Curricular Documentation Algebra I for HHS -...

1

Harrison School District

Curricular Documentation

Algebra I for HHS

2011-2012

Pam Jones

Curriculum Coordinator

2

The following curricular documents reflect a collaborative effort by the teachers

and administrators of the Harrison School District to meet the Arkansas Learning

Standards:

From the Arkansas Department of Education:

Arkansas’ Learning Standards are defined in the Arkansas Curriculum

Frameworks, which are discipline-based and clearly describe what students must

know and be able to do in each academic content area. The rigorous academic

content standards and the student learning expectations within each document

provide the focus for instruction for each local school district, without rigidly

prescribing every element of the local curriculum.

Student demonstration of the standards and learning expectations within the

Arkansas Curriculum Frameworks is the anchor for the entire education system,

with instructional programs, state-level assessments, professional development,

school improvement planning, teacher/administrator licensure, and

accountability sharing the common goal of improved student learning and

performance around these standards.

3

CURRICULUM MAP: Harrison School District


2011-2012 Grade: 10th-12th Subject: Algebra I

FRAMEWORKS CONTENT SKILLS

LA.1.AI.3

LA.1.AI.1 LA.1.AI.2

LA.1.AI.2 SEI.2.AI.8

LA.1.AI.1

LA.1.AI.1 DIP.5.AI.2

DIP.5.AI.3 LA.1.AI.1

SEI.2.AI.5

DIP.5.AI.2

DIP.5.AI.6

DIP.5.AI.4

DIP.5.AI.5

I. Algebra Introduction (Week #1 - #4)

A. Terms, operations, variables, exponents

B. Order of operations C. Equations & inequalities

D. Verbal models, problem solving

II. Rules of Algebra (Weeks #3 - #5)

A. Number line, absolute value B. Add, subtract, multiply, and

divide integers C. Add & subtract matrices

D. Distributive property

E. Rates & ratios F. Scalar multiplication

III. Statistics (Week #5)

A. Table, frequency distribution,

line plot, bar graph, timeline, circle graph

Mean, mode, median Stem & leaf plot, box & whisker plot

The student will be able to….

Represent numbers and operations

Use the order of operations to evaluate expressions, including variables and exponents Solve and check equations and inequalities

Translate verbal phrases and real-life problems into algebra

Graph and find opposite and absolute value using the number line

Add, subtract, multiply and divide integers Add and subtract matrices

Use the distributive property Use rates and ratios to relate quantities

Multiply a matrix by a scalar

Use tables and graphs to organize data

Construct a stem-and-leaf plot and box-and-whisker plot

Find and use measures of central tendency to describe data

ACTIVITIES ASSESSMENTS RESOURCES

Daily Practice

Released Items

Teacher Made Test

Notebook Released Items

Prentice Hall textbook Released items Calculators TI-Navigator System

4


SEI.2.AI.1

SEI.2.AI.1 SEI.2.AI.5

SEI.2.AI.8

LF.3.AI.5 DIP.5.AI.10


SEI. 2.AI.1

SEI.2.AI.4 DIP.5.AI.7

SEI.2.AI.4

LA.1.AI.3 NLF.4.AI.4

NLF.4AI.5 DIP.5.AI.10

LA.1.AI.3

LA.1.AI.4

IV. Solving equations (Week #6 - #10)

Solve multi-step equations Solve equations with variables on both sides

Problem solving using linear equations

Literal equations

V. Inequalities (Week #11 - #14)

A. Solve simple & compound inequalities

B. Absolute value inequalities C. Graph inequalities in two variables

VI. Exponents (Week #15 - #17) A. Multiply & divide with exponents

B. Negative & zero exponents C. Problem solving with exponents

D. Scientific notation


Solve equations using inverse operations

Use equations to solve real-life problems Solve literal equations, especially formulas, for a specified variable

Graph and solve simple and compound linear inequalities in one variable

Use a linear inequality as a model for a real-life situation Solve absolute value inequalities

Graph inequalities in two variables

Multiply and divide expressions with exponents Use negative and zero exponents in algebraic expressions

Use powers to model real-life situations Use scientific notation to express large and small numbers


Daily Practice

Released Items

Teacher Made Test Notebook

Released Items


5


LA.1AI.7

SEI.2.AI.1 LF.3.AI.5

LF.3.AI.6

LF.3.AI.8 LF.3.AI.9

NLF.4.AI.2 DIP.5.AI.1

DIP.5.AI.7

DIP.5.AI.9 SEI.2.AI.4

NLF.4.AI.2 NLF.4.AI.4

NLF.4.AI.5

LF.3.AI.8 LF.3.AI.8

DIP.5.AI.1 DIP.5.AI.9

SEI.2.AI.5


LF.3.AI.8

VII. Linear graphing (Week #18 - #21)

(Week #26 Abs Value) A. Graph points, vertical &

horizontal lines, table of

values, standard form, slope- intercept form

B. Graph absolute value, solve absolute value equations

VIII. Writing linear equations (Week #21 - #27)

A. Write linear equations in the Form y = mx + b

B. Line of best fit

C. Problem solving using linear models


Graph points

Graph vertical and horizontal lines

Graph using table of values Graph using intercepts

Graph using slope and y-intercept

Graph and solve absolute value equations

Write linear equations given slope, y-intecept, or points on the line

Find a linear equation that approximates a set of data points Create and use linear models to solve problems


Daily Practice Released Items

Teacher Made Test



6



SEI.2.AI.2


LF.3.AI.7 DIP.5.AI.10

SEI.2.AI.2

IX. Systems of equations (Week #28 - #29) A. Solve systems by graphing,

substitution, & linear combinations

B. Problem solving using systems C. Graph systems of inequalities


Solve a system of linear equations by graphing, substitution, and linear combination Write and use a linear system as a real-life model

Solve a system of linear inequalities by graphing

Determine by using slope if two lines are parallel, perpendicular, or neither


Daily Practice

Released Items

Teacher Made Test

Notebook

Released Items





NLF.4.AI.5 DIP.5.AI.7

NLF.4.AI.3

NLF.4.AI.3

X. Quadratic Equations (Week #30 - #34) A. Square roots

B. Pythagorean theorem C. Parabolas

D. Solve by finding square roots E. Quadratic formula


Evaluate and approximate square roots Use the Pythagorean theorem

Solve a quadratic equation by finding square roots Sketch the graphs of quadratic equations and inequalities

Use the quadratic formula to solve a quadratic equation


Daily Practice

Released Items

Teacher Made Test Notebook

Released Items


7


LA.1.AI.5


NLF.4.AI.3

XI. Polynomials & factoring (Week #35 - #39)

A. Add, subtract, & multiply polynomials

B. Factor polynomials C. Solve equations by factoring


Add and subtract polynomials

Multiply polynomials using FOIL and special patterns

Factor polynomials Use factoring to solve quadratic equations


Daily Practice Released Items

Teacher Made Test



8


LF.3.AI.1 LF.3.AI.3

NLF.4.AI.4 LF.3.AI.2

LF.3.AI.4


SEI.2.AI.8


XII. Functions (All year long) A. Relations & functions

B. Function notation C. Vertical line test

D. Domain & range

E. Independent & dependent variable

XIII. Proportions, percents, probability (End of year)

A. Ratios & proportion

B. Direct & inverse variation C. Problem solving using percents

D. Probability


Identify functions from mappings, tables, ordered pairs, graphs, and from real life

Use vocabulary associated with functions

Use function notation

Solve proportions Solve percent problems

Use direct and inverse variation Find the probability of an event


Daily Practice

Released Items

Teacher Made Test




LA.1.AI.1

SEI.2.AI.7 LA.1.AI.1

LA.1.AI.8


LA.1.AI.1

SEI.2.AI.7

LA.1.AI.1 LA.1.AI.8


XIV. Radicals (End of year)

A. Distance & midpoint formulas B. Simplifying radicals

C. Operations with radicals

D. Solving radical equations

XV. Rational Equations (End of year)

A. Simplify, multiply, divide

rational expressions B. Divide polynomials

C. Solve rational equations

Find the distance and midpoint between two points Simplify radicals

Add and subtract radical expressions

Solve radical equations

Simplify, multiply, and divide rational expressions

Divide a polynomial by a monomial or a binomial

Solve rational equations

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ACTIVITIES

ASSESSMENTS RESOURCES

Daily Practice

Released Items

Teacher Made Test



10



Algebra B HHS

2011-2012

Pam Jones


11



2011-2012 Grade: HHS Subject: Second Part Algebra I

Timeframe (9 Weeks/Month/Semester): August/September/October


Review as necessary

Algebra Language Literal Equations

Slope Slope-Intercept Form

Point-Slope Form

Graphs of Linear Equations Parallel and Perpendicular Lines

Standard Form Real Life Applications using Slope-Intercept

Form and Standard Form Functions and Function Notation



Daily practice with and without technology

Algebra Bingo – solving equations

Graphing with individual marker boards Vocabulary development – ―Personal Word Wall‖

Teacher made tests and quizzes

Calculator assessments

Algebra 1 (Prentice Hall) Making Practice Fun Developing Skills in Algebra 1 TI-84 Programs (D. Smeltz) Nasco ―Bingo‖

Timeframe (9 Weeks/Month/Semester): October/November


Systems of Equations and Inequalities


12


SEI.2.AI.8


LA.1.AI.1 LA.1.AI.5

SEI.2.AI.2

SEI.2.AI.8


Graphs of Systems

Substitution Method

Elimination Method

Applications of Systems

Linear Inequalities

Systems of Linear Inequalities

Solve systems of linear equations by finding the intersection point of the lines with and without technology. Check the solution analytically. Analyze systems with no solutions

and infinitely many solutions.

