In this topic students will create systems of linear inequalities from real-
world situations.
p.149 Section 3-3 Problems 1 - 3
Day 6
(9/18 – 19)
A Review and Assessment
Day 7
(9/20 – 21)
SECTION 3: Piecewise-Defined Functions 6 Days September 22 – October 13
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Introduction to
Piecewise-Defined Functions - Part 1
MAFS.912.F-IF.2.4 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.
MAFS.912.F-IF.3. 7b 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.
In this topics, students will explore and evaluate
piecewise-defined functions. Additionally, students will define key features for graphs of
piecewise-defined functions.
p.90-91 Concept Byte 2-4
Day 1 (9/22 – 25)
2 Introduction to
Piecewise-Defined Functions - Part 2
MAFS.912.F-IF.2.4 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.
MAFS.912.F-IF.3.7b 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.
In this topics, students will explore and evaluate
piecewise-defined functions. Additionally, students will define key features for graphs of
piecewise-defined functions.
p.90-91 Concept Byte 2-4
3
Graphing and Writing Piecewise- Defined Functions -
Part 1
MAFS.912.A.F-IF.2.4 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.
MAFS.912.F-IF.3.7b 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.
MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
In this topic, students will graph piece-wise defined functions. Additionally,
students will write piece-wise defined functions
and describe key features of the graphs.
p.90-91 Concept Byte 2-4
Day 2 (9/26 – 27)
4
Graphing and Writing Piecewise- Defined Functions -
Part 2
MAFS.912.A.F-IF.2.4 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. MAFS.912.F-IF.3.7b 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. MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
In this topic, students will graph piece-wise defined functions. Additionally,
students will write piece-wise defined functions
and describe key features of the graphs.
p.90-91 Concept Byte 2-4
5
Real World Examples of
Piecewise- Defined Functions
MAFS.912.F-IF.3.7b 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. MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
In this topic, students will look at real world
examples of piecewise- defined functions.
Students will write and graph the function that
represents the situation.
p.90-91 Concept Byte 2-4
Day 3 (9/28 - 29)
6 Absolute Value
Functions
MAFS.912.F-IF.3.7b 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. MAFS.912.A.F-IF.2.4 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. MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
In this topic, students will explore absolute value
functions. Students will make the connection that absolute value functions
can be written as piecewise-defined
function. Students will write and graph absolute
value functions.
p.107 Section 2-7 Problems 1 - 5
DAY 4 (10/2 – 3)
7 Transformations of Piecewise- Defined
Functions
MAFS.912.F-BF.2.3 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.
In this topic, students will apply their knowledge of
transformations of functions to piecewise-
defined functions.
p.107 Section 2-7 Problems 1 - 5
Day 5 (10/4 – 5)
A Review and Assessment
Day 6 (10/6 - 9)
SECTION 4: Quadratics Part 1 8 Days October 17 - November 5
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Real-Life Examples
of Quadratic Functions
MAFS.912.F-IF.2.4 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. MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
In this topic, students will determine and relate the
key features of a function within a real-
world context by examining the function’s graph. Students will also
consider using the gravitational constant to
write a quadratic function to represent a
real-life situation.
p.209 Section 4-3 Problem 2 p.226 Section 4-5 Problem 4
Day 1 (10/17-18)
2 Solving Quadratic
Equations by Factoring
MAFS.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. MAFS.912.A-REI.1.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution.
In this topic, students will factor a quadratic
expression to find the solutions.
p.216 Section 4-4 Problems 1,2,3 p.226 Section 4-5 Problem 1
Days 2 – 4 (10/19-26)
3
Solving Quadratic Equations by
Factoring - Special Cases - Part 1
MAFS.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines.
In this topic, students will students will factor a
quadratic expression to find the solutions. This topic focuses on perfect
square trinomials.
p.216 Section 4-4 Problems 4, 5
MAFS.912.A-REI.2.4.b Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for 𝑥> = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
4
Solving Quadratic Equations by
Factoring - Special Cases - Part 2
MAFS.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. MAFS.912.A-REI.2.4.b Solve quadratic equations in one variable. b..Solve quadratic equations by inspection (e.g., for 𝑥> = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
In this topic, students will look at special cases of
factoring. This topic focuses on difference of
two squares.
p.216 Section 4-4 Problems 4, 5 p.226 Section 4-5 Problem 1
5 Complex Numbers
- Part 1
MAFS.912.N-CN.1.1 Know there is a complex number, 𝑖, such that 𝑖2 = −1, and every complex number has the form 𝑎 + 𝑏𝑖 with 𝑎 and 𝑏 real. MAFS.912.N-CN.1.2 Use the relation 𝑖2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
In this topic, students will
use I to represent imaginary numbers. Students will add,
subtract, and multiply complex numbers and use 𝑖2 = −1 to write the answer as a complex
number.
p.248 Section 4-8 Problem1
Day 5 (10/27-30)
6 Complex Numbers
- Part 2
MAFS.912.N-CN.1.1 Know there is a complex number, 𝑖, such that 𝑖2 = −1, and every complex number has the form 𝑎 + 𝑏𝑖 with 𝑎 and 𝑏 real.
