algebra 1 and algebra 2 petal pacing guide lynchburg city ......algebra 1 and algebra 2 petal pacing...

Algebra 1 and Algebra 2 Petal Pacing Guide

Lynchburg City Schools 2013-2014

Curriculum Framework Algebra 1 VDOE: SOL Instructional Materials Curriculum Framework Algebra II 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

**Review of Algebra 1 & arithmetic skills as evidenced by PRE-TEST

Algebraic Expressions

A.1a Translate verbal quantitative situations into algebraic expressions and vice versa.

1-1, 1-7

1-1, 1-4, 1-5

ESS A.1ad Translate & Evaluate

ESS A.1c Evaluating Simplifying Expressions

ESS A3a Simplifying Square Roots

3 days

Total for this unit = 4

days




A.1b Model real-world situations w/ algebraic expressions in a variety of representations (concrete, pictorial, symbolic, verbal). A.1c Evaluate algebraic expressions for a given replacement set to include rational numbers. A.3a Express square roots of a whole number in simplest form. A.3b Express the cube root of a whole number in simplest form. A.1d Evaluate expressions that contain absolute value, square roots, & cube roots. A.4b Simplify expressions using the field properties of the real numbers and properties of equality to justify simplification.

1-2, 1-4, 1-5, 1-6

10-3, 11-1

Not in text!

Sq. Roots 11-4

No Cube, 1-4, 1-5, 1-6, 1-7 justify = 1-8

ESS A3.b Simplify Radical

ESS A.1ad Translate & Evaluate

ESS A4b A Mystery to Solve

Solving Linear Equations

A.4b Solve equations using the field properties of the real numbers & properties of equality to justify the solution.

2-1, 2-2

ESS A.4b a Mystery to Solve

Model solving equations = p.127

ESS A.4e Algebra Tiles & Equation Solving

Total for this unit = 5 days




A.4e Solve multi-step linear equations in one variable. A.4l Determine if a linear equation in one variable has one, an infinite number, or no solutions. A.4f Confirm algebraic solutions to linear equations using a graphing calculator. A.4a Solve a literal equation (formula) for a specific variable.

2-3, 2-4

2-4

p. 102

2-6

Model p.141

NLVM Algebra Balance Scales

NLVM Algebra Balance Scales – Negative

ESS A.4f Solving Linear Equations

Illuminations Lesson Geology Rocks Equations

ESS A.4a solve for Unknown

Solving Linear Inequalities

A.5a Solve multi-step linear inequalities in one variable A.5b Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers A.5c Solve real-world problems involving inequalities.

3-1, 3-2, 3-4

3-2, 3-3

3-1, 3-2, 3-3, 3-4

ESS A.5a Inequalities

ESS A.5b Greetings

Solve inequalities Virtual Lab


Relations Total for




A.7a Determine whether a relation, represented by a set of ordered pairs, a table, or a graph is a function.

A.7d Represent relations & functions using All.7a concrete, verbal, numeric, graphic & algebraic forms. Given one representation, students will be able to represent the relation in another form. A.7b Identify the domain, range, zeros & intercepts of a function presented algebraically or graphically. A.7c For each x in the domain of f, find f(x). A.7e Detect patterns in data and represent arithmetic and geometric patterns algebraically.

5-2

5-2, 5-3, 5-4

5-2. 5-3

5-2

5-4

ESS A.7d Square Patios

ESS A.7b Functions 2

ESS A.7a Functions 1

Domain and Range Using Graphs

NLVM Function Machine

Illuminations Lesson Do You Notice Sum Thing?

Illuminations Lesson Rates & Taxes

NLVM Function Grapher

Graph, Domain and Range of Common Functions

this unit = 4 days

Slope

Total for this unit




A.6f Recognize and describe a line with a slope that is positive, negative, zero, or undefined. A.6e Find the slope of a line, given the graph of a line. A.6c Find the slope of a line, given the equation of a linear function. A.6d Find the slope of a line, given the coordinates of two points on the line.