Solve systems of linear equations analytically using the substitution method. Check solution both graphically and analytically.

Solve systems of linear equations analytically using the elimination method, or linear combinations method. Verify solutions both analytically and graphically.

Write a system of linear equations to model a real life situation. Equations may be in either slope-intercept form or standard form.

Graph and appropriately shade linear inequalities. Model real life situations with linear inequalities.

Solve systems of linear inequalities by graphing. Model real life situations with a system of linear inequalities.


Graphing with individual marker boards Algebra Bingo – Solving Systems of Equations

Vocabulary development – ―Personal Word Wall‖ Daily practice with and without technology

Teacher made tests and quizzes Calculator assessments

Algebra 1 (Prentice Hall) Developing Skills in Algebra 1 TI-84 programs (D. Smeltz) Nasco ―Bingo‖

Timeframe (9 Weeks/Month/Semester): November


LA.1.AI.1

LA.1.AI.3 LA.1.AI.4

LA.1.AI.3 LA.1.AI.4

Exponent

Zero and Negative Exponents

Scientific Notation

Multiplication Properties


Apply the laws of zero and negative exponents to simplify and evaluate expressions.

Represent decimals in scientific notation. Apply exponential rules to simplify expressions and multiply numbers in scientific notation.

Multiply powers with the same bases. Raise a power and a product to a power. Apply exponential rules to divide powers with the same base and raise a quotient to a

power.

13

LA.1.AI.3

NLF.3.AI.4

NLF.3.AI.5

Division Properties

Exponential Functions

Evaluate and graph exponential functions.



Vocabulary development – ―Personal Word Wall‖



Algebra 1 (Prentice Hall) Developing Skills in Algebra 1 TI-84 programs (D. Smeltz)

Timeframe (9 Weeks/Month/Semester): December/January


LA.1.AI.5


SEI.2.AI.8 NLF.3.AI.1

Polynomials

Polynomial Operations

Multiplying and Factoring

Factoring


Describe a polynomial based on its degree and number of terms. Add and subtract

polynomial expressions by combining like terms.

Use the distributive property and FOIL to multiply polynomials. Multiply special binomials for pattern recognition i.e. difference of squares and perfect square trinomial. Factor a

common monomial from a polynomial. Factor polynomials in which the leading coefficient is one and when the leading coefficient

is not one. Recognize patterns in polynomials to factor a difference of squares and a

perfect square trinomial.



Factoring puzzle – matching expanded form with factored form Tic-Tac-Toe method for factoring polynomials

Vocabulary development – ―Personal Word Wall‖



Algebra 1 (Prentice Hall) Handley High School (web page) TI-84 programs (D. Smeltz) Making Practice Fun

14

Timeframe (9 Weeks/Month/Semester): January/February



NLF.3.AI.5 LA.1.AI.1

LA.1.AI.8

SEI.2.AI.7


NLF.3.AI.5



DIP.5.AI.10


NLF.3.AI.4

Quadratic Equations and Functions

Quadratic Graphs

Square Roots

Quadratic Solutions

Discriminant

Data Models

The student will be able to ….

Graph a quadratic equation in the form y=ax2, y=ax

2+c, and y=ax

2+bx+c. Determine a

graph’s axis of symmetry, vertex, minimum, maximum, and zeros. Apply the graph of a

quadratic equation to real life situations. Recognize a perfect square. Use perfect squares to estimate square roots, and calculate

square roots with a calculator. Evaluate radicals and classify the result as rational or

irrational. Solve quadratic equations by graphing and identifying its zero(s) with and without

technology. Solve quadratics in the form y=ax2+c using square roots. Solve quadratic

equations in the form y=ax2+bx+c by factoring and applying the zero-product property.

Solve quadratic equations by using the quadratic formula. Develop an understanding of

choosing the appropriate method for solving quadratic equations. Use the discriminant to determine the number of solutions for a quadratic equation.

Choose a linear, quadratic, or exponential equation to model data and/or a graph. Use two or more graphs (box-and-whisker, histograms, scatter plots to compare data sets.

Explain how sampling methods, bias, and phrasing of questions in data collection impact the conclusions.

Recognize when arguments based on data confuse correlation with causation.



Vocabulary Development – ―Personal Word Wall‖

Graphing with individual marker boards



Algebra 1 (Prentice Hall) Developing Skills in Algebra 1 TI-84 programs (D. Smeltz)

15

Timeframe (9 Weeks/Month/Semester): February/March


LA.1.AI.8 LA.1.AI.9

SEI.2.AI.7 LA.1.AI.1

LA.1.AI.1

LA.1.AI.8


Radical Expressions and Equations

Radical Simplification

Pythagorean Theorem

Distance and Midpoint

Radical Operations

Radical Equations


Simplify radical expressions. Simplify radical expressions involving products and quotients. Solve problems using the Pythagorean Theorem. Identify right triangles.

Find the distance between two points on a coordinate plane. Find the coordinates of the

midpoint of a line segment.

Simplify radical expressions by adding, subtracting, multiplying, and dividing. Apply formulas involving radicals to real life situations.

Solve equations involving radicals. Identify extraneous solutions.


Daily practice – group and individual Vocabulary development – ―Personal Word Wall‖

Teacher made tests and quizzes Calculator assessments

Algebra 1 (Prentice Hall) TI-84 programs (D. Smeltz)

Timeframe (9 Weeks/Month/Semester): March/April/May


SEI.2.AI.6

SEI.2.AI.8 NLF.4.AI.4

LA.1.AI.1 LA.1.AI.6

Rational Expressions

Inverse Variation

Graphs of Rational Functions

Rational Expression Simplification

Multiplication and Division

Rational Equations


Write equations to represent inverse variation given data. Compare inverse variation and

direct variation. Graph rational functions with and without technology. Recognize various families of

functions.

Simplify rational expressions by factoring.

Apply simplification techniques to multiply rational expressions. Convert division statements into multiplication by a reciprocal.

Solve rational equations by finding a least common denominator.



Vocabulary development – ―Personal Word Wall‖ Intensive review of all Algebra 1 topics in preparation for the

Algebra 1 End of Course Exam


Calculator assessments EOC practice

Algebra 1 (Prentice Hall) Making Practice Fun TI-84 programs (D. Smeltz) ALMS

16



Algebra II

2011-2012

Pam Jones


17



2011-2012 Grade: HHS Subject: Algebra II

Timeframe: August/September


LEI.2.AII.1 LEI.2.AII.5

RF.1.AII.1 RF.1.AII.2


LEI.2.AII.1


DAP.6.AII.1

LEI.2.AII.5

I. Algebra I Review

A. Subsets of Real Numbers

B. Equations with Irrational Numbers

C. Solutions and Graphs of Linear Equations and Inequalities

D. Basic Counting Methods and

Permutations

II. Models and Functions:

A. Relations and Functions – Notation, Composition, Operations

B. Slope of a Line

C. Graphical Models

D. Solutions and Graphs of

Absolute-Value Equations and Inequalities


Reviewing types of numbers (Rational and Irrational)

Solving equations using irrational numbers

Solving one-variable equations and inequalities Solving absolute-value equations and inequalities

Using basic counting methods

Finding permutations

Defining and using relations and functions; deciding whether a relation is a function; combining and adding functions; piece-wise and step functions

Defining and interpreting slope

Making predictions regarding linear functions Organizing data in tables, matrices, and graphs; representing data graphically

Solving and graphing equations and inequalities having two variables Graphing absolute-value equations having two variables

18

RF.1.AII.4 LEI.2.AII.1

DAP.6.AII.2

E. Vertical and Horizontal Translations

Analyzing vertical and horizontal translation of a function


Daily Practice

Translate functions TI-Navigator questioning/response

Pre-test Algebra I

Teacher made quizzes and tests TI-Navigator System

Algebra II book Skills and Concepts Review book Student Study materials

Timeframe : October


LEI.2.AII.1

LEI.2.AII.2


RF.1.AII.9

LEI.2.AII.5

LEI.2.AII.2

LEI.2.AII.4

RF.1.AII.9 LEI.2.AII.3

LEI.2.AII.3

III. Linear Systems

A. Systems of Equations and

Inequalities – Substitution,

Elimination, Graphs

B. Linear Programming

C. Systems of Equations in Three

Variables

IV. Matrices

A. Matrices of Statistical Data

B. Equal Matrices

Operations with Matrices-

Addition, Subtraction, Solutions, Scalar, Multiplication


Solving a system by graphing

Graphing systems of inequalities

Using substitution to solve a system of equations Using elimination to solve a system of equations