In this topic, students will
use I to represent imaginary numbers. Students will add,
p.248 Section 4-8 Problem1
MAFS.912.N-CN.1.2 Use the relation 𝑖2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
subtract, and multiply complex numbers and use 𝑖2 = −1 to write the answer as a complex
number.
7
Solving Quadratic Equations by
Completing the Square
MAFS.912.A-REI.2.4 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in 𝑥 into an equation of the form (𝑥 – 𝑝)> = 𝑞 that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for 𝑥> = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form. MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions.
In this topic, students will transform quadratic
equations by completing the square and then
solve the equation by taking the square root.
p.233 Section 4-6 Problem 4, 5
Day 6 (10/31-11/1)
8 Solving Quadratics Using the Quadratic Formula - Part 1
MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions. MAFS.912.A-REI.2.4.b Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for 𝑥 > = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝑎 ± 𝑏𝑖 for real numbers 𝑎 and 𝑏.
In this topic, students will use the quadratic formula to solve
quadratics.
p.240 Section 4-7 Problem 1
Day 7 (11/2-3)
9
Solving Quadratics Using the
Quadratic Formula - Part 2
MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions. MAFS.912.A-REI.2.4.b Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for 𝑥> = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation.
In this topic, students will use the quadratic formula to solve
quadratics.
p.240 Section 4-7 Problem 2
Recognize when the quadratic formula gives complex solutions and write them as 𝑎 ± 𝑏𝑖 for real numbers 𝑎 and 𝑏. MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A Review and Assessment
Day 8 (11/4-5)
SECTION 5: Quadratics Part 2 7 Days November 6 - 29
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Graphing
Quadratics in Standard Form
MAFS.912.F-IF.3.7a Graph functions
expressed symbolically and show key features
of the graph by hand in simple cases and
using technology for more complicated cases.
a. Graph linear and quadratic functions and
show intercepts, maxima, and minima.
MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
MAFS.912.A-REI.2.4.b Solve quadratic equations in one variable.
b. Solve quadratic equations by inspection (e.g., for 𝑥> = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
In this topic, students will review the key features of a quadratic function.
Additionally, they will use key features to sketch
the graph of the quadratic.
p.194 Section 4-1 Problems 1, 2 p.202 Section 4-2 Problems 1, 2
Day 1 (11/6-7)
2
Writing Quadratic Equations in
Standard Form from a Graph
MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
In this topic, students will identify key features from a graph and use
those to write the equation represented by
the graph.
p.194 Section 4-1 Problem 5 p.202 Section 4-2 Problems 1, 2
3
Graphing Quadratics in
Vertex Form – Part 1
MAFS.912.F-IF.3.7a Graph functions
expressed symbolically and show key features
of the graph by hand in simple cases and using
technology for more complicated cases.
a. Graph linear and quadratic functions and
In this topic, students
will identify key
features from the
vertex form.
p.194 Section 4-1 Problems 3, 4 p.202 Section 4-2 Problems 3, 4
Day 2 (11/8-9)
show intercepts, maxima, and minima.
MAFS.912.A-REI.2.4.b Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for 𝑥> = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
Students will use the features to graph the
function.
4
Graphing Quadratics in
Vertex Form – Part 2
MAFS.912.F-IF.3.7a Graph functions
expressed symbolically and show key features
of the graph by hand in simple cases and using
technology for more complicated cases.
a. Graph linear and quadratic functions and
show intercepts, maxima, and minima.
MAFS.912.F-IF.3.8.a Write a function defined
by an expression in different but equivalent
forms to reveal and explain different
properties of the function.
a. Use the process of factoring and completing
the square in a quadratic function to show
zeros, extreme values, and symmetry of the
graph, and interpret these in terms of a
context.
MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. MAFS.912.A-REI.2.4.b Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for 𝑥> = 49), taking square roots, completing the square, the quadratic formula,
In this topic, students write functions in vertex
form and identify key features. Students will
use the features to graph the function.
p.233 Section 4-6 Problem 6 p.194 Section 4-1 Problem 5 p.202 Section 4-2 Problem 3
and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
5
Writing Quadratic Equations in
Vertex Form from a Graph
MAFS.912.F-IF.3.8.a Write a function defined
by an expression in different but equivalent
forms to reveal and explain different
properties of the function.
a. Use the process of factoring and completing
the square in a quadratic function to show zeros,
extreme values, and symmetry of the graph, and
interpret these in terms of a context.
MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
In this topic, students will use the vertex and other
features to write the equation of the quadratic
in vertex form.
p.194 Section 4-1 Problems 3, 4, 5
Day 3 (11/13-14)
6 Converting Quadratic Equations
MAFS.912.A-SSE.2.3b Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
In this topic, students will write quadratic
equations in different forms.
p.202 Section 4-3 Problem 3 p.233 Section 4-6 Problems 4, 6
7
Writing Quadratic Equations When Given a Focus and
Directrix
MAFS.912.G-GPE.1.2 Derive the equation of a parabola given a focus and directrix.