6-1

6-1

6-2, 6-3

6-1

Math Forum Activity Slope of a Line

Interactive Activity Slop Slider

ESS A 6d Submarine

Illuminations Lesson Movement with f(x)s

Illuminations Lesson Rise Run Triangles

= 3 days

Graphing Linear Equations & Inequalities A.6a Graph linear equations in two variables, including those that arise from a variety of real- world problems. A.6b Use the parent function y = x and describe transformations defined by changes in the slope or y-intercept. A.6h Write an equation of a line when given the graph of a line. A.6g Use transformational graphing to investigate

6-2, 6-3, 6-4 7-5

(inequalities)

p. 290

6-2

NLVM Line Plotter

Line Grapher y=mx + b

ESS A.6b Transformationally Speaking

Interactive Activity Graphit

Illuminations Lesson Trout Pond equation of line





effects of changes in equation parameters on the graph of the equations. A.6j Write an equation of a line given the slope and a point on the line whose coordinates are integers. A.6i Write an equation of a line when given two points on the line whose coordinates are integers. A.6k Write an equation of a vertical line as x = a A.6l Write an equation of a horizontal line as y = c

p. 290

6-4

6-4

6-3

6-3

ESS A.6g Transformation Investigation

Seeing math Activity Linear Transformer

ESS A.6i Equations of Lines

ESS A.6i Slippery Slope

ESS A.6k slope 2 slope

Direct & Inverse Variation A.8a Given a situation, including a real-world situation, determine whether a direct variation exists. A.8c Write an equation for a direct variation, give a set of data. A.8e Graph an equation representing a direct variation, given a set of data.

5-5

5-5

5-5

ESS a.8a Direct Variation

Illuminations Lesson Mow Whole Thing?

Interactive Activity Graphit

ESS A.8b Inverse Variation





A.8b Given a situation, including a real-world situation, determine whether an inverse variation exists. A.8d Write an equation for an inverse variation, given a set of data.

12-1

12-1

Solving Systems of Linear Equations & Inequalities A.4h Given a system of two linear equations in two variables that has a unique solution, solve the system graphically by identifying the point of intersection. A.4g Given a system of two linear equations in two variables that has a unique solution, solve the system by substitution of elimination to find the ordered pair which satisfies both equations. A.4i Determine whether a system of two linear equations has one solutions, no solution, or infinite solutions. A.4j Write a system of two linear equations that models a real-world situation.

7-1

7-2, 7-3

7-1, 7-2, 7-3

7-1, 7-2, 7-3,

ESS A.4h Spring Fling Carnival

ESS A4.g All.c How Much is that Tune

Illuminations Lesson Supply & Demand

ESS A.4i Road Trip

ESS A.4j2 Exercise Fields




A.4k Interpret and determine the reasonableness of the algebraic or graphical solution of a system of two linear equations that models a real-world situation. A.5d Solve systems of linear inequalities algebraically and graphically.

7-4

7-1, 7-2, 7-3, 7-4

7-6

ESS A.5d Graphing System Inequalities

Interactive Activity Linear Inequalities

Polynomials A.2a Simplify monomial expressions & ratios of monomial expressions in which the exponents are integers, using the laws of exponents. A.2b Model sum & difference of polynomials w/ concrete objects & their related pictorial representations. A.2c Relate concrete & pictorial manipulations that model polynomial operations to their corresponding symbolic representations. A.2d Find sums & differences of polynomials. A.2b Model products of polynomials w/ concrete

8-1, 8-2, 8-3

Not in text!

Not in text!

9-1

p.466

(For 8-1) ESS A2a Exponents

(for 8-2) ESS A2 a Scientifically Speaking (sci. not.)

Algebra Tiles (see A.2d, A.2e, A.2f)

Virtual Algebra Tiles

ESS A2.d Add Subtract Polynomials Alg Tiles

(Algebra Tiles (see A.2d, A.2e, A.2f)

Total for this unit

= 10 days




objects & their related pictorial representations. A.2c Relate concrete & pictorial manipulations that model polynomial operations to their corresponding symbolic representations. A.2e Find the products of polynomials. The factors will have no more that five total terms. A.2b Model quotients of polynomials w/ concrete objects & related pictorial representations. A.2c Relate concrete & pictorial manipulations that model polynomial operations to their corresponding symbolic representations. A.2f Find the quotient of polynomials, using a monomial or binomial divisor, or a complete factored divisor.

Not in text!

9-2, 9-3, 9-4

Not in text!

Not in text!

9-2 (monomial)

12-5 (binomial)

NLVM Algebra Tiles

ESS A.2e Multiply Poly With Alg Tiles

ESS A2.f Divide Poly with Alg. Tiles

Flex days/Remediation

2 days

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




SOL & Enabling Objective: Description

Text


Time

Frame

Factoring Polynomials A.2g Factor completely first-and second-degree polynomials w/ integral coefficients A.2h Identify prime polynomials A.2i Use the x-intercepts from the graphical representation of the polynomial to determine & confirm its factors

9-5, 9-6

Not in text!

