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Advanced Algebra 2 Pacing Guide Lynchburg City Schools 2013-2014

Curriculum Framework Algebra 2 VDOE: SOL Instructional Materials Teacher Direct

Grading Period: 1st Nine Weeks Total Days to Teach = 44 days

SOL & Enabling Objectives: Description

Text

Recommended Activities

Time

Frame

Begin the school year with relationship building activities – continue integrating relationship building throughout the school year

Activity Ideas

PRE-TEST (for Teacher Evaluation & School Improvement: Interactive Achievement) will be released by the division to be administered at a time TBA

Begin teaching the 3rd day of school. DO NOT FEEL BOUND TO THE TEXT BOOK! PLEASE USE ONLINE RESOURCES, APPLETS, & HANDS-ON ACTIVITIES CPM = Connections to Precalculus Masters (Prentice Hall)

Properties of the Real Number System

A113.b Determine which field properties apply to the complex number system.

1-1

ESS All3.a-h Complex Numbers

Total

for this unit = 5



All3.f Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, & natural. Testing the field Properties and Density

1-2

CPM p.1-2

Operations with Complex numbers Ti 83

Lesson Field Properties

days

Solving Absolute Value Equations & Inequalities

A11.4a Solve absolute value equations & inequalities algebraically & graphically.

1-3, 1-4, 1-5

ESS All4.a Absolute Value Equations & Inequalities

Compound inequality game

Graphing Function Transformations

Absolute Value Inequality Number Line

Total for this unit = 5 days

Intro to Domain, Range, and Functions

All.7a Identify the domain, range, zeros, & intercepts of a function presented algebraically & graphically.

2-1, 2-2, 2-3

Finding the Domain & Range of a Function from a

graph

Function Grapher




Graph, Domain & Range of Common Functions

Illuminations Lesson Rates & Taxes Absolute Value Functions

All.6a Recognize graphs of parent functions. All.6b Given a transformation of a parent function, identify the graph of the transformed function. All.6c Given the equation & using a transformation approach, graph a function. All.6d Given the graph of a function, identify the parent function. All.6e Given the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image. All.6f Using a transformational approach, write the equation of a function given its graph.

2-5, 2-6

ESS A11.6a-f Transformational Graphing

Transformation Activity for Exponential and Absolute Value


Function Grapher


Piecewise Functions Examples: Floor & Ceiling Functions Total for



Supports All.7 Floor and Ceiling Functions Graphing Piecewise Functions Writing Functions Given the Graph Identify Domain & Range of a Piecewise Function

CPM p. 3-4

Guided Discovery: Piecewise Functions

PowerPoint Instruction Piecewise Functions

Illuminations Activity Cell Phone Cost Per Minute

this unit = 5 days

Properties of Quadratics

All.6a Recognize graphs of parent functions All.6b Given a transformation of a parent function, identify the graph of the transformed function. All.6c Given the equation & using a transformation approach, graph a function All.6d Given the graph of a function, identify the parent function. All.6e Given the graph of a function, identify the transformations that map the pre-image to the image in order to determine the equation of the image. All.6f Using a transformational approach, write the

5-2 5-3


Interactive Multi-Function Data Flyer

Illuminations Lesson Hanging Chains

Function Grapher

Matching parabola to equation

Graph, Domain, and Range of Common Functions




equation of a function given its graph. All.7a Identify the domain, range, zeros, & intercepts of a function presented algebraically & graphically.

Factoring Polynomials

All.1h Factor polynomials by applying general patterns including difference of squares, sum & difference of cubes, & perfect square trinomials. All.1i Factor polynomials completely over the integers. All.1j Verify polynomial identities: difference of squares, sum & difference of cubes, & perfect square trinomials.

5-4, 6-4

ESS All.1hi Factoring


Solving Quadratic Equations by Factoring

All.7a Identify the domain, range, zero, & intercepts of a function presented algebraically & graphically. All.8a Describe the relationship among solutions of an equation, zeros of a function, x-intercepts of a graph, & factors of a polynomial expression.

