Download Hope College Prep High School: Curriculum Map 2013-2014

Hope College Prep High School: Curriculum Map 2013-2014
Teacher
First and Last Name
Yolanda D. Garcia
Course
Algebra II
Subject Area
Mathematics
Grade Level
11th
Units Calendar
Unit 1 Title
Foundations for Functions
Dates (school calendar weeks)
20 days
Unit 2 Title
Linear Functions
Dates (school calendar weeks)
25 days
Unit 3 Title
Linear Systems
Dates (school calendar weeks)
25 days
Unit 4 Title
Quadratic and Polynomial Functions
Dates (school calendar weeks)
25 days
Unit 5 Title
Trigonometric Functions
Dates (school calendar weeks)
25 days
Unit 6 Title
Exponential and Logarithmic Functions
Dates (school calendar weeks)
25 days
Unit 7 Title
Rational and Radical Functions
Dates (school calendar weeks)
25 days
Unit 8 Title
Data Analysis and Probability
Dates (school calendar weeks)
25
Unit 1 Summary + Curriculum Alignment
Unit Title
Foundations of Algebra
Major Topics
Set of Numbers, Properties of Real Numbers, Square Roots, Simplifying Algebraic Expressions, Properties of
Exponents, Relations and Functions, and Function Notation
Description of
Primary
Performance
Task
NOTE: One task
per unit
Common Core
Standard(s)
Related to Task
N.RN.3 Use properties of rational and irrational numbers. Explain why the sum or product of rational numbers is
rational; that the sum of a rational number and an irrational number is irrational; and that the product of a
nonzero rational number and an irrational number is irrational.
N.RN.1 Extend the properties of exponents to rational exponents. Explain how the definition of the meaning of
rational exponents follows from extending the properties of integer exponents to those values, allowing for a
notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5
because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.
SSE.1 Interpret the structure of expressions. Interpret expressions that represent a quantity in terms of its
context.
F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set
(called the domain) to another set (called the range) assigns to each element of the domain exactly one element
of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to
the input x. The graph of f is the graph of the equation y = f(x).
CRS Supporting
Skills
College
Bound
XEI 13-16 301 Substitute whole numbers for unknown quantities to evaluate expressions
NCP 24-27.605 Work with squares and square roots of numbers
FUN 24-27. 601 Evaluate polynomial functions, expressed in function notation, and integer values
Pre-Accelerated XEI 16-19.302 Solve one-step equations having integer or decimal answers
NCP 24-27.605 with squares and square roots of numbers
FUN 24-27. 601 Evaluate polynomial functions, expressed in function notation, and integer values
Honors
XEI 20-23.503 Solve routine first-degree equations
NCP 24-27.605 Work with squares and square roots of numbers
FUN 24-27. 601 Evaluate polynomial functions, expressed in function notation, and integer values
Industry or
Subject Specific
Standards
Interdisciplinary
Integrations /
Perimeter, Area, Circumference, Volume, Similar Triangles, Pythagorean Theorem
Thematic
Connections
Connections to
Writing
Framework
Assessment
Written explanation on how to solve a problem
Graphic organizers
Word problems
Critical Thinking Questions
Diagnostic/
PreAssessment
Are You Ready?
Formative
Bell-Ringers, Exit Tickets, Interactive Notebooks, Writing Prompts, Questions and Answers,
Classwork, Group work, Quizzes, Homework, Cornell Notes Summary
Summative
Chapter Test, Ready to Go On, College Entrance Exam, and Performance Task
Supplementary
Text
Description/
Title
Lexile
Pearson Algebra II
Flesch
Reading Ease
Nonfiction, Fiction,
Informational
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
How does knowledge of integers help when working with rational and irrational numbers?
Why structure expressions in different ways?
How can the relationship between quantities best be represented?
Unit Content
Questions
How can you tell if a number belongs to the set of rational numbers?
Which property states a fact about addition and multiplication at the same time?
How do you choose what to multiply by to rationalize a denominator?
Why are x and x2 not like terms?
How can you multiply a number by a power of 10 by moving the decimal point of the number?
How are relations and functions similar, and how are they different?
How do you know which set of values to plot on the horizontal axis and which points to plot on the vertical axis?
Unit 2 Summary + Curriculum Alignment
Unit Title
Linear Functions
Major Topics
Solving Linear Equations and Inequalities, Graphing Linear Functions, Writing Linear Equations, Linear Inequalities
in Two Variables, and Solving Absolute Value Equations and Inequalities
Description of
Primary
Performance
Task
NOTE: One task
per unit
Common Core
Standard(s)
Related to Task
A.REI.3 Solve equations and inequalities in one variable. Solve linear equations and inequalities in one variable,
including equations with coefficients represented by letters.
A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x-coordinates of the points
where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find
the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
A.REI.10 Represent and solve equations and inequalities graphically. Understand that the graph of an equation in
two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a
line).
A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x-coordinates of the points
where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find
the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
CRS Supporting
Skills
College
Bound
GRE 24-27 .601 Identify the graph of a linear inequality on the number line
Pre-Accelerated GRE 24-27 .701 Apply properties of 30-30-90, 45-45-90, similar, and congruent triangles
Honors
GRE 24-27 .701 Apply properties of 30-30-90, 45-45-90, similar, and congruent triangles
Industry or
Subject Specific
Standards
Interdisciplinary
Integrations /
Biology, Chemistry, Physics, Statistics, Travel, Recreation
Thematic
Connections
Connections to
Writing
Framework
Assessment
Supplementary
Text
Written explanation on how to solve a problem
Graphic organizers
Word problems
Critical Thinking Questions
Diagnostic/
PreAssessment
Are You Ready?