Not in text!

ESS A.2g Factoring

NLVM Algebra Tiles


days

Finding Roots of Expressions & Quadratic Equations

A.3c Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values. A.4c Solve quadratic equations. A.4d Identify the roots or zeros of a quadratic function over the real number system as the solutions to the quadratic equation that is

11-1

10-4, 10-5

10-4

Cutting Corners solving quadratic equations lesson

Solving quadratic equation practice

ESS A4.d Factoring for Zeros


days




formed by setting the given quadratic expression equal to zero. A.4f Confirm algebraic solutions to quadratic equations, using a graphing calculator.

10-1, 10-2

Statistics

A.9a Analyze descriptive statistics to determine the implications for the real-world situations from which the data drive. A.9b Given data, including data in a real-world context, calculate & interpret the mean absolute deviation of a data set. A.9c Given data, including data in a real-world context, calculate variance & standard deviation of a data set & interpret the standard deviation. A.9d Given data, including data in a real-world context, calculate & interpret z-score for a data set. A.9e Explain ways in which standard deviation

Not in text!

Not in text!

Not in text!

Not in text!

Not in text!

ESS A.9a Analyzing Interpreting Stats

Interactive Activity Measures

Interactive Activity Normal Distribution

ESS A9.b Exploring Stats

ESS A.9c Calculating Measures Dispersion

ESS A9.d Z-scores


days




addresses dispersion by examining the formula for standard deviation. A.9f Compare & contrast mean absolute deviation & standard deviation in real-world context. A.10 Compare, contrast,& analyze data, including data from real-world situations displayed in box-and-whisker plots.

Not in text!

p. 740

ESS A10 Box-and Whisker Plots

Illuminations Activity Box Plotter

Illuminations lesson plan_NBA & box plots

Properties of the Real Number System

Akk3.b Determine which field properties apply to the complex number system. All3.f Place the following sets of numbers in a hierarchy of subsets: complex, pur imaginary, real, rational, irrational, integers, whole, & natural.

1-1

1-2

ESS All 3.a-h Complex Numbers

Operations with Complex Numbers Ti-83


Solving Absolute Value Equations and Inequalities

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

1-3, 1-4, 1-5

ESS All.4a Absolute Value Equations & Inequalities

NLVM Solving equations with balance scales

NLVM Graphing Function Transformations


days




Absolute Value Inequality Number Line

Compound Inequality Game

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 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.

2-5

2-6

ESS All.6a-f Transformational Graphing

Transformation Activity Exponential & Absolute Value




days




Flex days & Remediation 2 days

SOL Review & Testing 10 days

Mid-term Exam 1 day

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


Text


Time

Frame

Linear and Quadratic Regressions All.9a Collect & analyze data All.9b Investigate scaterplots 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 would best describe the data.

2-4

5-1

Illuminations Lesson Exploring Linear Data

Illuminations Lesson How Tall?

NLVM Block Patterns curve of bets fit

Illuminations Activity Line of Best Fit

Illuminations Lesson Barbie Bungee


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

5-2

5-3



Matching garabola to equation

Illuminations Lesson Hanging Chains

Graph, Domain, and Range of Common Functions


days

Factoring Polynomials Total




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

5-4

6-4

ESS All.1hi Factoring

for this unit = 4

days

Solving Quadratic Equations by Factoring

All.7a Identify the domain, range, zeros, & 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 a polynomial expression. 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.

5-5

ESS All.8abc Factors Zeros & Solutions

Finding the Domain and Range of a Function from a graph



days




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.

Complex Numbers 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.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


days




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

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, zeros, & 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. 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 apply the completion of squares to a quadratic equation in standard form.