5-5

ESS All.8abc Factors Zeros & Solutions

Finding the Domain and Range of a Function from a graph

Function Grapher




All.8b Define a polynomial function, given its zeros. All.8c Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function. All.8d For a function, identify zeros of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function.

Linear and Quadratic Regressions All.9a Collect & analyze data. All.9b Investigate scatterplots to determine if patterns exist & then identify the patterns All.9c Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, & logarithmic functions. All.9d Make predictions, using data, scatterplots, or the equation of the curve of best fit. All.9e Given a set of data, determine the model that

2-4, 5-1

Illuminations Activity: Exploring Linear Data

Illuminations Activity: Making Predictions using Body Measurements

Interactive: Regression Plotting

Block Patterns to create curve of best fit

Illuminations Activity Line of Best Fit

Illuminations Lesson Barbie Bungee (Regression)




would best describe the data.

Complex Number System

All.1d Simplify radical expressions containing positive rational numbers & variables All.3a Recognize that the square root of -1 is represented as i. All.3b Determine which field properties apply to the complex number system. All.3c Simplify radical expressions containing negative rational numbers & express in a + bi form All.3d Simplify powers of i. All.3e +, -, and x complex numbers. All.3f Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, & natural. All.3g Write a real number in a + bi form

p. 262

5-6

ESS All.3a-h Complex Numbers

Operations with Complex Numbers Ti-83

Arithmetic operations with complex numbers from vectors




All.3h Write a pure imaginary number in a +bi form

Flex days/Remediation

3 days

Grading Period: 2nd Nine Weeks Total Days to Teach = 45 days

SOL & Enabling Objective: Description

Text


Time

Frame

Complex Number System

All.1d Simplify radical expressions containing positive rational numbers & variables. All.3a Recognize that the square root of -1 is represented as i. All.3b Determine which field properties apply to the complex number systems. All.3c Simplify radical expressions containing negative rational numbers & express in a + bi form

p. 262

5-6

ESS All.3a-h Complex Numbers

Operations with Complex Numbers Ti-83

Arithmetic operations with complex numbers from vectors

Total for this unit = 2

days



All.3d Simplify power of i. All.3e +, -, and x complex numbers. All.3f Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole, & natural. All.3g Write a real number in a + bi form. All.3h Write a pure imaginary number in a + bi form.

More on Solving Quadratic Equations

All.4b Solve a quadratic equation over the set of complex numbers using an appropriate strategy. All.4c Calculate the discriminant of a quadratic equation to determine the number of real & complex solutions. All.7a Identify the domain, range, zeroes, &

5-7 5-8


Function Grapher

Illuminations Activity: Proof without words:

completing the square


days



intercepts of a function presented algebraically & graphically. All.8a Describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, & factors of a polynomial expression. All.8e Given a polynomial equation, determine the number of real solutions & non-real solutions. All.4h Recognize that the quadratic formula can be derived by applying the completion of squares to a quadratic equation in standard form.

Solve quadratic equations graphically

The discriminant calculator

Discriminant and roots of quadratic



Solving Non-Linear Systems

All.5a Predict the numbers of solutions to a nonlinear system of 2 equations. All.5b Solve a linear-quadratic system of 2 equations algebraically & graphically. All.5c Solve a quadratic-quadratic system of 2 equations algebraically & graphically.

p.577

CPM p. 9-10

ESS All.5abc Nonlinear Systems of Equations

Function Grapher

Illuminations Activity Pan Balance with expressions


days

Higher Order Polynomials

All.7e Describe the end behavior of a function. All.9e Given a set of data, determine the model that would best describe the data. All.9c Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, & logarithmic functions.

p. 306

6-1

Illuminations Lesson Shrinking Candles

ESS All.7abce Functions Domain Range End Behavior

Activity: page 300 text



days



Solving Polynomial Functions

All.7c Given the graph of a function, identify intervals on which the function is increasing & decreasing. All.8c Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function. All.8d For a function, identify zeros of multiplicity greater that 1 and describe the effect of those zeros on the graph of the function. All.8e Given a polynomial equation, determine the number of real solutions & non-real solutions.

