1 Harrison School District Harrison School District Harrison School District Harrison School District Curricular Documentation Curricular Documentation Curricular Documentation Curricular Documentation Harrison High School Harrison High School Harrison High School Harrison High School Math Math Math Math 2007-2008 Pam Jones Curriculum Coordinator
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Harrison School DistrictHarrison School DistrictHarrison School DistrictHarrison School District
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.
14
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)
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)
Harrison School District Teacher: Estes August 2007 - May 2008 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
30
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
31
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
32
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
33
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
34
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
35
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
36
Harrison School DistrictHarrison School DistrictHarrison School DistrictHarrison School District
-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.
48
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.
49
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
50
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
51
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
52
Harrison School DistrictHarrison School DistrictHarrison School DistrictHarrison School District
August 2007 - May 2008 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
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
54
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
55
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
56
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
57
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
58
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
59
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
60
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.
61
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
62
Harrison School DistrictHarrison School DistrictHarrison School DistrictHarrison School District
Transitions to College MathTransitions to College MathTransitions to College MathTransitions to College Math
2007-2008
Pam Jones
Curriculum Coordinator
63
CURRICULUM MAP: Harrison School District
Harrison School District Teacher: Fast/Stahler
August 2007 - May 2008 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 changeIdentify 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
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
64
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
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,
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