In this topic, students will understand the
relationship between the directrix and focus of a parabola and use those
features to write the equation of the
parabola.
p.622 Section 10-2 Problem 1, 3, 4
Day 4 (11/15-16)
8
Systems of Equations with Quadratics –
Part 1
MAFS.912.A-REI.3.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line 𝑦 = − 3𝑥 and the circle 𝑥2 + 𝑦2 = r2
MAFS.912.A-REI.4.11 Explain why the x-coordinates of the points where the graphs of the
In this topic, students will solve systems of
equations that contain linear and quadratic equations, as well as
systems of two quadratics.
p.258 Section 4-9 Problem 1
Day 5 (11/17-20)
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.
9 Systems of
Equations with Quadratics - Part 2
MAFS.912.A-REI.3.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line 𝑦 = − 3𝑥 and the circle 𝑥2 + 𝑦2 = r2
MAFS.912.A-REI.4.11 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.
In this topic, students will solve systems of
equations that contain linear and quadratic equations, as well as
systems of two quadratics.
p.258 Section 4-9 Problem 1 p.661 Concept Byte 10-6
10 Transformations with Quadratic
Functions
MAFS.912.F-BF.2.3 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.
In this topic, students will apply their knowledge of
transformations of functions specifically to
quadratic functions.
p.194 Section 4-1 Problem 2,3,4
Day 6 (11/21-27)
11 Key Features of
Quadratic Functions
MAFS.912.F-IF.2.4 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,
In this topic, students will review all the key of quadratic functions.
p.194 Section 4-1 Problem 3 p.282 Section 5-1 Key Concept
decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
12
Classifying Quadratic
Functions and Finding Inverses
MAFS.912.F-BF.2.4 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. b. Verify by composition that one function is the inverse of another. c. Read values of an inverse function from a graph or a table, given that the function has an inverse. d. Produce an invertible function from a non-invertible function by restricting the domain. MAFS.912.F-BF.2.3 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.
In this topic, students will classify quadratic
functions as even, odd, or neither. Additionally,
they will find inverses of quadratic functions and
restrict domains to produce and invertible
function.
p.194 Section 4-1 Problem 3 p.282 Section 5-1 Key Concept
A Review and Assessment
Day 7 (11/28-29)
SECTION 6: Polynomial Functions 6 Days November 30 – December 15
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Classifying
Polynomials and Closure Property
MAFS.912.A-APR.1.1 Understand that
polynomials form a system analogous to the
integers; namely, they are closed under the
operations of addition, subtraction, and
multiplication; add, subtract, and multiply
polynomials.
MAFS.912.A-APR.3.4 Prove polynomial identities and use them to describe numerical relationships.
In this topic, students will classify polynomials
which leads into a review of the closure property as
applied to polynomials.
p.281 Section 5-1 Problem 1
Day 1 (11/30 – 12/1)
2 Polynomial
Identities - Part 1
MAFS.912.A-SSE.1.2 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). MAFS.912.A-APR.3.4 Prove polynomial identities and use them to describe numerical relationships.
In this topic, students will prove polynomial
identities. Students will use those identities to
write equivalent expressions and describe numerical relationships.
p.318 Concept Byte 5-5 Polynomial Identities
3 Polynomial
Identities - Part 2
MAFS.912.A-SSE.1.2 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). MAFS.912.A-APR.3.4 Prove polynomial identities and use them to describe numerical relationships.
In this topic, students will prove polynomial
identities. Students will use those identities to
write equivalent expressions and describe numerical relationships.
p.216 Section 4-4 Quadratics and Special Cases p.240 Section 4-7 Quadratic Formula
4 Recognizing End
Behavior of Graphs of Polynomials
MAFS.912.F-IF.2.4 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.
In this topic, students will review graphs and make generalities about end behavior of polynomial functions. Students will
use those generalities to determine the end
behavior when given a polynomial function.
p.280 Section 5-1 Problem 4
Day 2 (12/4-5)
5 Using Successive
Differences
MAFS.912.F-IF.2.4 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.
MAFS.912.F-IF.2.6 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.
In this topic, students will explore zeroes of
polynomial functions and how this relates to the degree of the function.
p.280 Section 5-1 Problem 5
6 Understanding
Zeroes of Polynomials
MAFS.912.F-IF.2.4 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.
MAFS.912.A-APR.2.3 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.
In this topic, students will explore zeroes of
polynomial functions and how this relates to the degree of the function.
p.288 Section 5-2 Problem 1,2
Day 3 (12/6-7)
7 Factoring
Polynomials
MAFS.912.A-SSE.2.3 Choose and produce an
equivalent form of an expression to reveal and
explain properties of the quantity represented
by the expression.