Solving linear programming problems

Graphing points in three dimensions

Graphing equations in three dimensions Using elimination to solve systems with three variables

Using substitution to solve systems with three variables

Organizing data into matrices

Solving matrix equations

Adding and subtracting matrices

Multiplying matrices Using scalars to multiply

Evaluate determinants of square matrices

19


Daily Practice

TI-Navigator questioning/response

Teacher made quizzes and tests

TI-Navigator System

Algebra II book Skills and Concepts Review book Student Study materials Interactive e-beam

Timeframe: November


RF.1.AII.4

LEI.2.AII.3

LEI.2.AII.3

RF.1.AII.3

LEI.2.AII.3


LEI.2.AII.5

RF.1.AII.1

QEF.3.AII.3 QEF.3.AII.5

DAP.6.AII.3

DAP.6.AII.4

C. Translations and Dilations

D. Finite and Directed Graphs

E. Inverses

F. Systems of Equations - Matrices

G. Matrices and the Graphing

Calculator

V. Quadratic Equations and

Functions

A. Quadratic Functions


Representing translations and dilations with matrices

Drawing and interpreting finite graphs

Drawing and interpreting directed graphs

Finding and using the inverse of a 2 x 2 matrix

Using inverse matrices to solve matrix equations

Solving systems of equations using inverse matrices Comparing methods used to solve systems

Using the graphing calculator to graph matrices and perform operations with matrices

Recognizing and using quadratic functions

Deciding whether to use a linear or a quadratic model with and without the use of technology

20

RF.1.AII.4 QEF.3.AII.3

QEF.3.AII.5

B. Parabolas – Comparisons and Translations

Finding the minimum or maximum value of a quadratic function Graphing a parabola in vertex form


Daily Practice Develop a parabola

Use graphing calculators to solve systems of equations TI-Navigator questioning/response

Teacher made quizzes and tests TI-Navigator system

Algebra II book Skills and Concepts Review book Student Study materials Graphing Calculators

21

Timeframe: December


QEF.3.AII.3

QEF.3.AII.5


QEF.3.AII.5

QEF.3.AII.3

QEF.3.AII.5

C. Vertex and Standard Form of a

Parabola

D. Inverse and Square Root Functions

E. Zero Product Property


Finding the vertex of a function written in standard form

Writing equations in vertex and standard forms

Finding the inverse of a function Using square root functions

Solving quadratic equations by factoring, finding square roots, and graphing


Daily Practice TI-Navigator questioning/response

Teacher made quizzes and tests TI-Navigator system


Timeframe: January



QEF.3.AII.1


QEF.3.AII.4

QEF.3.AII.2

QEF.3.AII.5

F. Complex Numbers

G. Quadratic Equations – Complete

the Square, Quadratic Formula

H. Discriminant of Quadratic

Formula


Identifying and graphing complex numbers Adding, subtracting, and multiplying complex numbers

Solving quadratic equations by completing the square

Rewriting quadratic equations in vertex form Derive the quadratic formula and use it to solve quadratic equations

Determining types of solutions using the discriminant

22

RF.1.AII.1


QEF.3.AII.1 PRF.4.AII.2

PRF.4.AII.5

PRF.4.AII.8


PRF.4.AII.2 PRF.4.AII.7

PRF.4.AII.8


PRF.4.AII.2

RF.1.AII.4


PRF.4.AII.1

QEF.3.AII.2




PRF.4.AII.1

VI. Polynomials and Polynomial

Functions

A. Power Functions and Their

Inverses

B. Powers and Roots

C. Polynomial Functions

D. Models of Data for Polynomial

Functions

E. Factored Form of a Polynomial

F. Factors and Zeros of a

Polynomial Function

G. Solutions of Equations by Graphs and Factors

H. Division of Polynomials – Long

Exploring graphs of power functions

Using exponents for radicals

Using powers and roots to solve equations

Describing graphs of polynomial functions

Fitting polynomial models to data

Analyzing the factored form of a polynomial

Writing a polynomial from its zeros

Analyzing multiple zeros and factors

Solving polynomial equations by factoring Solving polynomial equations by graphing

Dividing polynomials

23

PRF.4.AII.2

and Synthetic

Finding all the zeros of a polynomial


Daily Practice

Teacher made quizzes and tests Algebra II book Skills and Concepts Review book Student Study materials Graphing Calculators

Timeframe: February


PRF.4.AII.3

PRF.4.AII.3

QEF.3.AII.1 PRF.4.AII.8

QEF.3.AII.1

PRF.4.AII.7

PRF.4.AII.8

QEF.3.AII.1

RF.1.AII.2

RF.1.AII.9

I. Binomial Expansions and

Pascal’s Triangle

J. The Binomial Theorem

VII. Roots and Radicals

A. Roots and Radical Expressions

B. Radical Expression

Operation

C. Rational Exponents

D. Radical Equations

E. Function Operations


Using Pascal’s triangle

Using the binomial theorem

Simplify nth roots

Add, subtract, multiply, and divide radical expressions

Simplify expressions with rational exponents

Solve radical equations

Add, subtract, multiply, and divide functions

Find composite of two functions

24


Daily Practice



TI-Navigator System

Algebra II book Skills and Concepts Review book Student Study materials Graphing Calculators Interactive E-beam

Timeframe: March


RF.1.AII.2

RF.1.AII.3


PRF.4.AII.8

ELF.5.AII.1

ELF.5.AII.2 ELF.5.AII.3

RF.1.AII.9

ELF.5.AII.1 DAP.6.AII.4


ELF.5.AII.5

ELF.5.AII.6

F. Inverse Relations and

Functions

G. Radical Functions

VIII. Exponential and Logarithmic Functions

A. Exponential Functions – Models

and Graphs

B. Models of Growth and Decay

C. The Number ―e‖

D. Logarithmic Expressions –

Evaluation and Written Forms


Finding the inverse of a relation or a function

Graphing radical functions

Graphing exponential functions

Identifying the role of constants in y = ab^(kx)

Identifying domain, range, intercepts, asymptotes, and end behavior Using other bases, identify the effects on the graph

Modeling exponential growth and decay with and without the use of technology

Using ―e‖ as a base

Using logarithmic notation

Evaluating logarithmic expressions

Graphing logarithmic functions


Daily Practice

M & M Exponential Growth and Decay Lab TI-Navigator questioning/response


TI-Navigator system


25

Timeframe: April


ELF.5.AII.5


QEF.3.AII.1

ELF.5.AII.4

ELF.5.AII.5



PRF.4.AII.6

QEF.3.AII.1

E. Properties of Logarithms

F. Equations Containing Exponents

or Radicals

G. Exponential and Logarithmic

Equations

H. Natural Logarithms

IX. Rational Functions

A. Rational Expressions –

Simplification, Multiplication, Division, Addition, Subtraction

B. Conjugates


Condensing and expanding logarithmic expressions

Applying properties of logarithms

Solving equations with exponents

Using logarithms to solve exponential equations

Using exponents to solve logarithmic equations

Relating natural logarithms to the function Y = e^(x)

Solving equations using natural logarithms

Simplifying rational expressions

Multiplying and dividing rational expressions Adding and subtracting rational expressions

Identifying and classifying discontinuities of rational functions

Identifying behavior near asymptotes

Using conjugates to simplify radicals


Daily Practice



TI-Navigator system


26

Timeframe: May


DAP.6.AII.5

DAP.6.AII.5

DAP.6.AII.6

RF.1.AII.6


X. Data Analysis and Probability

A. Data Analysis

B. Standard Deviation

C. Normal Distributions

XI. Periodic Functions

A. Periodic Data


Calculate measures of central tendencies and draw and interpret box-and-whisker plots

Compute and explain percentiles

Compute and explain measures of spread including range, variance, and standard

deviation

Describe the characteristics of a Gaussian normal distribution

Recognize periodic phenomena (sine or cosine functions such as sound waves, length of daylight, circular motion)

Investigate and identify key characteristics of period functions and their graphs (period, amplitude, maximum, and minimum)

Use basic properties of frequency and amplitude to solve problems


Daily practice

RAFT projects on terminology ―Who has, I have‖



RAFT projects TI-Navigator system

Algebra II book Skills and Concepts Review book Student Study materials Graphing Calculators Interactive e-beam

27



Algebraic Connections

2011-2012

Pam Jones


28


Harrison School District 2011-2012 Grade: 10th-12th Subject: Algebraic Connections