5-7

5-8

Finding the Domain and Range of a Function from a graph


Illuminations Activity Completing the Square

Solve Quadratic Equations Graphically

The Discriminant calculator

The discriminant and roots of quadratic


days




Solving Non-Linear Systems

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

p. 577

ESS All.5abc Nonlinear Systems of Equations

Function Grapher

Illuminations Pan Balance with expressions


days

High 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.7avce f(x)s: Domain Range End Behavior

Activity: page 300 text

NVLM Block Patterns curve of best fit


days

Simplifying Radicals

All.1d Simplifying radical expressions containing

7-1





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

7-2

7-3

days

Radical Equations

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

7-4

7-5



days

Radical Functions

All.6a Recognize graphs of parent functions. All.6b Given a transformation of a parent function, identify the graph of 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

7-8



Graph, Domain and Range of Common Functions


days




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

Direct, Inverse, and Joint Variation

All.10a Translate “y varies jointly as x 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 All.10d Given a situation, determine the value of the content of proportionally. All.10e Set up & solve problems, including real- world problems, involving inverse variation, joint variation, & a combination of direct & inverse variations.

2-3

9-1

9-2

Variation activity with Ti-83

Illuminations Lesson Inverse Variation


days

Rational Functions

All.7a Identify the domain, range, zeros, &

9-3

Finding the Domain and Range of a Function from





intercepts of a functions presented algebraically & graphically. All.7b Describe restricted/discontinued domains & ranges. All.7c Given the graph of a function, identify intervals on which the function is increasing & decreasing. All.7d Find the equation of vertical & horizontal asymptotes of functions. All.7e Describe the end behavior of a function.

a graph

Illuminations Lesson Domain Representations


Rational Functions graphs, asymptotes, and holes

Graph, domain and Range of Common Functions

Illuminations lesson Whelk-Come

days

Flex days/Remediation

2 days

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


Text


Time

Frame

Simplifying Rational Expressions

All.1a +, -, x, ÷ rational algebraic expressions.

9-4

ESS All.1abc Rational Expressions





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

9-5

days

Solving Rational Equations

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

9-6

ESS All.4df Rational Equations



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 Give a set of data, determine the model that would best describe the data. All.6a Recognize graphs of parent functions.

8-1

8-2

Illuminations Lesson Finding f(x)s with regression

Illuminations Lesson Paying for Wheels

NLVM Block patterns curve of best fit

Graphing exponential functions with asymptote, domain, and range

Transformation activity exponential & absolute

value


days




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 Give 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 equation of a function given its graph.



EggMath Embryo Exponential explanation

Exponential penny growth word problems

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.

8-3

(8-4)

Drawing an Inverse

Illuminations Lesson Counting Trains


days




All.7h Investigate exponential & logarithmic functions, using the graphing calculator.

Graph Domain and Range of Common Functions

EggMath Embryo exponential explanation

Solving Logarithmic Equations

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

8-5

Frogger game with log expressions


days

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 a geometric sequence. All.2e Given formulas, write the first n terms and

find the sum, of the first n terms of of an arithmetic or a geometric sequence. All.2f Given the formulas, find the sum of a convergent infinite series.

11-2

11-4

11-3

11-5

ESS All.2abcde Arith & Geo Sequence & Series

NLVM Function Machine explicit & recursive definitions

Illuminations Activity Sums infinite series

Geometric Series and sum calculations

Visualizing an infinite series


days




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

Illuminations activity data Grapher

Illuminations activity sampling distribution

Illuminations lesson do I have to mow whole thing?

Illuminations Activity Histograms

Properties of the normal distribution curve


days

Permutations & Combinations All.12a Compare & contrast permutations &

6-7

Permutation braid





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.

days

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

1 day

SOL Review & Testing:

11 Days

Final Exam Review & Testing

2 days

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

Illuminatinos_NCTM Henrico Algebra 1 Resources Algebra 1 resources Algebra Bits

Project interactive Suffolk Algebra 1 Resources Texas Instruments Activities




National Library of Virtual Manipulatives NVLM Florida lesson plans Jefferson Lab Sol Review

Henrico Algebra 2 Resources

Suffolk Algebra 2 Resources

Algebra 1: Math Cross Walk 2001 and 2009 SOLs

Changes to the reporting categories for Algebra 1 sol test: Now there are 3 reporting categories instead of 4. Relations & functions and statistics

have been combined into 1 strand. Also, the Algebra 1 Formula Sheet has been revised.

2001 2009

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

Expressions & Operations

A.1, A.2a-c, A.3 12 24% 12 24%

Equations & Inequalities

A.4a-f, A.5a-d, A6 a-b

18 36% 18 36%

Functions & Statistics

A.7a-f, A.8, A.9, A.10, A.11

20 40% 20 40%

algebra 1 and algebra 2 petal pacing guide lynchburg city ......algebra 1 and algebra 2 petal pacing...

Documents