6-2 6-3 6-4 6-5 6-6

ESS all. 8abc Factors Zeros & Solutions

Using tangent line to show increasing and decreasing

Include:

Synthetic Division with Complex Zeros

Fundamental Theorem of Algebra

Descartes Rule of Signs

Total for this unit =9 days

Simplifying Radicals

All.1d Simplify radical expressions containing positive rational numbers & variables. All.1g x and ÷ radical expressions not requiring rationalizing the denominators. All.1f +, and – radical expressions.

7-1 7-2 7-3


days



Radical Equations

All.1e Convert from radical notation to exponential notation, & vice versa. Solve an equation containing a radical expression. All.4e Algebraically & graphically

7-4

7-5

Rules of exponents game

Function Grapher


days

Radical Functions All.6a Recognize graphs of parent functions. All.6b Given a transformation of a parent function, identify the graph of the transformed function. All.6c Given the equation & using a transformation approach, graph a function. All.6d Given the graph of a function, identify the parent function. All.6e Given the graph of a function, identify the transformations that map the pre-image to the image in order to determine the equation of the image.

EXT. 7-7

7-8


Function Grapher

Graph: Domain and Range of Common Functions


days



All.6f Using a transformational approach, write the equation of a function given its graph.

Exam Review & Testing

4 days


2 days

Grading Period: 3rd Nine Weeks Total Days to Teach = 48 days


Text


Time

Frame

Direct, Inverse, & Joint Variation

All.10a Translate “y varies jointly as ax and z” as y=kxz All.10b Translate “y is directly proportional to x” as y= kx All.10c Translate “y is inversely proportional to x”as y = k/x.

2-3

9-1

9-2

Variation activity with Ti-83

Illuminations Lesson Inverse Variation


days



All.10d Given a situation, determine the value of the constant of proportionality. All.10e Set up & solve problems, including real- world problems, involving inverse variation, joint variation, & a combination of direct & inverse variations.

Rational Functions All.7a Identify the domain, range, zeros, & intercepts of a function presented algebraically & graphically. All.7b Describe restricted/discontinuous domains & ranges. All.7c Given the graph of a function, identify intervals on which the function is increasing & decreasing. All.7d Find the equations of vertical & horizontal asymptotes of functions.

9-3

CPM p. 17-18


Function Grapher

Rational Functions graphs, asymptotes, and holes


Illuminations Lesson whelk Come to Math

Illuminations Lesson Domain Representations


days



All.7e Describe the end behavior of a function

Simplifying Rational Expressions

All.1a +, -, x, ÷ rational algebraic expressions. All.1b Simplify a rational algebraic expression w/ c common monomial or binomial factors. All.1c Recognize a complex algebraic fraction, & simplify it as a quotient or product of simple algebraic fractions.

9-4 9-5

ESS All.1abc Rational Expressions

Rational Expressions Review

Total for this unit =

10 days

Solving Rational Equations All.4d Solve equations containing rational algebraic expressions w/ monomial or binomial denominators algebraically & graphically.

4-4

ESS All.4df Rational Equations

Function Grapher


days



More Regression Equations

All.9c Find an equation for the curve of best fit for data, using a graphing calculator . Models will include polynomial, exponential, & logarithmic functions. All.9d Make predictions, using data, scatterplots, or the equation of the curve of best fit. All.9e Given a set of data, determine the model that would best describe the data. All.6a Recognize graphs of parent functions All.6b Given a transformation of a parent function, identify the graph of the transformed function. All.6c Given the equation & using a transformation approach, graph a function. All.6d Given the graph of a function, identify the parent function. All.6e Given the graph of a function, identify the

8-1 8-2

Illuminations Lesson Determining f(x)s using regression

Illuminations Lesson – Paying for your wheels


Graphing Exponential Functions with asymptote,

domain, and range

Transformation activity for exponential and absolute value

Graphing Function: Transformations

Function Grapher

EggMath: Embryo exponential explanation

Exponential penny growth word problem


days



transformations that map the pre-image to the image in order to determine the equation of the image. All.6f Using a transformational approach, write the equation of a function given its graph.

Functions and Their Inverses

All.7f Find the inverse of a function. All.7g Graph the inverse of a function as a reflection across the line y = x All.7h Investigate exponential & logarithmic functions, using the graphing calculator.