MAFS.912.A-SSE.1.2 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). MAFS.912.A-APR.2.3 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.
In this topic, students will apply their prior
knowledge of factoring and polynomial identities to factor polynomials of
higher degrees.
p.216 Section 4-4 Problems 1 – 4 p.288 Section 5-2 Problem 1 p.296 Section 5-3 Problems 1 - 3
Day 4 (12/8-11)
8 Sketching Graphs
of Polynomials
MAFS.912.A-APR.2.3 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.
MAFS.912.F-IF.3.7c Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.
c. Graph polynomial functions, identifying
zeros when suitable factorizations are
available and showing end behavior.
MAFS.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. MAFS.912.A-SSE.1.2 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).
In this topic, students will apply their knowledge of zeroes and end behavior of polynomials to sketch the graph of polynomial
functions of higher degrees.
p.289 Section 5-2 Problems 2-4
Day 5 (12/12-13)
A Review and Assessment
Day 6
(12/14-15)
Scrimmage 2 Days allowed for this assessment
Section 7: Rational Expressions and Equations 6 Days January 9 – January 29
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 The Remainder
Theorem
MAFS.912.A-APR.2.2 Know and apply the Remainder Theorem: For a 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).
In this topic, students will understand and apply the
remainder theorem to determine if an
expression is a factor of a polynomial function.
p.303 Section 5-4 Problem 1, 3, 5
1 Day (1/9-10)
2 Solving Rational
Equations
MAFS.912.A-REI.1.2 Solve simple rational and
radical equations in one variable, and give
examples showing how extraneous solutions
may arise.
MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
In this topic, students will solve a rational equation
in one variable.
p.527 Section 8-4 Problem 1 p.534 Section 8-5 Problems 2, 3 p.542 Section 8-6 Prob 1 2 Days
(1/11-17)
3 Solving Systems of Rational Equations
MAFS.912.A-REI.4.11 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.
MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
In this topic, students will solve a system of rational
equations.
p.549 8-6 Concept Byte Systems with Rational Equations
1 Day (1/18-19)
4
Using Rational Equations to Solve
Real World Problems
MAFS.912.A-CED.1.1 Create equations and
inequalities in one variable and use them to
solve problems. Include equations arising
from linear and quadratic functions and simple
rational, absolute, and exponential functions.
MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
In this topic, students will use rational equations
solve real-world situations.
p.542 Section 8-6 Problem 2,3
1 Day (1/22-23)
5 Graphing Rational
Functions
MAFS.912.F-IF.3.7d Graph functions expressed
symbolically and show key features of the
graph by hand in simple cases and using
technology for more complicated cases.
d. Graph rational functions, identifying zeros
and asymptotes when suitable factorizations
are available and showing end behavior.
MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
In this topic, students will explore the key features of rational functions and use those to graph the
function.
p. 515 Section 8-3
1 Day (1/24-25)
A Review and Assessment
1 Day (1/26-29)
SECTION 8: Expressions and Equations with Radicals and Rational Exponents 5 Days January 30 – February 13
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1
Expressions with Radicals and
Radical Exponents – Part 1
MAFS.912.N-RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we
define (51
3)3 = 5(1
3)3
, to hold, so (51
3)3 must equal 5.
MAFS.912.N-RN.1.2 Rewrite expressions
involving radicals and rational exponents using
the properties of exponents.
In this topic, students
will understand
rational exponents
using the properties of
integer exponents.
Students will also convert between expressions
with radicals and rational exponents.
p.360 Concept Byte Properties of Exponents p.361 section 6-1 Problem 3 p.367 Section 6-2 Problems 1 – 4
Day 1 (1/30-31)
2
Expressions with Radicals and
Radical Exponents – Part 2
MAFS.912.N-RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we
define (51
3)3 = 5(1
3)3
, to hold, so (51
3)3 must equal 5.
MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
In this topic, students
will understand
rational exponents
using the properties of
integer exponents.
Students will also convert between expressions
with radicals and rational exponents.
p.381 Section 6-4 Problems 1 – 4
Day 2 (2/1-5)
3
Solving Equations with Radicals and
Rational Exponents - Part 1
MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
In this topic, students will write and solve
equations with radicals and rational exponents.
Students will also understand what
extraneous solutions are.
p.390 Section 6-5 Problems 1,2,4
Day 3 (2/6-7)
4
Solving Equations with Radicals and
Rational Exponents - Part 2
MAFS.912.A-CED.1.1 Create equations and
inequalities in one variable and use them to
solve problems. Include equations arising from
linear and quadratic functions and simple
rational, absolute, and exponential functions.
In this topic, students will write and solve
equations with radicals and rational exponents.
Students will also
p.390 Section 6-5 Problems 3
MAFS.912.A-REI.1.2 Solve simple rational and
radical equations in one variable, and give
examples showing how extraneous solutions
may arise.
