curricular documentation algebra i for hhs -...
TRANSCRIPT
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
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
FRAMEWORKS CONTENT SKILLS
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.3
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Released Items
Teacher Made Test Notebook
Released Items
Prentice Hall textbook Released items Calculators TI-Navigator System
5
FRAMEWORKS CONTENT SKILLS
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
SEI.2.AI.8 LF.3.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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice Released Items
Teacher Made Test
Notebook Released Items
Prentice Hall textbook Released items Calculators TI-Navigator System
6
FRAMEWORKS CONTENT SKILLS
SEI.2.AI.2 LF.3.AI.7
SEI.2.AI.2
SEI.2.AI.5 SEI.2.AI.8
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Released Items
Teacher Made Test
Notebook
Released Items
Prentice Hall textbook Released items Calculators TI-Navigator System
FRAMEWORKS CONTENT SKILLS
LA.1.AI.1 SEI.2.AI.7
NLF.4.AI.2 NLF.4.AI.4
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Released Items
Teacher Made Test Notebook
Released Items
Prentice Hall textbook Released items Calculators TI-Navigator System
7
FRAMEWORKS CONTENT SKILLS
LA.1.AI.5
LA.1.AI.6 NLF.4.AI.1
NLF.4.AI.3
XI. Polynomials & factoring (Week #35 - #39)
A. Add, subtract, & multiply polynomials
B. Factor polynomials C. Solve equations by factoring
The student will be able to….
Add and subtract polynomials
Multiply polynomials using FOIL and special patterns
Factor polynomials Use factoring to solve quadratic equations
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice Released Items
Teacher Made Test
Notebook Released Items
Prentice Hall textbook Released items Calculators TI-Navigator System
8
FRAMEWORKS CONTENT SKILLS
LF.3.AI.1 LF.3.AI.3
NLF.4.AI.4 LF.3.AI.2
LF.3.AI.4
SEI.2.AI.6 SEI.2.AI.5
SEI.2.AI.8
DIP.5.AI.10 DIP.5.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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Released Items
Teacher Made Test
Notebook Released Items
Prentice Hall textbook Released items Calculators TI-Navigator System
FRAMEWORKS CONTENT SKILLS
LA.1.AI.1
SEI.2.AI.7 LA.1.AI.1
LA.1.AI.8
LA.1.AI.9 SEI.2.AI.1
LA.1.AI.1
SEI.2.AI.7
LA.1.AI.1 LA.1.AI.8
LA.1.AI.9 SEI.2.AI.1
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
9
ACTIVITIES
ASSESSMENTS RESOURCES
Daily Practice
Released Items
Teacher Made Test
Notebook Released Items
Prentice Hall textbook Released items Calculators TI-Navigator System
10
Harrison School District
Curricular Documentation
Algebra B HHS
2011-2012
Pam Jones
Curriculum Coordinator
11
CURRICULUM MAP: Harrison School District
Harrison School District
2011-2012 Grade: HHS Subject: Second Part Algebra I
Timeframe (9 Weeks/Month/Semester): August/September/October
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
ACTIVITIES ASSESSMENTS RESOURCES
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
FRAMEWORKS CONTENT SKILLS
Systems of Equations and Inequalities
The student will be able to….
12
SEI.2.AI.2 SEI.2.AI.7
SEI.2.AI.8
SEI.2.AI.2 SEI.2.AI.8
LA.1.AI.1 LA.1.AI.5
SEI.2.AI.2
SEI.2.AI.8
SEI.2.AI.1 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.