Timeframe: First Nine Weeks


LF.2.AC.3

LF.2.AC.3 NF.4.AC.6

NF.4.AC.6

LF.2.AC.4

LF.2.AC.5 LF.2.AC.6

LF.2.AC.7

LF.2.AC.4 LF.2.AC.5

LF.2.AC.6

LF.2.AC.7

LF.2.AC.8

LF.2.AC.4

LF.2.AC.5 LF.2.AC.7

LF.2.AC.4

LF.2.AC.5

Graphical Models

Relations and Functions- Notation, Composition, Operations

Vertical and Horizontal Translations

Slope and Slope Intercept Form of a Line

Linear Equations in Slope Intercept and Standard Forms

Piecewise Functions

Equations of Lines Using Slope Intercept

Form

Equations of Lines Given the Slope and a Point


Organize data in tables, matrices, and graphs Represent data graphically

Define and use relations and functions Decide whether a relation is a function

Combine and add functions

Analyze vertical and horizontal translation of a function

Define and interpret slope

Use the slope-intercept form to write equations

Write linear equations in slope-intercept and standard forms Make predictions regarding linear functions

Graph piecewise functions

Use the slope intercept form to write an equation of a line

Model a real-life situation with a linear equation

Use slope and any point on a line to write an equation of the line


29

LF.2.AC.7

LF.2.AC.4

LF.2.AC.5

LF.2.AC.7

LF.2.AC.4 LF.2.AC.5

LF.2.AC.7

LF.2.AC.4

LF.2.AC.5 LF.2.AC.7

PS.1.AC.5

PS.1.AC.5

PS.1.AC.5

Equations of Lines Given Two Points

Standard Form of a Linear Equation

Point-Slope Form of the Equation of a Line

Inductive and Deductive Reasoning

Estimation and Graphs

Problem Solving

Write an equation of a line given two points on the line


Transform a linear equation into standard form Model a real-life situation using the standard form of a linear equation

Use the point-slope form to write an equation of a line

Model a real-life situation using the point-slope form of a linear equation

Understand and use inductive reasoning

Understand and use deductive reasoning

Use estimation techniques to arrive at an approximate answer to a problem

Apply estimation techniques to information given by graphs

Solve problems using the organization of the four-step problem-solving process


Daily practice Use the graphing calculator in problem solving and using

information derived from the graph of a linear equation

Teacher made quizzes and tests Daily Observation/Participation

Algebra II book Algebra I book Thinking Mathematically book Student study materials TI-Navigator system

Timeframe: Second Nine Weeks


PS.1.AC.3

Basic Set Concepts


Apply set notation to sets of natural numbers

Recognize equal and equivalent sets

30

PS.1.AC.3

PS.1.AC.3

PS.1.AC.3

PS.1.AC.3

Connection

Connection

Connection

NF.4.AC.2

NF.4.AC.2

Connection

SEI.3.AC.6

NF.4.AC.5

Venn Diagrams and Subsets

Venn Diagrams and Set Operations

Set Operations and Venn Diagrams with

Three Sets

Surveys and Cardinal Numbers

Number Theory: Prime and Composite

Numbers

The Integers; Order of Operations

The Rational Numbers

The Irrational Numbers

Real Numbers and Their Properties

Exponents and Scientific Notation

Arithmetic and Geometric Sequences

Understand the basic ideas of Venn diagrams Determine the number of subsets of a set

Use Venn diagrams to visualize set relationships Perform operations with sets

Use Venn diagrams with three sets

Use Venn diagrams to illustrate equality of sets

Use Venn diagrams to vfisualize a survey's results

Use survey results to complete Venn diagrams and answer questions about the survey

Write the prime factorization of a composite number

Find the greatest common divisor and the least common multiple of two numbers

Solve problems using the greatest common divisor and the least common multiple

Define and graph integers on a number line Perform operations with integers

Define and reduce rational numbers Perform operations with rational numbers

Define irrational numbers

Simplify and perform operations with square roots Rationalize the denominator

Recognize subsets of the real numbers Recognize properties of real numbers

Use properties of exponents

Convert from scientific notation to decimal notation, vice versa

Perform computations using scientific notation Solve applied problems using scientific notation

Write terms of an arithmetic and geometric sequence

Use the formula for the general term of an arithmetic and geometric sequence

31

SEI.3.AC.1

SEI.3.AC.1 SEI.3.AC.3

SEI.3.AC.6

SEI.3.AC.6 NF.4.AC.5

SEI.3.AC.6

SEI.3.AC.1

NF.4.AC.1

NF.4.AC.1

NF.4.AC.3

Algebraic Expressions and Formulas

Linear Equation solutions

Applications of Linear Equations

Ratio, Proportion, and Variation

Linear Inequality Solutions

Polynomial Factoring

Quadratic Equation Solutions

Evaluate, understand the vocabulary, and simplify algebraic expressions Evaluate formulas

Solve linear equations Solve for a variable in an equation or formula

Identify equations with no solution or infinitely many solutions

Solve problems using linear equations

Find ratios and solve proportions Solve problems using proportions, direct variation, and inverse variation

Graph the solutions of an inequality on a number line Solve linear inequalities and applied problems using linear inequalities

Factor polynomials that have a monomial factor, that are the difference of two perfect

squares, and that are perfect-square trinomials

Factor a quadratic trinomial or recognize that it cannot be factored Use factoring to solve quadratic equations

Multiply binomials using the FOIL method

Factor trinomials Solve quadratic equations by factoring

Solve quadratic equations using the quadratic formula


Daily practice

Tic-Tac-Toe Factoring Method AC Factoring Method

Tic-Tac-Toe Match the Factors Use graphing calculators in working with quadratic

equations

Teacher made quizzes and tests Vocabulary Journal (kept in notebook)

RAFT project on terminology Daily Observation/Participation

Algebra I book Thinking Mathematically book Student study materials TI-Navigator system

32

Timeframe: Third Nine Weeks


SEI.3.AC.4

LF.2.AC.4 LF.2.AC.5

LF.2.AC.7

NF.4.AC.4

NF.4.AC.5

NF.4.AC.6

SEI.3.AC.1

SEI.3.AC.2

SEI.3.AC.1

SEI.3.AC.2

SEI.3.AC.5

Graphs and Functions

Linear Functions and Their Graphs

Quadratic Functions and Their Graphs

Exponential Functions

Systems of Linear Equations

Linear Inequalities in Two Variables

Measurement


Plot ordered pairs in the rectangular coordinate system

Graph functions and equations Use f(x) notation and the vertical line test

Obtain information about a function from its graph

Use intercepts to graph a linear equation Calculate slope

Use the slope and y-intercept to graph a line

Graph horizontal and vertical lines Interpret slope and y-intercept in applied situations

Graph parabolas

Solve applied problems based on knowing a parabola's vertex

Graph exponential functions Solve applied problems using exponential functions

Decide whether an ordered pair is a solution of a linear system

Solve linear systems by graphing, substitution, and elimination

Identify systems that do not have exactly one ordered-pair solution Solve problems using systems of linear equations

Graph a linear inequality

Graph a system of linear inequalities

Use dimensional analysis to change units of measurement Use square units to measure area

Use dimensional analysis to change units for area

Use cubic units to measure volume

33

SEI.3.AC.4

SEI.3.AC.5

PS.1.AC.1

PS.1.AC.1

PS.1.AC.1

PS.1.AC.2

PS.1.AC.3

PS.1.AC.4

PS.1.AC.1

PS.1.AC.3

PS.1.AC.4

Geometry

The Fundamental Counting Principle

Permutations

Combinations

Fundamentals of Probability

Probability with the Fundamental Counting

Principle, Permutations, and Combinations

Events Involving Not, Or, and And; Odds;

Conditional Probability

Understand points, lines, and planes as the basis of geometry

Solve problems involving angle measures Solve problems involving angles formed by parallel lines and trnsversals

Solve problems involving angle relationships in triangles

Solve problems involving similar triangles Solve problems using the Pythagorean Theorem

Name certain polygons according to the number of sides Recognize the characteristics of certain quadrilaterals

Use area formulas to compute the areas of plane rgions and solve applied problems

Use formulas for a circle's circumference and area Use volume formulas to compute the volumes of three-dimensional figures and solve

applied problems Compute the surface area of a three-dimensional figure

Use the lengths of the sides of a right triangle to find trigonometric ratios Use trigonometric ratios to find missing parts of right triangles

Use the Fundamental Counting Principle to determine the number of possible outcomes

in a given situation

Use the Fundamental Counting Principle to count permutations

Evaluate factorial expressions

Distinguish between permutation and combination problems Solve problems involving combinations using the combinations formula

Compute theoretical and empirical probability

Compute probabilities with permutations and combinations

Find the probability that an event will occur

Find the probability of one event or a second event occurring Understand and use odds

Compute conditional probabilities

34


Daily practice Use the graphing calculators in working with probabilities

and solving system of equations


Thinking Mathematically book Student study materials TI-Navigator system

Timeframe: Fourth Nine Weeks


PS.1.AC.5 LF.2.AC.1

PS.1.AC.5

LF.2.AC.2

SEI.3.AC.6

Sampling, Frequency Distributions, and Graphs

Measures of Central Tendency

The Normal Distribution, Scatter Plots, Correlations, and Regression Lines

Consumer Mathematics and Financial Management


Describe the population whose properties are to be analyzed Select an appropriate sampling technique