MAFS.912.A-CED.1.4 Rearrange formulas to
highlight a quantity of interest using the same
reasoning as in solving equations. For
example, rearrange Ohm’s law, 𝑉 = 𝐼𝑅, to highlight resistance, 𝑅.
understand what extraneous solutions are.
5
Graphing Square Root and Cube Root Functions-
Part 1
MAFS.912.F-IF.3.7 b 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. MAFS.912.F-IF.2.4 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. MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the
In this topic, students will graph square root and
cube root functions. Students will use the graphs to solve real-
world problems. Additionally, students
will apply their knowledge of
transformations of functions.
p.414 Section 6-8 Problems 1 – 4
Day 4 (2/8-9)
quantitative relationship it describes. For example, if the function h(n) 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. MAFS.912.F-BF.2.3 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.
6
Graphing Square Root and Cube
Root Functions – Part 2
MAFS.912.F-IF.3.7 b 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. MAFS.912.F-IF.2.4 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. MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
In this topic, students will graph square root and
cube root functions. Students will use the graphs to solve real-
world problems. Additionally, students
will apply their knowledge of
transformations of functions.
p.414 Section 6-8 Problems 1 – 4
MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) 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. MAFS.912.F-BF.2.3 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.
A Review and Assessment
Day 5 (2/12-13)
SECTION 9: Exponential and Logarithmic Functions 7 Days February 14 – March 8
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1
Real World Exponential
Growth and Decay - Part 1
MAFS.912.A-CED.1.1 Create equations and
inequalities in one variable and use them to
solve problems. Include equations arising from
linear and quadratic functions and simple
rational, absolute, and exponential functions.
MAFS.912.A-CED.1.2 Create equations in two or
more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
MAFS.912.A-CED.1.3 Represent constraints by
equations or inequalities and by systems of
equations and/or inequalities, and interpret
solutions as viable or nonviable options in a
modeling context. For example, represent
inequalities describing nutritional and cost
constraints on combinations of different foods.
MAFS.912.F-IF.3.8.b Write a function defined by
an expression in different but equivalent forms
to reveal and explain different properties of the
function.
b. Use the properties of exponents to interpret
expressions for exponential functions.
MAFS.912.F-LE.2.5 Interpret the parameters in a linear or an exponential function in terms of a context.
In this topic, students will explore and solve
problems involving exponential growth and decay in the context of real-world situations.
p.434 Section 7-1 Problems 1 - 5
Days 1, 2 (2/14-20)
2
Real World Exponential
Growth and Decay - Part 2
MAFS.912.A-CED.1.1 Create equations and
inequalities in one variable and use them to
solve problems. Include equations arising from
linear and quadratic functions and simple
rational, absolute, and exponential functions.
Students will write an
equation in one
variable that
represents a real-
world context.
p.434 Section 7-1 Problems 1 - 5
MAFS.912.A-CED.1.2 Create equations in two or
more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
MAFS.912.A-CED.1.3 Represent constraints by
equations or inequalities and by systems of
equations and/or inequalities, and interpret
solutions as viable or nonviable options in a
modeling context. For example, represent
inequalities describing nutritional and cost
constraints on combinations of different foods.
MAFS.912.F-IF.3.8.b Write a function defined by
an expression in different but equivalent forms
to reveal and explain different properties of the
function.
b. Use the properties of exponents to interpret
expressions for exponential functions.
MAFS.912.F-LE.2.5 Interpret the parameters in a linear or an exponential function in terms of a context.
Students will write
and solve an equation
in one variable that
represents a real-
world context.
Students will identify
the quantities in a
real-world situation
that should be
represented by
distinct variables.
In this topic, students will
explore and solve problems involving
exponential growth and decay in the context of real-world situations.
3 Interpreting Exponential Equations
MAFS.912.F-IF.3.8b Write a function defined by
an expression in different but equivalent forms
to reveal and explain different properties of the
function.
b. Use the properties of exponents to
interpret expressions for exponential
functions.
MAFS.912.A-CED.1.1 Create equations and
inequalities in one variable and use them to
solve problems. Include equations arising from
linear and quadratic functions and simple
rational, absolute, and exponential functions.
MAFS.912.A-SSE.2.3c Choose and produce an
In this topic, students will
write exponential functions in equivalent
forms to make observations about what the function represents in a real-world context.
Additionally, they will use the functions to solve
problems.
p.434 Section 7-1 Problems 3,4
equivalent form of an expression to reveal and
explain properties of the quantity represented
by the expression.
c. Use the properties of exponents to
transform expressions for exponential
functions.
MAFS.912.A-SSE.1.1b Interpret expressions
that represent a quantity in terms of its
context.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
4 Euler’s Number
No standards listed In this video, students
will investigate how
we derive Euler's
Number.
Euler's Number will be used in succeeding
videos.
p.442 Section 7-2 Problem 5
Days 3, 4 (2/21-26)
5 Graphing
Exponential Functions
MAFS.912.F-IF.2.4 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. MAFS.912.A-REI.4.11 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.