ACTIVITIES ASSESSMENTS RESOURCES
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
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily practice with and without technology
Vocabulary development – ―Personal Word Wall‖
Teacher made tests and quizzes
Calculator assessments
Algebra 1 (Prentice Hall) Developing Skills in Algebra 1 TI-84 programs (D. Smeltz)
Timeframe (9 Weeks/Month/Semester): December/January
FRAMEWORKS CONTENT SKILLS
LA.1.AI.5
LA.1.AI.5 NLF.3.AI.1
SEI.2.AI.8 NLF.3.AI.1
Polynomials
Polynomial Operations
Multiplying and Factoring
Factoring
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily practice with and without technology
Factoring puzzle – matching expanded form with factored form Tic-Tac-Toe method for factoring polynomials
Vocabulary development – ―Personal Word Wall‖
Teacher made tests and quizzes
Calculator assessments
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
FRAMEWORKS CONTENT SKILLS
NLF.3.AI.2 NLF.3.AI.4
NLF.3.AI.5 LA.1.AI.1
LA.1.AI.8
SEI.2.AI.7
NLF.3.AI.1 NLF.3.AI.3
NLF.3.AI.5
NLF.3.AI.3 NLF.3.AI.5
DIP.5.AI.5 DIP.5.AI.7
DIP.5.AI.10
DIP.5.AI.11 DIP.5.AI.12
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily practice with and without technology
Vocabulary Development – ―Personal Word Wall‖
Graphing with individual marker boards
Teacher made tests and quizzes
Calculator assessments
Algebra 1 (Prentice Hall) Developing Skills in Algebra 1 TI-84 programs (D. Smeltz)
15
Timeframe (9 Weeks/Month/Semester): February/March
FRAMEWORKS CONTENT SKILLS
LA.1.AI.8 LA.1.AI.9
SEI.2.AI.7 LA.1.AI.1
LA.1.AI.1
LA.1.AI.8
LA.1.AI.9 SEI.2.AI.8
Radical Expressions and Equations
Radical Simplification
Pythagorean Theorem
Distance and Midpoint
Radical Operations
Radical Equations
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
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
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily practice with and without technology
Vocabulary development – ―Personal Word Wall‖ Intensive review of all Algebra 1 topics in preparation for the
Algebra 1 End of Course Exam
Teacher made tests and quizzes
Calculator assessments EOC practice
Algebra 1 (Prentice Hall) Making Practice Fun TI-84 programs (D. Smeltz) ALMS
16
Harrison School District
Curricular Documentation
Algebra II
2011-2012
Pam Jones
Curriculum Coordinator
17
CURRICULUM MAP: Harrison School District
Harrison School District
2011-2012 Grade: HHS Subject: Algebra II
Timeframe: August/September
FRAMEWORKS CONTENT SKILLS
LEI.2.AII.1 LEI.2.AII.5
RF.1.AII.1 RF.1.AII.2
RF.1.AII.5 RF.1.AII.4
LEI.2.AII.1
RF.1.AII.1 RF.1.AII.9
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
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
FRAMEWORKS CONTENT SKILLS
LEI.2.AII.1
LEI.2.AII.2
LEI.2.AII.4 LEI.2.AII.5
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
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
FRAMEWORKS CONTENT SKILLS
RF.1.AII.4
LEI.2.AII.3
LEI.2.AII.3
RF.1.AII.3
LEI.2.AII.3
LEI.2.AII.3 LEI.2.AII.4
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
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
FRAMEWORKS CONTENT SKILLS
QEF.3.AII.3
QEF.3.AII.5
RF.1.AII.3 QEF.3.AII.3
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
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 Graphing Calculators
Timeframe: January
FRAMEWORKS CONTENT SKILLS
QEF.3.AII.1 QEF.3.AII.2
QEF.3.AII.1
QEF.3.AII.2 QEF.3.AII.3
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
The student will be able to….
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
RF.1.AII.3 RF.1.AII.4
QEF.3.AII.1 PRF.4.AII.2
PRF.4.AII.5
PRF.4.AII.8
RF.1.AII.4 QEF.3.AII.1
PRF.4.AII.2 PRF.4.AII.7
PRF.4.AII.8
RF.1.AII.1 QEF.3.AII.1
PRF.4.AII.2
RF.1.AII.4
PRF.4.AII.2 PRF.4.AII.4
PRF.4.AII.1
QEF.3.AII.2
PRF.4.AII.1 PRF.4.AII.2
QEF.3.AII.1 QEF.3.AII.2
PRF.4.AII.1 PRF.4.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
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Teacher made quizzes and tests Algebra II book Skills and Concepts Review book Student Study materials Graphing Calculators
Timeframe: February
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
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 Graphing Calculators Interactive E-beam
Timeframe: March
FRAMEWORKS CONTENT SKILLS
RF.1.AII.2
RF.1.AII.3
RF.1.AII.4 RF.1.AII.9
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.3 ELF.5.AII.5
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
M & M Exponential Growth and Decay Lab 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
25
Timeframe: April
FRAMEWORKS CONTENT SKILLS
ELF.5.AII.5
ELF.5.AII.6 ELF.5.AII.7
QEF.3.AII.1
ELF.5.AII.4
ELF.5.AII.5
ELF.5.AII.6 ELF.5.AII.7
ELF.5.AII.6 ELF.5.AII.7
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
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 Graphing Calculators
26
Timeframe: May
FRAMEWORKS CONTENT SKILLS
DAP.6.AII.5
DAP.6.AII.5
DAP.6.AII.6
RF.1.AII.6
RF.1.AII.7 RF.1.AII.8
X. Data Analysis and Probability
A. Data Analysis
B. Standard Deviation
C. Normal Distributions
XI. Periodic Functions
A. Periodic Data
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
Daily practice
RAFT projects on terminology ―Who has, I have‖
TI-Navigator questioning/response
Teacher made quizzes and tests
RAFT projects TI-Navigator system
Algebra II book Skills and Concepts Review book Student Study materials Graphing Calculators Interactive e-beam