8-3 8-4

Drawing an Inverse

Illuminations Lesson Counting the Trains


EggMath: Embryo Exponential explanation


days

Solving Logarithmic Equations

All.7i Convert between logarithmic & exponential forms of an equation w/ bases consisting of natural numbers

8-5

CPM p. 15-16

optional EXT: 8-6

Frogger game with log expressions


days


5 days



Grading Period: 4th Nine Weeks Total Days to Teach = 43 days


Text


Time

Frame

Sequences and Series All.2a Distinguish between a sequence & a series All.2b Generalize patterns in a sequence using explicit & recursive formulas. All.2c Use & interpret the notations

All.2d Given the formula, find (the nth term) for an arithmetic or geometric sequence. All.2e Given formulas, write the first n terms and find the sum, of the first n terms of an arithmetic or a geometric sequence. All.2f Given the formula, find the sum of a

11-2

11-4

11-3

11-5

ESS All.2abcde Arith & Geo Sequence & Series

Function Machine for explicit and recursive definitions

Use limits to show sums of infinite series

Geometric Series and sum calculations

Visualizing An Infinite Series


days



convergent infinite series.

The Normal Curve

All.11a Identify the properties of a normal probability distribution. All.11b Describe how the standard deviation & mean affect the graph of the normal distribution. All.11c Compare 2 sets of normally distributed data using a standard normal distribution & z- scores. All.11d Represent probability as area under the curve of a standard normal probability distribution. All.11e Use the graphing calculator or a standard normal probability table to determine probabilities or percentiles based on z- scores

12-3 12-4 12-7

Interactive Activity Fitted Normal distribution

Data grapher with box, scatter, and histogram

Illuminations activity sampling distribution

Illuminations lesson mow whole thing

Illuminations activity histogram tool

Properties of the normal distribution curve

Interactive activity normal distribution


days

Permutations and Combinations

Total for this



All.12a Compare & contrast permutations & combinations. All.12b Calculate the number of permutations of n objects taken r at a time. All.12c Calculate the number of combinations of n objects taken r at a time. All.12d Use permutations & combinations as counting techniques to solve real-world problems.

6-7

EXT. 6-8

Permutation braid unit = 4 days

OPTIONAL CONIC SECTIONS Concrete on h,k form of a conic section Graph using translations of parent

10-1

10-6

Interactive: Cross Section Grapher Interactiveate: Conic Flyer

Activity: Exploring Conic Sections

Illuminations Lesson Cutting Conics


days

POST-TEST (for Teacher Evaluation & School Improvement – use same test as PRE-TEST

1 day



SOL Review & Testing:

13 Days

Final Exam Review & Testing

5 days

RECOMMENDED WEBSITES for additional lesson plans, activities, virtual manipulatives, and applets:

Illuminatinos_NCTM Henrico Algebra Resources Algebra Bits

Project interactive Suffolk Resources Texas Instruments Activities

National Library of Virtual Manipulatives NVLM Jefferson Lab Sol Review

Algebra 2: Math Cross Walk 2001 and 2009 SOLs

Changes to the reporting categories for Algebra 1 s2l test: Now there are 3 reporting categories instead of 5. Relations & functions has become

Functions & Statistics; Analytical Geometry and Systems of Equations/Inequalities strands have been removed. The 3 reporting categories for

Algebra 2 now coincide with the Algebra 1 categories/strands.



Notice that the Functions & Statistics reporting category contains nearly all of the new/revised content of the 2009 Algebra 2 standards (All. 6,

All.7sde & f, All.9, All.10, All.11, and All.12). See the VDOE’s SOL crosswalk for additional details. Now the Functions & Statistics strand will

encompass nearly 50% of the new math SOL test!!!

2001 2009

Reporting Category 2009 SOL # items % of test # of items % of test

Expressions & Operations

All.1a-d, All.3 10 20% 13 26%

Equations & Inequalities

All.4a-d, All.5 10 20% 13 26%

Functions & Statistics

All.2, All.6, All.7a-h, All.8, All.9, All.10,

All.11, All.12

16 32% 24 48%

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