MATH NATION ALGEBRA 2 2017-2018 SCOPE AND SEQUENCE …€¦ · Transformations of Functions ... Quadratic: p.144 Section 4-1 Problems 1,2 . 12 Comparing Functions MAFS.912.F-IF.3.9

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

http://www.cpalms.org/Public/PreviewStandard/Preview/5547





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


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


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


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.





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.


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.








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




two variables.









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








In the topic, students

will solve systems of

equations by

substitution. They will

explore why the x-

coordinates of the

points where the









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




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




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.


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


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.3.7b Graph functions




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.






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




b. Graph square root, cube root, and piecewise-

defined functions, including step functions and

absolute value functions.


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.


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.









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.


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.


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.


Day 5 (10/4 – 5)


Day 6 (10/6 - 9)







SECTION 4: Quadratics Part 1 8 Days October 17 - November 5


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


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.


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


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.


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.









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.


Day 8 (11/4-5)



SECTION 5: Quadratics Part 2 7 Days November 6 - 29


Correlation

Days Needed

1 Graphing

Quadratics in Standard Form

MAFS.912.F-IF.3.7a Graph functions


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


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







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)







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.3.8.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.


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.


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.


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


Day 7 (11/28-29)



SECTION 6: Polynomial Functions 6 Days November 30 – December 15


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.


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.


Day 2 (12/4-5)

5 Using Successive

Differences







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.


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.


Day 5 (12/12-13)









Day 6

(12/14-15)

Scrimmage 2 Days allowed for this assessment

Section 7: Rational Expressions and Equations 6 Days January 9 – January 29


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




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



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


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)


1 Day (1/26-29)





SECTION 8: Expressions and Equations with Radicals and Rational Exponents 5 Days January 30 – February 13


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.


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.


will understand

rational exponents

using the properties of

integer exponents.

Students will also convert between expressions

with radicals and rational exponents.


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



solve problems. Include equations arising from

linear and quadratic functions and simple


In this topic, students will write and solve

equations with radicals and rational exponents.

Students will also

p.390 Section 6-5 Problems 3










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.


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.






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.


Day 5 (2/12-13)



SECTION 9: Exponential and Logarithmic Functions 7 Days February 14 – March 8


Correlation

Days Needed

1

Real World Exponential

Growth and Decay - Part 1














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.


Days 1, 2 (2/14-20)

2

Real World Exponential

Growth and Decay - Part 2






Students will write an

equation in one

variable that

represents a real-

world context.
















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



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.


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



function.

b. Use the properties of exponents to

interpret expressions for exponential

functions.






MAFS.912.A-SSE.2.3c Choose and produce an


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.









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.


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.





6 Transformations of


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.


transformations of functions to exponential

functions.


7 Key Features of


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..


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.


Day 6 (3/5 – 6)


Day 7 (3/7 – 8)

SECTION 10: SEQUENCES AND SERIES 4 Days March 26 – April 5


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.


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





forms.





recursive formula for an arithmetic sequence.


situations.

3 Geometric

Sequences - Part 1





forms.






recursive formula for a geometric sequence.


situations.


1 Day (3/28-29)

4 Geometric

Sequences - Part 2





forms.






recursive formula for a geometric sequence.


situations.





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.


1 Day (4/2-3)

6 Introduction to

Geometric Series – Part 2


In this topic, students will apply the formula for the sum of a finite geometric

series.


7 Sum of Geometric

Series


In this topic, students will apply the formula for the sum of a finite geometric

series.


8 Calculating Loan

Payments


In this topic, students will use the formula for the

sum of a finite geometric series to calculate loan

payments.



1 Day (4/4-5)

SECTION 11: Probability 4 Days April 5 – April 19


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


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.


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


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.


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.


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.


The assessment will be after Section 12

SECTION 12: Statistics 2 Days April 20 – April 27


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.


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.


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


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










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











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.



this time

9 Interpreting Data MAFS.912.S-IC.2.6 Evaluate reports based on data.



this time


1 Day (4/26-27)

Includes material from Section 11

SECTION 13: Trigonometry – Part 1 2 Days April 30 – May 3


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


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.

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.


In this topic, students will find missing angles and radian measures on a

unit circle using knowledge of converting


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




unit circle using knowledge of special

right triangle and reference angles.


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.


unit circle using knowledge of special

right triangle and reference angles.


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


length to real-world scenarios.


The assessment will be after Section 14

SECTION 14: Trigonometry – Part 2 3 Days May 5 – May 11


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


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


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


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.


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.


Documents

MATH NATION ALGEBRA 2 2017-2018 SCOPE AND SEQUENCE …€¦ · Transformations of Functions ... Quadratic: p.144 Section 4-1 Problems 1,2 . 12 Comparing Functions MAFS.912.F-IF.3.9