Organize and present data Identify deceptions in visual displays of data

Determine the mean, median, mode, and midrange for a set of data

Recognize characteristics of normal distributions Understand and use percentiles

Make a scatter plot for a table of data items

Interpret information given in a scatter plot Compute the correlation coefficient

Write the equation of regression line

Work with percent problems Calculate simple and compound interest

Engage in the Installment Buying process

Understand and determine the Cost of Home Ownership Understand Investing in Stocks, Bonds, and Mutual Funds


Daily practice Graphic Organizers

Use the graphing calculators in working with scatter plots and regression lines

Teacher made quizzes and tests Vocabulary Journal (kept in notebook)

RAFT project on terminology Daily Observation/Participation

Thinking Mathematically book Student study materials TI-Navigator system

35



Geometry

2011-2012

Pam Jones


36



2011-2012 Grade: HHS Subject: Geometry


FRAMEWORK

S

CONTENT SKILLS

LG.1.G.1

LG1.G.3

LG.1.G.2

LG.1.G.3

LG.1.G.2

LG.1.G.5

LG.1.G.4

LG.1.G.6

CGT.5.G.1

M.3.G.2,M.3.G.3

,C.G.T.5.G.1

I. Tools of Geometry

A. Patterns and Inductive

Reasoning

B. Points, Lines, and Planes

C. Segments, Rays, Parallel Lines

and Planes

D. Angle and Segment

Measurement

E. The Coordinate Plane –

distance and midpoint

F. Perimeter, Circumference &

Area


Use inductive reasoning to make conjectures

Understand basic terms of geometry

Understand basic postulates of geometry

Relate segments and rays to lines

Recognize parallel lines and parallel planes

Find the length of a segment or the measure of an angle

Find the distance between two points in a coordinate plane

Find the coordinates of the midpoint of a segment in a coordinate plane

Find perimeter of squares, rectangles, and circumference of circles

Find the area of rectangles, squares and circles.


Daily Practice

Cabri Geometry calculator activities


Daily Observations

TI-Navigator poll/short quiz

Geometry TextbookSkills and Concepts Review

book

Student Study materials

Graphing Calculators

37

Timeframe: October


LG.1.G.1

LG.1.G.1,

LG.1.G.6

LG.1.G.6

LG.1.G.4

LG.1.G.6

Conditional statements

Deductive Reasoning

Reasoning and algebra

Proving Angles congruent


Recognize conditional statements

Write the converse, inverse and contrapositive of conditional statements.

Define , identify deductive reasoning.

Justify steps in a logical argument.

Identify vertical angels, adjacent angles, complementary angles, supplementary angles

Prove and apply theorems about angles.


Daily Practice


Daily Observations



book



38

Timeframe: October


LG.1.G.5

LG.1.G.6

R.4.G.2

LG.1.G3

M.3.G.3

R.4.G.2

CGT.5.G.1

CGT.5.G.2

CGT.5.G.1

CGT.5.G.2

PROPERTIES OF Parallel lines

Parallel lines and the Triangle Angle-Sum

Theorem.

The polygon angle-sum theorems.

Lines in the coordinate plane.

Slopes of parallel and perpendicular lines


Identify angles formed by two lines and a transversal.

Prove properties of parallel lines.

To classify triangles and find the measures of their angles.

Classify polygons

Find the sums of the measures of the interior and exterior angles of polygons.

Graph lines given their equation.

Write equations of lines parallel to a given line through a given point.

Write the equation of a line perpendicular to a line through a given point.

Write the equation of the perpendicular bisector of a line segment.

Relate slope and parallel and perpendicular lines.

Write the equations for a line parallel or perpendicular to the given line.


Daily Practice

Cabri geometry activities


Daily Observations



book



39

Timeframe: October/November


LG.1.G6

T.2.G.1

LG.1.G.6

T.2.G.1

T.2.G.3

M.3.G.3

LG.1.G.6

T.2.G.1

T.2.G.3

R.4.G.2

LG.1.G.6

T.2.G.3

LG.1.G.6

T.2.G.1

Congruent figures

Triangle Congruence by SSS, SAS,

ASA, and AAS

Isosceles and Equilateral Triangles

Congruence in Right Triangles

Using Corresponding Parts of Congruent

Triangles

Students will be able to recognize:

Congruent figures and their corresponding parts.

Prove two triangles congruent using SSS and SAS postulates.

Prove two triangles congruent using the ASA postulate and the AAS postulate.

Use and apply properties of isosceles triangles.

Prove triangles congruent using the HL Theorem.

Identify congruent overlapping triangles.

Prove two triangles congruent by first proving tow other triangles congruent.


Daily Practice


Daily Observations



book



Timeframe: November


T.2.G.3

M.3.G.3

M.3.G.5

T.2.G.3

T.2.G.3

M.3.G.3

R.4.G.6

LG.1.G.1

Midsegments of Triangles

Bisectors of Triangles

Concurrent Lines, Medians, and Altitudes

Inverses, Contrapositives, and Indirect

The student will be able to: Use properties of midsegments to solve problems.

Use properties of perpendicular bisectors and angle bisectors.

Identify properties of perpendicular lines and angle bisectors.

Identify properties of medians and altitudes of atriangles.

Write the negation of a statement and the inverse and contrapositive of a conditional statement.

40

LG.1.G.6

T.2.G.2

M.3.G.3

R.4.G.4

Reasoning

Inequalities in Triangles

Use Inequalities involving angles and sides of triangles.


Daily Practice


Daily Observations


Timeframe: December


LG.1.G.3

R.4.G.1

CGT.5.G.5

LG.1.G.6

R.4.G.1

R.4.G.2

M.3.G.5

LG.1.G.3

LG.1.G.6

R.4.G.1

LG.1.G.3

M.3.G.3

R.4.G.1

R.4.G.1

R.4.G.2

R.4.G.1

CGT.5.G.1

Classifying Quadrilaterals

Properties of Parallelograms

Proving That a Quadrilateral is a

Parallelogram

Special Parallelograms

Trapezoids and Kites

Placing Figures in the Coordinate Plane

Define and classify special types of triangles.

Use relationships among sides and among angles of parallelograms,

Use relationships involving diagonals of parallelograms or transversals.

Determine whether a quadrilateral is a parallelogram.

Use properties of diagonals of rhombuses and rectangles.

Determine whether a parallelogram is a rhombus or a rectangle.

Verify and use properties of trapezoids and kites.

Prove theorems using the coordinate plane.

41


Daily Practice


Daily Observations



book



Timeframe: January


M.3.G.2

CGT.5.G.1

T.2.G.4

M.3.G.2

T.2.G.5

M.3.G.2

T.2.G.5

M.3.G.2

T.2.G.5

M.3.G.2

R.4.G.2

LG.1.G.3

R.4.G.5

LG.1.G.3

M.3.G.3

R.4.G.5

R.4.G.6

M.3.G.1

Areas of Parallelograms and Triangles

The Pythagorean Theorem and It’s Converse

Special Right Triangles

Areas of Trapezoids, Rhombuses, and Kites

Areas of Regular Polygons

Circles and Arcs

Areas of Circles and Arcs

Geometric Probability

Find the area of a parallelogram.

Find the area of a triangle.

Use the Pythagorean Theorem and its converse.

Use the properties of the 45-45-90 and the 30-60-90 triangle.

Find the area of a trapezoid, rhombus and a kite.

Find the area of a regular polygon.

Find the measures of central angles and arcs.

Find the areas of circles, sectors and segments of circles.

Use segment and area models to find the probability of events.


Daily Practice

Cabri Geometry graphing calculator activities


Daily Observations



book



42

Timeframe: January/February

FRAMEWORK

S

CONTENT SKILLS

M.3.G.4

TG.2.G.1

M.3.G.4

T.2.G.1

M.3.G.4

T.2.G.1

M.3.G.4

M.3.G.3

M.3.G.4

M.3.G.5

M.3.G.3

M.3.G.4

Ratios and Proportions

Similar Polygons

Proving Triangles Similar

Similarity in Right Triangles

Proportions in Triangles

Perimeter and Areas of Similar Figures

Students will be able to:

Write ratios and solve proportions.

Identify similar polygons.

Apply similar polygons.

Use and apply AA, SAS, and SSS similarity statements.

Find and use relationships in similar right triangles.

Use the side splitter theorem.

Use the triangle-angle-bisector theorem.

Find the perimeters and areas of similar figures.


Daily Practice


Daily Observations



book



Timeframe: February/ March

FRAMEWORK

S

CONTENT SKILLS

T.2.G.6

T.2.G.7

T.2.G.6

T.2.G.7

M.3.G

The Tangent Ratio

Sine and Cosine Ratios

Use tangent ratios to determine side lengths in triangles.

Use sine and cosine to determine side lengths in triangles.

43

T.2.G.6

T.2.G.7

Angles of Elevation and Depression

Use angles of elevation and depression to solve problems.