27
Harrison School District
Curricular Documentation
Algebraic Connections
2011-2012
Pam Jones
Curriculum Coordinator
28
CURRICULUM MAP: Harrison School District
Harrison School District 2011-2012 Grade: 10th-12th Subject: Algebraic Connections
Timeframe: First Nine Weeks
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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
Model a real-life situation with a linear equation
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
Model a real-life situation with a linear equation
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
ACTIVITIES ASSESSMENTS RESOURCES
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
FRAMEWORKS CONTENT SKILLS
PS.1.AC.3
Basic Set Concepts
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
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
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
Daily practice Use the graphing calculators in working with probabilities
and solving system of equations
Teacher made quizzes and tests Daily Observation/Participation
Thinking Mathematically book Student study materials TI-Navigator system
Timeframe: Fourth Nine Weeks
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
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
Harrison School District
Curricular Documentation
Geometry
2011-2012
Pam Jones
Curriculum Coordinator
36
CURRICULUM MAP: Harrison School District
Harrison School District
2011-2012 Grade: HHS Subject: Geometry
Timeframe: August/September
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Cabri Geometry calculator activities
Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
37
Timeframe: October
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
38
Timeframe: October
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Cabri geometry activities
Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
39
Timeframe: October/November
FRAMEWORKS CONTENT SKILLS
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
Timeframe: November
FRAMEWORKS CONTENT SKILLS
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Timeframe: December
FRAMEWORKS CONTENT SKILLS
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
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
Timeframe: January
FRAMEWORKS CONTENT SKILLS
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Cabri Geometry graphing calculator activities
Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
Timeframe: March/April
FRAMEWORKS CONTENT SKILLS
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
Timeframe: April/May
44
FRAMEWORKS CONTENT SKILLS
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice Teacher made quizzes and tests
Daily Observations
TI-Navigator poll/short quiz
Geometry TextbookSkills and Concepts Review
book
Student Study materials
Graphing Calculators
45
Harrison School District
Curricular Documentation
Investigating Geometry
2011-2012
Pam Jones
Curriculum Coordinator
46
CURRICULUM MAP
Harrison School District 2011-2012 Grade: HHS Subject: Investigating Geometry
Timeframe: Semester I
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
-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,
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Checkpoint Quizzes
Teacher Made Test Notebook; Vocabulary Journal
-Discovering Geometry; Text -ACTAAP released Items - Geometer’s Sketch Pad
Timeframe: Semester I
FRAMEWORKS CONTENT SKILLS
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.
ACTIVITIES ASSESSMENTS RESOURCES
-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
Timeframe: Semester I
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
-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
ACTIVITIES ASSESSMENTS RESOURCES
-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
FRAMEWORKS CONTENT SKILLS
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.
ACTIVITIES ASSESSMENTS RESOURCES
Daily Practice
Quizzes
Teacher made test
Notebook/ Vocabulary Journal
Discovering Geometry; Text ACTAAP Released Items Geometer’s Sketch Pad
49
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
-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.
ACTIVITIES ASSESSMENTS RESOURCES
-Tessellation Project
-Daily Practice
-Quizzes -Project
-Teacher Made Test -Notebook/ Vocabulary Journal
-Discovering Geometry ; text and resources - ACTAAP Released Items
Timeframe: Semester II
FRAMEWORKS CONTENT SKILLS
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
ACTIVITIES ASSESSMENTS RESOURCES
-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
Timeframe: Semester II
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
-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.
ACTIVITIES ASSESSMENTS RESOURCES
-Daily Practice
g. Quizzes
h. Teacher Made Test
i. Notebook/ Vocabulary Journal
- Discovering Geometry; Text and resources -ACTAAP Released Items
51
Harrison School District
Curricular Documentation
Pre-Calculus
2011-2012
Pam Jones
Curriculum Coordinator
52
CURRICULUM MAP
Harrison School District
2011-2012 Grade: 11,12 Subject: Pre-Calculus
Timeframe: August/September
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
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
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Textbook and Teacher generated
assignments, quizzes, and tests.
Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—Chapter 1
Advanced Mathematical Concepts by Glencoe
54
Timeframe: October/November
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Unitedstreaming Math Factor, Numbers 16,20,22,29
Textbook and Teacher generated assignments, quizzes, and tests.
Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—
Chapter 2
Advanced Mathematical Concepts by
Glencoe
55
Timeframe: December
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Unitedstreaming, Math Factor, Numbers 14,18,19,31,33,36
Textbook and Teacher generated
assignments, quizzes, and tests.
Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—Chapter 3
Advanced Mathematical Concepts by Glencoe
56
Timeframe: January
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Unitedstreaming, Math Factor, Numbers
3,9,12,15,27,45,50,54
Textbook and Teacher generated
assignments, quizzes, and tests.
Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—
Chapter 4
Advanced Mathematical Concepts by Glencoe
57
Timeframe: January/February
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Unitedstreaming, Math Factor, Numbers 13,52
Textbook and Teacher generated
assignments, quizzes, and tests.
Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—
Chapter 5
Advanced Mathematical Concepts by Glencoe
58
Timeframe: February/March
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Textbook and Teacher generated
assignments, quizzes, and tests.
Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—Chapter 6
Advanced Mathematical Concepts by Glencoe
Timeframe : March
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Unitedstreaming, Math Factor, Numbers 17,23,24,40
Textbook and Teacher generated
assignments, quizzes, and tests.
Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—Chapter 7
Advanced Mathematical Concepts by Glenco Timeframe: April
FRAMEWORKS CONTENT SKILLS
SS.4.PCT.1 SS.4.PCT.2
SS.4.PCT.4 SS.4.PCT.5
SS.4.PCT.3 SS.4.PCT.5
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)
The student will be able to….
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
ACTIVITIES ASSESSMENTS RESOURCES
Unitedstreaming Math Factor, Numbers
4,5,6,7,8,10,11,21,25,26,30,37,38,39,42,43,46,47,48
Textbook and Teacher generated
assignments, quizzes, and tests.
Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—Chapter 9
Advanced Mathematical Concepts by Glenco
Timeframe: May
FRAMEWORKS CONTENT SKILLS
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
The student will be able to….
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.
ACTIVITIES ASSESSMENTS RESOURCES
Textbook and Teacher generated assignments, quizzes, and tests.
Precalculus--Graphical, Numerical, Algebraic by Demana, Waits, Foley, Kennedy—
Chapter 10
Advanced Mathematical Concepts by Glenco
61
Harrison School District
Curricular Documentation
Transitions to College Math
2011-2012
Pam Jones
Curriculum Coordinator
62
CURRICULUM MAP
Harrison School District
2011-2012 Grade: 12th Subject: Transitions to College Math
Timeframe: First Nine Weeks
FRAMEWORKS CONTENT SKILLS
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
Explain, conjecture, summarize, and defend results orally, in writing and through the use of appropriate technology
ACTIVITIES ASSESSMENTS RESOURCES
Daily practice
"The speeding dilemma" activity "Estimating Age" activity
"Drinking in the Desert" activity
"Telephone Service" activity Comparing golf drives project
Teacher made quizzes and tests
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
FRAMEWORKS CONTENT SKILLS
EF.1.TM.1
EF.1.TM.2 EF.1.TM.3
III. Exponential Functions
polynomial operations; exponents; composition; growth/decay factor and
The student will be able to....
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
Explain, conjecture, summarize, and defend results orally, in writing and through the use of appropriate technology
ACTIVITIES ASSESSMENTS RESOURCES
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
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: Third Nine Weeks
FRAMEWORKS CONTENT SKILLS
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
Make inferences and predictions
Explain, conjecture, summarize, and defend results orally, in writing and through the use of appropriate technology
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
Make inferences and predictions
Explain, conjecture, summarize, and defend results orally, in writing and through the use of appropriate technology
ACTIVITIES ASSESSMENTS RESOURCES
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
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: Fourth Nine Weeks
FRAMEWORKS CONTENT SKILLS
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
The student will be able to....
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
ACTIVITIES ASSESSMENTS RESOURCES
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
Teacher made quizzes and tests Daily Observation/Participation
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
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Harrison School District
Curricular Documentation
AP Calculus AB Course Outline
2011-2012
Pam Jones
Curriculum Coordinator
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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
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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
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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