In this topic, students will graph exponential
functions and find the solution for a system of exponential functions.
p.442 Section 7-2 Problems 1-5
6 Transformations of
Exponential Functions
MAFS.912.F-BF.2.3 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.
In this topic, students will apply their knowledge of
transformations of functions to exponential
functions.
p.442 Section 7-2 Problems 1-5
7 Key Features of
Exponential Functions
MAFS.912.F-IF.2.4 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
In this topic, students will explore the key features
of exponential functions..
p.442 Section 7-2 Problems 1-5
8 Logarithmic
Functions - Part 1
MAFS.912.F-BF.2.4 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) = 2×3 or 𝑓(𝑥) = (𝑥 + 1)/(𝑥– 1) for 𝑥 ≠ 1.
In this topic, students will discover that a
logarithmic function is the inverse of an
exponential function.
p.451 Section 7-3 Problem 1 p.469 Section 7-5 Problem 1, 2
Day 5 (2/27 – 3/2)
9 Logarithmic
Functions - Part 2
MAFS.912.F-BF.2.4 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) = 2×3 or 𝑓(𝑥) = (𝑥 + 1)/(𝑥– 1) for 𝑥 ≠ 1. MAFS.912.F-IF.3.7e. Graph functions expressed symbolically and show key features of the graph by
In this topic, students will continue to build their
understanding of logarithmic functions, as
well as graph the functions.
p.451 Section 7-3 Problem 1 p.469 Section 7-5 Problem 1, 2
hand in simple cases and using technology for more complicated cases. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude and using phase shift.
10 Common and
Natural Logarithms
MAFS.912.F-LE.1.4 For exponential models, express as a logarithm the solution to 𝑎𝑏ct = 𝑑, where 𝑎, 𝑐, and 𝑑 are numbers and the base, 𝑏, is 2, 10, or 𝑒; evaluate the logarithm using technology. MAFS.912.F-BF.2.a Use the change of base formula.
In this topic, students will extend their knowledge of logarithms to bases
other than 10. Students will learn and apply the Change of Base formula.
p.478 Section 7-6 Problems 1-4
Day 6 (3/5 – 6)
A Review and Assessment
Day 7 (3/7 – 8)
SECTION 10: SEQUENCES AND SERIES 4 Days March 26 – April 5
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Arithmetic
Sequences - Part 1
MAFS.912.F-BF.1.2 Write arithmetic and
geometric sequences both recursively and
with an explicit formula, use them to model
situations, and translate between the two
forms.
MAFS.912.F-BF.1.1a Write a function
that describes a relationship
between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
In this topic, students will write an explicit and
recursive formula for an arithmetic sequence.
Students will apply the formula to real-world
situations.
p.572 Section 9-2 Problems 1,2,4
1 Day (3/26-27)
2 Arithmetic
Sequences - Part 2 MAFS.912.F-BF.1.2 Write arithmetic and
geometric sequences both recursively and In this topic, students will
write an explicit and
p.572 Section 9-2 Problems 1,2,4
with an explicit formula, use them to model
situations, and translate between the two
forms.
MAFS.912.F-BF.1.1a Write a function
that describes a relationship
between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
recursive formula for an arithmetic sequence.
Students will apply the formula to real-world
situations.
3 Geometric
Sequences - Part 1
MAFS.912.F-BF.1.2 Write arithmetic and
geometric sequences both recursively and
with an explicit formula, use them to model
situations, and translate between the two
forms.
MAFS.912.F-BF.1.1a Write a function
that describes a relationship
between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
In this topic, students will write an explicit and
recursive formula for a geometric sequence.
Students will apply the formula to real-world
situations.
p.580 Section 9-3 Problems 1,2,3
1 Day (3/28-29)
4 Geometric
Sequences - Part 2
MAFS.912.F-BF.1.2 Write arithmetic and
geometric sequences both recursively and
with an explicit formula, use them to model
situations, and translate between the two
forms.
MAFS.912.F-BF.1.1a Write a function
that describes a relationship
between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
In this topic, students will write an explicit and
recursive formula for a geometric sequence.
Students will apply the formula to real-world
situations.
p.580 Section 9-3 Problems 1,2,3
5 Introduction to
Geometric Series – Part 1
MAFS.912.A-SSE.2.4 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.
In this topic, students will be introduced to the concept of geometric
series.
p.597 Section 9-5 Problems 1, 2, 3
1 Day (4/2-3)
6 Introduction to
Geometric Series – Part 2
MAFS.912.A-SSE.2.4 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.
In this topic, students will apply the formula for the sum of a finite geometric
series.
p.597 Section 9-5 Problems 1, 2, 3
7 Sum of Geometric
Series
MAFS.912.A-SSE.2.4 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.
In this topic, students will apply the formula for the sum of a finite geometric
series.
p.597 Section 9-5 Problems 1, 2, 3
8 Calculating Loan
Payments
MAFS.912.A-SSE.2.4 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.