Daily Practice


Daily Observations



book



Timeframe: March/April


R.4.G.4

R.4.G.7

R.4.G.7

R.4.G.8

M.3.G.2

M.3.G.3

M.3.G.2

M.3.G.2

T.2.G.2

M.3.G.2

M.3.G.2

M.3.G.3

M.3.G.4

Space Figures and Nets

Space Figures and Drawings

Surface Areas of Prisms and Cylinders

Surface Areas of Pyramids and Cones

Volumes of Prisms and Cylinders

Volumes of Pyramids and Cones

Surface Areas and Volumes of Spheres

Areas and Volumes of Similar Solids

Recognize nets of space figures.

Make isometric and orthographic drawings.

Describe cross sections of three-dimensional figures.

Find the surface area of a prism.

Find the surface area of a cylinder.

Find the surface area of a pyramid.

Find the surface area of a cone.

Find the volume of a prism and a cylinder.

Find the volume of a pyramid and a cone.

Find the surface area and volume of a sphere.

Find relationships between the ratios of areas and volumes of similar solids.


Daily Practice Teacher made quizzes and tests

Daily Observations



book



Timeframe: April/May

44


R.4.G.5

R.4.G.5

R.4.G.5

R.4.G.6

R.4.G.5

CGT.5.G.6

CGT.5.G.7

CGT.5.G.7

CGT.5.G.7

R.4.G.3

CGT.5.G.7

Tangent Lines

Chords and Arcs

Inscribed Angles

Angle Measures and Segment Lengths

Circles in The Coordinate Plane

Reflections

Translations

Rotations

Tessellations

Dilations

Students will be able to:

Use relationships between a radius and a tangent.

Use relationships between two tangents from one point.

Use congruent chords, arcs, and central angles.

Recognize properties of lines through the center of a circle.

Find the measure of an inscribed angle.

Find the measure formed by a tangent and a chord.

Find the measures of angles formed by chords, secants and tangents.

Find the lengths of segments associated with circles.

Write and equation of a circle.

Find the center and radius of a circle.

Identify isometries.

Find the reflection of an image.

Describe translations using vectors.

Find translation images using matrix and vector sums.

Draw and identify rotation images of figures.

Identify Figures that will tessellate.

Locate dilation images of figures.


Daily Practice Teacher made quizzes and tests

Daily Observations



book



45



Investigating Geometry

2011-2012

Pam Jones


46

CURRICULUM MAP

Harrison School District 2011-2012 Grade: HHS Subject: Investigating Geometry

Timeframe: Semester I


L.G.1.G.2

R.4.G.2

C.G.T.G. 1

R.4.G.1

R.4.G.5

Building Blocks of Geometry

Coordinate Geometry

Quadrilaterals

Circles


-Represent point, line, plane, ray, and segment with proper notation and description or definition.

-define and classify polygons according to the number of sides.

-use midpoint formula to find midpoint of a segment.

-define and classify quadrilaterals according to their properties.

-define circles and their parts including: arcs, chords, tangents, secants,


Daily Practice

Checkpoint Quizzes

Teacher Made Test Notebook; Vocabulary Journal

-Discovering Geometry; Text -ACTAAP released Items - Geometer’s Sketch Pad



R.4.G.7

R.4.G.8

L.G.1.G.1

Geometric Solids

Reasoning

The student will be able to…. -define and identify geometric solids including: prisms, pyramids, cylinders, cones,

spheres. -identify and sketch cross sections of various solids

-define, compare and contrast inductive and deductive reasoning. -apply inductive reasoning to find the next term in the sequence, find the nth term.

-apply mathematical models to solve problems.

47

L.G.1.G.4

L.G.1.G.5

C.G.T.5.G.2

C.G.T.5.G.1 R.4.G.6

Angle Relationships

Transversals and Parallel Lines

Slopes, Parallel, perpendicular lines

Points of Concurrency and

construction.

-identify and apply properties for vertical, complementary, supplementary, and angles

formed by perpendicular lines.

-find angle measures based on alternate interior angles, corresponding angles, and

consecutive interior angles. -determine whether lines are parallel, perpendicular, or neither based on the slope of the

line. -construct the points of concurrency and solve problem involving inscribed and

circumscribed circles.


-Build Geometric solids using polydron and greeting cards -Construct Points of concurrency using compass

- Daily Practice

-Quizzes -Teacher Made Tests

-Project

-Prentice Hall Mathematics -ACTAAP Released Items -Discovering Geometry; Text -Geometer’s Sketch Pad



T.2.G.3

R.4.G.2

T.2.G.2

T.2.G.1

L.G.1.G.6

Special Segments of Triangles

Properties of Triangles

Congruent Triangles


-construct and define median, altitude, angle bisector, perpendicular bisector of

triangles.

-use sum of angle measures of a triangle to find angle measures in regular and irregular polygons.

-use the triangle inequality theorem to determine whether three segments form a

triangle. -order angles in relation to corresponding lengths of sides.

-apply properties of isosceles triangles.

-use SSS, SAS, ASA, AAS postulates to prove triangles congruent and to find missing

parts. -use CPCTC and congruence postulates and flow charts to prove segments congruent.

48


-Class activity using compass to construct special segments.

- Spaghetti activity for Triangle Inequality Theorem - Daily Practice

Quizzes

Teacher made test Notebook/Vocabulary journal

Discovering Geometry; Text ACTAAP released items Geometer’s Sketch Pad

Timeframe: Semester II


R.4.G.2

R.4.G.1

T.2.G.3

R.4.G.1

R.4.G.5

M.3.G.2

Polygons

Properties of Circles

Circumference & Diameter

The student will be able to…. -Find the sum of interior angle measures of polygons

-find the sum of exterior angle measures of polygons -define and apply properties of kites and trapezoids

-define and apply properties of mid-segments -use properties of parallelograms to find angle measures.

-apply properties of squares and rectangles to find missing information.

-apply properties of chords of circles and their central angles.

-use intersection of perpendicular bisector to locate the center of a circle. - determine measure of intercepted arc of inscribed angles and vice versa.

-use relationship between circumference and diameter to solve problems.

-apply formula for circumference to solve real world problems.


Daily Practice

Quizzes

Teacher made test

Notebook/ Vocabulary Journal

Discovering Geometry; Text ACTAAP Released Items Geometer’s Sketch Pad

49


C.G.T.5.G.5

R.4.G.3

M.3.G.2

M.3.G.1

T.2.G.4

T.2.G.5

Transformation & symmetry

Tessellation

Area

Geometric Probability

Pythagorean Theorem

Special Triangles


-draw and interpret the results of transformation and successive transformations on figures in the coordinate plane.

-identify and explain why figures tessellate.

-use appropriate formula to find area of common polygons and circles. -use area formulas to solve problems.

-find surface area of prisms, cylinders, pyramids, cones and spheres. -find the probability of hitting a particular area on a dart board.

-apply Pythagorean Theorem and its converse in solving problems

-use special triangle relationships to solve problems involving 30-60-90; 45-45-90 special ratios.


-Tessellation Project

-Daily Practice

-Quizzes -Project

-Teacher Made Test -Notebook/ Vocabulary Journal

-Discovering Geometry ; text and resources - ACTAAP Released Items



C.G.T.5.G.1

C.G.T.5.G.3

C.G.T.G.4

M.3.G.2

R.4.G.4 R.4.G.7

T.2.G.1

Coordinate Geometry

Volume

Platonic Solids Orthographic Drawings

Similarity

The student will be able to…. -use distance formula to find length of line segment.

-determine the type of figure based on properties given a set of points.

-write the equation for a circle in standard form given the center of the circle and the radius.

-use appropriate formulas to find volume of prisms, cylinders, pyramids, cones, spheres, hemispheres.

-Identify the attributes of the five platonic solids -use orthographic drawings to represent three-dimensional figures

-use properties of similar figures to find missing parts of geometric figures and explain

50

M.3.G.4

Proportional Reasoning

why.

-use proportional reasoning to solve problems involving indirect measurement


-daily Practice

-Build Platonic Solids Ornament Project

a. Quizzes b. Teacher Made Test

c. Notebook/ Vocabulary

Journal

d. Discovering Geometry; Text and Resources

e. ACTAAP Released Items f. Geometer’s Sketch Pad



M.3.G.3

M.3.G.5

L.G.1.G.1

T.2.G.6

Proportions with area and volume

Proportional Segments and parallel lines

Conditional Statements and forms of valid reasoning

Trigonometric ratios


-determine how changing the radius or height will effect the area and volume .

-apply relationship between ratios of parts into which parallel lines cut the sides of a triangle.

-determine the inverse, converse, and contrapositive of a conditional statement and determine its truth value.

-use sine, cosine, tangent, angle of elevation and angle of depression to find angle

measures and lengths of sides in right triangles.


-Daily Practice

g. Quizzes

h. Teacher Made Test

i. Notebook/ Vocabulary Journal

- Discovering Geometry; Text and resources -ACTAAP Released Items

51



Pre-Calculus

2011-2012

Pam Jones


52

CURRICULUM MAP


2011-2012 Grade: 11,12 Subject: Pre-Calculus



Algebra

Review Material

I. Prerequisites (8+ days)

A. Real Numbers

B. Cartesian Coordinate System

C. Linear Equations and Inequalities

D. Lines in the Plane

E. Solving Equations Graphically,

Numerically, and Algebraically

F. Complex Numbers

G. Solving Inequalities Algebraically

and Graphically

H. Solving Systems of Two Equations

I. Matrix Algebra


Convert between decimals and fractions, write inequalities, apply the basic properties of algebra, and work with exponents and scientific notation.

Graph points, find distances and midpoints on a number line and in a coordinate plane,

and write standard-form equations of circles.

Solve linear equations and inequalities in one variable.

Use the concepts of slope and y-intercept to graph and write linear equations in two

variables.

Solve equations involving quadratic, absolute value, and fractional expressions by finding

x-intercepts or intersections on graphs, by using algebraic techniques, or by using numerical techniques.

Add, subtract, multiply, and divide complex numbers; and find complex zeros of

quadratic functions.

Solve inequalities involving absolute value, quadratic polynomials, and expressions

involving fractions.

Solve systems of equations graphically and algebraically.

Find sums, differences, products, and inverses of matrices.


Mnemonic devices, Geoboards, Quadratic Formula song, Tic-

Tac-Toe factoring, Graphing Calculator Activities

Textbook and Teacher generated

assignments, quizzes, and tests.

Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—

Chapters P and 8

53

Advanced Mathematical Concepts by Glencoe

Prentice Hall Mathematics—Algebra 2 Timeframe: October


PRF.1.PCT.1

PRF.1.PCT.4

II. Functions and Graphs (14+ days) A. Modeling and Equations Solving

B. Functions and Their Properties

C. Twelve Basic Functions

D. Building Functions from Functions

E. Graphical Transformations

F. Modeling with Functions


Use numerical, algebraic, and graphical models to solve problems and be able to

translate from one model to another.

Represent functions numerically, algebraically, and graphically, determine the domain

and range for functions, and analyze function characteristics such as extreme values, symmetry, asymptotes, and end behavior.

Recognize graphs of twelve basic functions, determine domains of functions related to

the twelve basic functions and combine the twelve basic functions in various ways to

create new functions.

Build new functions from basic functions by adding, subtracting, multiplying, dividing, and composing functions.

Algebraically and graphically represent translations, reflections, stretches, and shrinks of

functions.

Identify appropriate basic functions with which to model real-world problems and be able to produce specific functions to model data, formulas, graphs, and verbal

descriptions.




Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—Chapter 1


54

Timeframe: October/November


PRF.1.PCT.2

PRF.1.PCT.1

PRF.1.PCT.3

PRF.1.PCT.2

PRF.1.PCT.3

III. Polynomial, Power, and Rational

Functions (16+ Days) A. Linear and Quadratic Functions and

Modeling

B. Power Functions with Modeling

C. Polynomial Functions of Higher

Degree with Modeling

D. Real Zeros of Polynomial Functions

E. Complex Zeros and the Fundamental Theorem of Algebra

F. Graphs of Rational Functions

G. Solving Equations in One Variable

H. Solving Inequalities in One Variable


Recognize and graph linear and quadratic functions, and use these functions to model

situations and solve problems.

Sketch power functions in the form of f(x)=kx^a (where k and a are rational numbers).

Graph polynomial functions, predict their end behavior, and find their real zeros using a

grapher or an algebraic method.

Divide polynomials using long division or synthetic division; to apply the Remainder Theorem, Factor Theorem, and Rational Zeros Theorem; and find upper and lower

bounds for zeros of polynomials.

Factor polynomials with real coefficients using factors with complex coefficients.

Describe the graphs of rational functions, identify horizontal and vertical asymptotes,

and predict the end behavior of rational functions.

Solve equations involving fractions using both algebraic and graphical techniques and

identify extraneous solutions.

Solve inequalities involving polynomials and rational functions by using both algebraic and graphical techniques.


Unitedstreaming Math Factor, Numbers 16,20,22,29

Textbook and Teacher generated assignments, quizzes, and tests.


Chapter 2

Advanced Mathematical Concepts by

Glencoe

55

Timeframe: December


ELF.2.PCT.1

ELF.2.PCT.4

ELF.2.PCT.1

ELF.2.PCT.2

ELF.2.PCT.3

ELF.2.PCT.5

IV. Exponential, Logistic, and Logarithmic

Functions (12+ Days) A. Exponential and Logistic Functions

B. Exponential and Logistic Modeling

C. Logarithmic Functions and Their

Graphs

D. Properties of Logarithmic Functions

E. Equations Solving and Modeling

F. Mathematics of Finance


Evaluate exponential expressions and identify and graph exponential and logistic

functions.

Use exponential growth, decay, and regression to model real-life problems.

Convert equations between logarithmic form and exponential form, evaluate common

and natural logarithms, and graph common and natural logarithmic functions.

Apply the properties of logarithms to evaluate expressions and graph functions, and be

able to re-express data.

Apply the properties of logarithms to solve exponential and logarithmic equations algebraically and solve application problems using these equations.

Use exponential functions and equations to solve business and finance applications

related to compound interest and annuities.


Unitedstreaming, Math Factor, Numbers 14,18,19,31,33,36





56

Timeframe: January


TF.5.PCT.2

TF.5.PCT.1

TF.5.PCT.4

TF.5.PCT.1

TF.5.PCT.3 TF.5.PCT.5

TF.5.PCT.6

TF.5.PCT.7

TF.5.PCT.8

TF.5.PCT.7 TF.5.PCT.7

TF.5.PCT.7

TF.5.PCT.9

TF.5.PCT.6

V. Trigonometric Functions (14+ days)

A. Angles and Their Measures

B. Trigonometric Functions of Acute

Angles

C. Trigonometry Extended: The

Circular Functions

D. Graphs of Sine and Cosine:

Sinusoids

E. Graphs of Tangent, Cotangent, Secant, and Cosecant

F. Graphs of Composite Trigonometric Functions

G. Inverse Trigonometric Functions

H. Solving Problems with Trigonometry


Convert between radians and degrees, find arc lengths, convert to nautical miles, and solve problems involving angular speed.

Define the six trigonometric functions using the lengths of the sides of a right triangle.

Solve problems involving the trigonometric functions of real numbers and the properties

of the sine and cosine as periodic functions.

Generate the graphs of the sine and cosine functions and explore various

transformations of these graphs.

Generate the graphs for the tangent, cotangent, secant, and cosecant functions and to explore various transformations of these graphs.

Graph sums, differences, and other combinations of the trigonometric and algebraic functions.

Relate the concept of inverse functions to trigonometric functions.

Apply the concepts of trigonometry to solve real-world problems.


Unitedstreaming, Math Factor, Numbers

3,9,12,15,27,45,50,54




Chapter 4


57

Timeframe: January/February


TEI.7.PCT.3

TEI.7.PCT.1

TEI.7.PCT.2

TEI.7.PCT.2

OT.6.PCT.1 OT.6.PCT.2

OT.6.PCT.1

OT.6.PCT.2

VI. Analytic Trigonometry(11+ days)

A. Fundamental Identities

B. Proving Trigonometric Identities

C. Sum and Difference Identities

D. Multiple-Angle Identities

E. The Law of Sines

F. The Law of Cosines


Use the fundamental identities to simplify trigonometric expressions and solve

trigonometric equations.

Decide whether an equation is an identity and to confirm identities analytically.

Apply the identities for the cosine, sine, and tangent of a difference or sum.

Apply the double-angle identities, power-reducing identities, and half-angle identities.

Understand the proof of the Law of Sines and use the computational applications of the Law of Sines to solve a variety of problems.

Apply the Law of Cosines to solve acute and obtuse triangles and to determine the area

of a triangle in terms of the measures of the sides and angles.


Unitedstreaming, Math Factor, Numbers 13,52




Chapter 5


58

Timeframe: February/March


OT.6.PCT.3 OT.6.PCT.4

OT.6.PCT.5

PC.8.PCT.1

PC.8.PCT.2 PC.8.PCT.3

PC.8.PCT.4

VII. Applications of Trigonometry (12+

days)

A. Vectors in the Plane

B. Dot Product of Vectors

C. Polar Coordinates

D. Graphs of Polar Equations


Apply the arithmetic of vectors and use vectors to solve real-world problems.

Calculate dot products and projections of vectors.

Convert points and equations from polar to rectangular coordinates and vice versa.

Graph polar equations and determine the maximum r-value and the symmetry of a

graph.






Timeframe : March


C.3.PCT.1 C.3.PCT.2

C.3.PCT.3

PC.8.PCT.4

IX. Analytic Geometry in Two and Three

Dimensions (11+ days)

A. Conic Sections and Parabolas

B. Ellipses

C. Hyperbolas

D. Translation and Rotation of Axes

E. Polar Equations of Conics


Finds the equation, focus, and directrix of a parabola.

Find the equation, vertices, and foci of an ellipse.

Find the equation, vertices, and foci of a hyperbola.

Determine equations for translated and rotated axes for conic sections.

Understand the general focus-directrix definition of a conic section and will be able to

59

F. Three-Dimensional Cartesian

Coordinate System

write equations of conic sections in polar form.