In this topic, students will use the formula for the
sum of a finite geometric series to calculate loan
payments.
p.597 Section 9-5 Problems 1, 2, 3
A Review and Assessment
1 Day (4/4-5)
SECTION 11: Probability 4 Days April 5 – April 19
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Sets and Venn
Diagrams - Part 1
MAFS.912.S-CP.1.1 Describe events as subsets of a sample space (the set of outcomes) using
characteristics (or categories) of the outcomes, or
In this topic, students will explore and be able to
identify the basic
Not Available in the Pearson Resource
1 Day (4/6-9)
as unions, intersections, or complements of other events (“or,” “and,” “not”).
elements of Venn diagrams including
intersection, union, and complement.
2 Sets and Venn
Diagrams - Part 2
MAFS.912.S-CP.1.1 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”).
In this topic, students will create and analyze Venn
diagrams using the various components of
intersection, union, and complement.
Not Available in the Pearson Resource
3 Probability and the
Addition Rule - Part 1
MAFS.912.S-CP.2.7 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
MAFS.912.S-CP.1.4 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.
In this topic, students will find probability of one event taking place and
apply the addition rule to find the probability that one event OR a separate
event will take place
p.681 Section 11-2 Problem 1
1 Day
(4/12-13)
4 Probability and the
Addition Rule - Part 2
MAFS.912.S-CP.2.7 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
MAFS.912.S-CP.1.4 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
In this topic, students will find probability of one event taking place and
apply the addition rule to find the probability that one event OR a separate
event will take place.
p.681 Section 11-2 Problem 3 p.688 Section 11-3 Problem 2,3
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.
5 Probability and Independence
MAFS.912.S-CP.1.5 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. MAFS.912.S-CP.1.2 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.
In this topic, students will determine whether or
not two events are dependent or
independent, and use that knowledge to
calculate probabilities of those events.
p.688 Section 11-3 Problem 1
6
Conditional Probability
MAFS.912.S-CP.1.3 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. MAFS.912.S-CP.2.6 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. MAFS.912.S-CP.1.5 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. MAFS.912.S-CP.1.2 Understand that two events 𝐴 and 𝐵 are independent if the probability of 𝐴 and 𝐵 occurring together is the product of their
p.696 Section 11-4 Problem 3
1 Day (4/16-17)
probabilities, and use this characterization to determine if they are independent.
7 Two-Way
Frequency Tables - Part 1
MAFS.912.S-CP.1.4 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. MAFS.912.S-CP.1.3 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. MAFS.912.S-CP.1.5 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. MAFS.912.S-CP.2.6 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.
In this topic, students will find and interpret
probability from a two-way frequency table.
p.703 Section 11-5 Problem 4
1 Day (4/18-19)
8 Two-Way
Frequency Tables - Part 2
MAFS.912.S-CP.1.4 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
In this topic, students will create two- way
frequency tables, as well as find and interpret probability from the tables they create.
p.713 Section 11-6 Problem 3
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. MAFS.912.S-CP.1.3 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. MAFS.912.S-CP.1.5 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. MAFS.912.S-CP.2.6 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.
A Review and Assessment
The assessment will be after Section 12
SECTION 12: Statistics 2 Days April 20 – April 27
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Statistics and Parameters
MAFS.912.S-IC.1.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
In this topic, students will identify the population,
sample, variable of interest, parameters, and
statistics of interest in various real-world
situations.
p.725 Section 11-8 Problems 1 - 3
1 Day (4/20-23) 2
Statistical Studies – Part 1
MAFS.912.S-IC.1.1 Understand statistics as a
process for making inferences about population
parameters based on a random sample from that
population.
MAFS.912.S-IC.2.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
In this topic, students will learn the different ways to gather data, as well as
the 3 principles of experimental design, and
use this knowledge to identify the best method
of data collection different situations.
p.725 Section 11-8 Problems 1 - 3
3 Statistical Studies –
Part 2
MAFS.912.S-IC.1.1 Understand statistics as a
process for making inferences about population
parameters based on a random sample from that
population.
In this topic, students will identify bias in various
sampling techniques, and determine which
sampling techniques
p.725 Section 11-8 Problems 1 - 3
MAFS.912.S-IC.2.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
work for differing situations.
4 The Normal
Distribution – Part 1
MAFS.912.S-ID.1.4 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.
MAFS.912.S-IC.2.6 Evaluate reports based on data.
In this topic, students will use the Empirical Rule to
determine the percentage of values between two data
points.
p.719 Section 11-7 Problem 1 – 3 p.739 Section 11-10 Problems 1 - 3
1 Day (4/24-25)
5 The Normal
Distribution – Part 2
MAFS.912.S-ID.1.4 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.
MAFS.912.S-IC.2.6 Evaluate reports based on data.
In this topic, students will calculate and interpret the z-score in various real-world situations.
p.719 Section 11-7 Problem 1, 2, 3 p.739 Section 11-10 Problems 1 - 3
6 The Normal
Distribution – Part 3
MAFS.912.S-ID.1.4 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.