Draw three-dimensional figures and analyze vectors in space.


Unitedstreaming, Math Factor, Numbers 17,23,24,40




Advanced Mathematical Concepts by Glenco Timeframe: April


SS.4.PCT.1 SS.4.PCT.2



X. Discrete Mathematics (15+ days)

A. Basic Combinatorics

B. The Binomial Theorem

C. Probability

D. Sequences

E. Series

F. Mathematical Induction

G. Statistics and Data (Graphical)

H. Statistics and Data (Algebraic)


Use the multiplication principle of counting, permutations, or combinations to count the number of ways that a task can be done.

Expand a power of a binomial using the binomial theorem or Pascal’s triangle and also find the coefficient of a given term of a binomial expansion.

Identify a sample space and calculate probabilities and conditional probabilities in sample

spaces with equally likely or unequally likely outcomes.

Express arithmetic and geometric sequences explicitly and recursively; and be able to

find limits of convergent sequences.

Use sigma notation and find finite sums of terms in arithmetic and geometric sequences and be able to find sums of convergent geometric series.

Use the principle of mathematical induction to prove mathematical generalizations.

Distinguish between categorical and quantitative variable and use various kinds of graphs to display data.

Use measures of center, the five-number summary, a boxplot, standard deviation, and normal distribution to describe quantitative data.

60


Unitedstreaming Math Factor, Numbers

4,5,6,7,8,10,11,21,25,26,30,37,38,39,42,43,46,47,48




Advanced Mathematical Concepts by Glenco

Timeframe: May


Enrichment

XI. An Introduction to Calculus: Limits,

Derivatives, and Integrals (7+ days) A. Limits and Motion: The Tangent

Problem

B. Limits and Motion: The Area

Problem

C. More on Limits

D. Numerical Derivatives and Integrals


Calculate instantaneous velocities and derivatives using limits.

Calculate definite integrals using areas.

Use the properties of limits and evaluate one-sided limits, two-sided limits, and limits

involving infinity.

Estimate derivatives and integrals using numerical techniques.


Textbook and Teacher generated assignments, quizzes, and tests.


Chapter 10

Advanced Mathematical Concepts by Glenco

61



Transitions to College Math

2011-2012

Pam Jones


62

CURRICULUM MAP


2011-2012 Grade: 12th Subject: Transitions to College Math

Timeframe: First Nine Weeks


LF.1.TM.1

LF.1.TM.3 LF.1.TM.4

LF.1.TM.1

LF.1.TM.2 LF.1.TM.3

LF.1.TM.4

I. Function Sense

domain/range; function notation; graph descriptions

II. The Algebra of Linear Functions

slope/rate of change; intercepts; equations of lines; regression equations;

systems of equations

The student will be able to....

Extend their knowledge of linear equations by using student-generated data to represent rates of change

Identify a linear relationship by a table, graph, and symbolic forms Make inferences and predictions

Explain, conjecture, summarize, and defend results orally, in writing and through the use of appropriate technology

Identify a linear relationship by a table, graph, and symbolic forms Determine the initial condition and the rate of change in real-world situations described

y=mx + b Make inferences and predictions



Daily practice

"The speeding dilemma" activity "Estimating Age" activity

"Drinking in the Desert" activity

"Telephone Service" activity Comparing golf drives project


Daily Observation/Participation TI-Navigator observations/quizzes

Lab notebooks/projects

Student presentations

Algebra II book Thinking Mathematically book Student study materials TI-Navigator system TI Easy Link and sensors Appropriate technology and activity/project materials

Timeframe: Second Nine Weeks


EF.1.TM.1

EF.1.TM.2 EF.1.TM.3

III. Exponential Functions

polynomial operations; exponents; composition; growth/decay factor and


Students will enhance their knowledge of exponential functions by exploring the nature

of multiplicative change Identify exponential growth or decay by creating tables, graphs, and mathematical

63

EF.1.TM.4

EF.1.TM.5 EF.1.TM.6

rate; compound interest; exponential

regression

models

Compare exponential models Compare and contrast linear and exponential models

Make inferences and predictions

Develop, with appropriate technology, an algebraic model through the regression process



Daily practice

"Growth and Decay" worksheet activities "Chill Out: How Hot Objects Cool" project

"Charging Up, Charging Down" project

"Bounce Back" Project "Sour Chemistry: The Exponential pH Change" project

"The Medicine Problem" activity "Building Bridges" activity

"Keep Taking The Tablets" activity

Teacher made quizes and tests

Daily Observation/Participation TI-Navigator observations/quizzes

Lab notebooks/projects



Timeframe: Third Nine Weeks


MM.1.TM.1

MM.1.TM.2 MM.1.TM.3

MM.1.TM.4

MM.1.TM.1 MM.1.TM.2

MM.1.TM.3

IV. Quadratic and Higher Order Functions

parabola-domain, range, intercepts, equation solutions; factor; quadratic

regression graphs; complex numbers; quadratic models

V. Rational Functions power functions; polynomial functions;

asymptotes-vertical/horizontal; graph-

The student will be able to......

Students will expand their use of mathematical models to describe continuous,

discontinuous, and discrete phenomena Establish connections between tables and graphs and the symbolic form using geometric

and algebraic models Apply, with appropriate technology, matrices to real world problems and decision making



Establish connections between tables and graphs and the symbolic form using geometric and algebraic models

Apply, with appropriate technology, matrices to real world problems and decision making

64

MM.1.TM.4 rational functions; rational equation

solutions




Daily practice "Keeping Things Balanced" activity

"Crosses" activity "Books from Andonov" activity

"Travel Times" activity

"Light and Sound" project

Teacher made quizes and tests Daily Observation/Participation

TI-Navigator observations/quizzes Lab notebooks/projects



Timeframe: Fourth Nine Weeks


PS.4.TM.1 PS.4.TM.3

PS.4.TM.4

PS.4.TM.2

PS.4.TM.4 PS.4.TM.5

VI. Probability Theoretical; odds; Tree diagrams;

counting principal; permutations;

combinations; binomial probability

VII. Statistics

sampling; frequency; distribution; central tendency; normal curve


Students will develop strategies that will enable them to make decisions based upon appropriate analysis of data

Formulate questions that can be addressed with data and, with appropriate technology,

collect, organize, and display relevant data to answer the questions Use counting methods, permutations, and combinations to evaluate the likelihood of

events occurring Make inferences and predictions

Describe and summarize data numerically using central tendency variation, position

statistics, and distributions Make inferences and predictions

Explain, conjecture, summarize, and defend results orally, in writing, and through the use of technology


Daily practice "Should I Play?" activity

"The Probability Dilemma" activity "What is the probability that spaghetti pieces form a

triangle?" activity

"Helium vs. Air Football" activity "Comparing Data Sets- Peanut Butter" activity

"Master Minds" activity


TI-Navigator observations/quizzes Lab notebooks/projects

Mandatory Final Individual Project

Algebra II book Thinking Mathematically book Student study materials TI-Navigator system TI Easy Link and sensors

65



AP Calculus AB Course Outline

2011-2012

Pam Jones


66

AP Calculus AB Course Outline

Harrison Public Schools

(Follows the AP Calculus guidelines)

August

I. Functions – models, properties, problems.

A. Linear Functions

B. Polynomial Functions

C. Exponential Functions

D. Logarithmic Functions

E. Trigonometric Functions

F. Parametric Equations

September

II. Limits and Continuity

A. Limits

i. Definition and Properties

ii. One – sided and Two – sided Limits

iii. Sandwich Theorem

iv. Infinite Limits

v. End Behavior Models

vi. Rates of Change

vii. Slope

B. Continuity

i. Point

ii. Properties of Continuous Functions

iii. Intermediate Value Theorem

67

October

III. Derivatives

A. Definitions

B. Notation

C. Left and Right – Hand Derivatives

D. Intermediate Value Theorem

E. Rules

i. Constant

ii. Power

iii. Constant Multiple

iv. Sum and Difference

v. Product

vi. Quotient

vii. Chain

November

F. Trigonometric Derivatives

G. Implicit Differentiation

H. Exponential and Logarithmic Derivatives

December

IV. Application of Derivatives

A. Graphs of f’ and f’’

B. Extreme Values

C. Rates of Change

D. Mean Value Theorem for Derivatives

E. Antiderivatives and Slope Fields

F. Modeling and Optimization

G. Linearization

H. Differential Equations

I. Related Rates

68

January

V. Indefinite Integrals

A. Definition

B. Estimating with Riemann Sums

i. LRAM, RRAM, MRAM

ii. Defn. of Integrals as a Limit of Riemann Sums

C. Notation and Terminology

D. Integral Formulas

E. Integration by Substitution

F. Integration by Parts

G. Exponential Growth and Decay

February

VI. Definite Integrals

A. Properties

B. Mean Value Theorem of Definite Integrals

C. Fundamental Theorem of Calculus

D. Trapezoidal Rule

March

VII. Applications of Definite Integrals

A. Integrals as Net Change

B. Area

C. Volume

April

VIII. Review

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