MAFS.912.S-IC.2.6 Evaluate reports based on data.
In this topic, students
will find the
probability that an
event will occur
using the mean and
standard deviation
to calculate the z-
score.
Students will combine their knowledge of z-
core and the Empirical Rule to interpret data.
p.719 Section 11-7 Problem 1, 2, 3 p.739 Section 11-10 Problems 1 - 3
7 Estimating Means and Proportions
MAFS.912.S-IC.2.4 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.
Not developed at this time Not developed at
this time Not developed at
this time
8 Comparing Treatments
MAFS.912.S-IC.2.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Not developed at this time Not developed at
this time Not developed at
this time
9 Interpreting Data MAFS.912.S-IC.2.6 Evaluate reports based on data.
Not developed at this time Not developed at
this time Not developed at
this time
A Review and Assessment
1 Day (4/26-27)
Includes material from Section 11
SECTION 13: Trigonometry – Part 1 2 Days April 30 – May 3
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 The Unit Circle -
Part 1
MAFS.912.F-TF.1.2 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.
In this topic, students will use their knowledge of
special right triangles to find the angles measure of the angles formed by
rays intersecting the unit circle and coordinates on
the unit circle.
p.835 Concept Byte Special Right Triangles p.836 Section 13-2 Problems 1, 4
1 Day (4/30-5/1)
2 The Unit Circle -
Part 2
MAFS.912.F-TF.1.2 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.
In this topic, students will use their knowledge of
special right triangles to find the angles measure of the angles formed by
p.836 Section 13-2 Problems 2, 4, 5
rays intersecting the unit circle and coordinates on
the unit circle.
3 Radian Measure -
Part 1
MAFS.912.F-TF.1.1 Understand radian
measure of an angle as the length of the arc on
the unit circle subtended by the angle; convert
between degrees and radians.
MAFS.912.F-TF.1.2 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.
In this topic, students will find missing angles and radian measures on a
unit circle using knowledge of converting
between degrees and radians.
p.843 Concept Byte Measuring Radians p.844 Section 13-3 Problems 1, 2, 4
1 Day (5/2-3)
4 Radian Measure -
Part 2
MAFS.912.F-TF.1.1 Understand radian
measure of an angle as the length of the arc on
the unit circle subtended by the angle; convert
between degrees and radians.
MAFS.912.F-TF.1.2 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.
In this topic, students will find missing angles and radian measures on a
unit circle using knowledge of special
right triangle and reference angles.
p.843 Concept Byte Measuring Radians p.844 Section 13-3 Problems 1, 2, 4
5 More Conversions
with Radians
MAFS.912.F-TF.1.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; convert between degrees and radians.
In this topic, students will find missing angles and radian measures on a
unit circle using knowledge of special
right triangle and reference angles.
p.843 Concept Byte Measuring Radians p.844 Section 13-3 Problems 1, 2, 4
6 Arc Measure
MAFS.912.F-TF.1.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; convert between degrees and radians.
In this topic, students will find the length of the arc
on the unit circle subtended by the angle.
Students will also use the arc length to find the
measure of the central angle, as well as apply their knowledge of arc
p.844 Section 13-3 Problem 3
length to real-world scenarios.
A Review and Assessment
The assessment will be after Section 14
SECTION 14: Trigonometry – Part 2 3 Days May 5 – May 11
Topic Title Standards Objective Pearson Textbook
Correlation
Days Needed
1 Pythagorean
Identities
MAFS.912.F-TF.3.8 Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to calculate trigonometric ratios.
In this topic, students will prove the Pythagorean
Identity, and use it to calculate trigonometric
ratios.
1 Day (5/4-7)
2 Sine and Cosine Graphs - Part 1
MAFS.912.F-TF.2.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
In this topic, students will explore periodic
functions and identify the period, amplitude, and
frequency; and use
special right triangle ratios to graph
trigonometric functions.
3 Sine and Cosine Graphs - Part 2
MAFS.912.F-TF.2.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
In this topic, students will explore periodic
functions and identify the period, amplitude, and
frequency; and use special right triangle
ratios to graph trigonometric functions.
4 Transformations on
Trigonometric Functions
MAFS.912.F-TF.2.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
In this topic, students will use and apply their
knowledge of transformations to graph
various trigonometric functions. Students will identify key features of
trigonometric functions including period,
amplitude and frequency.
1 Day (5/8-9)
5 Modeling with Trigonometric
Graphs
MAFS.912.F-TF.2.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
In this topic, students will use and apply their
knowledge of transformations to graph
various trigonometric functions. Students will identify key features of
trigonometric functions including period,
amplitude and frequency.
A Review and Assessment
b
1 Day (5/10-11)
Includes material from Section 13
HONORS only standards
MAFS.912.A-APR.3.5: Know and apply the Binomial Theorem for the expansion of (x 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.