Formative
Bell-Ringers, Exit Tickets, Interactive Notebooks, Writing Prompts, Questions and Answers,
Classwork, Group work, Quizzes, Homework, Cornell Notes Summary
Summative
Chapter Test, Ready to Go On, College Entrance Exam, and Performance Task
Description/
Title
Pearson Algebra II
Nonfiction, Fiction,
Informational
Informational
Lexile
Flesch
Reading Ease
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
In what ways can the problem be solved, and why should one method be chosen over another?
Unit Content
Questions
How do you know which operations to use in order to isolate the variable?
What kind of triangles can you use to model the heights of objects and their shadows?
If you know one point on a line, how can you use the slope to find other points on the line?
Does it matter which points you choose from the table to find the slope?
Why is (0,0) often a good point to use to determine shading?
How is the vertical stretch and compression of an absolute-value function similar to a vertical stretch or
compression of a linear function? How is it different?
Unit 3 Summary + Curriculum Alignment
Unit Title
Linear Systems
Major Topics
Using Graphs and Tables to Solve Linear Systems, Using Algebraic Methods to Solve Linear Systems, Solving
Systems of Linear Inequalities
Description of
Primary
Performance
Task
NOTE: One task
per unit
Common Core
Standard(s)
Related to Task
A.REI.6 Solve systems of equations. Solve systems of linear equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in two variables.
A.REI.7 Solve systems of equations. Solve a simple system consisting of a linear equation and a quadratic equation
in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x
and the circle x^2 + y^2 = 3.
A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x-coordinates of the points
where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find
the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
CRS Supporting
Skills
College
Bound
GRE 28-32.701 Interpret and use information from graphs in the coordinate plane
Pre-Accelerated GRE 28-32.701 Interpret and use information from graphs in the coordinate plane
Honors
GRE 28-32.701 Interpret and use information from graphs in the coordinate plane
Industry or
Subject Specific
Standards
Interdisciplinary
Integrations /
Consumer Math, Business, Zoology, Exercise
Thematic
Connections
Connections to
Writing
Framework
Assessment
Supplementary
Text
Written explanation on how to solve a problem
Graphic organizers
Word problems
Critical Thinking Questions
Diagnostic/
PreAssessment
Are You Ready?
Formative
Bell-Ringers, Exit Tickets, Interactive Notebooks, Writing Prompts, Questions and Answers,
Classwork, Group work, Quizzes, Homework, Cornell Notes Summary
Summative
Chapter Test, Ready to Go On, College Entrance Exam, and Performance Task
Description/
Title
Pearson Algebra II
Lexile
Flesch
Reading Ease
Nonfiction, Fiction,
Informational
Informationsl
Flesch-Kincaid Reading Level
Framing Questions
Essential
In what ways can the problem be solved, and why should one method be chosen over another?
Question(s)
Unit Content
Questions
Does it help to put equations in slope-intercept form?
Will solving for x first rather than y give the same solution?
How do you know which lines are parallel?
Unit 4 Summary + Curriculum Alignment
Unit Title
Quadratic Functions
Major Topics
Properties of Quadratic Functions in Standard Form, Solving Quadratic Equations by Graphing and Factoring,
Solving Quadratic Equations by Completing the Square, Solving Quadratic Equations by Complex Numbers and
Roots, and The Quadratic Formula
Description of
Primary
Performance
Task
NOTE: One task
per unit
Common Core N.CN.7 Use complex numbers in polynomial identities and equations. Solve quadratic equations with real
Standard(s)
coefficients that have complex solutions.
Related to Task A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.
A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function
it defines.
A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square,
the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x-coordinates of the points
where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find
the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
CRS Supporting College Bound FUN 20-23.501 Evaluate algebraic expressions by substituting integers for unknown quantities
Skills
Pre-Accelerated FUN 24-27.601 Evaluate polynomial functions, expressed in function notation, at integer values
Honors
FUN 24-27.601 Evaluate polynomial functions, expressed in function notation, at integer values
Industry or
Subject Specific
Standards
Interdisciplinary
Integrations /
Biology, Physics, Areas of Composite Figures
Thematic
Connections
Connections to
Writing
Framework
Assessment
Supplementary
Text
Written explanation on how to solve a problem
Graphic organizers
Word problems
Critical Thinking Questions
Diagnostic/
PreAssessment
Are You Ready?
Formative
Bell-Ringers, Exit Tickets, Interactive Notebooks, Writing Prompts, Questions and Answers,
Classwork, Group work, Quizzes, Homework, Cornell Notes Summary
Summative
Chapter Test, Ready to Go On, College Entrance Exam, and Performance Task
Description/
Title
Pearson Algebra II
Lexile
Flesch
Reading Ease
Nonfiction, Fiction,
Informational
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
How does knowledge of real numbers help when working with complex numbers?
In what ways can the problem be solved, and why should one method be chosen over another?
Why structure expressions in different ways?
Unit Content
Questions
How does the sign of a affect the graph of a quadratic function?
How do you use the values of a and b to find the vertex?
How can you identify the zeros of a quadratic function from a graph?
How do you find the term needed to complete the square?
How do you identify the values of a, b, and c when the quadratic equation is in standard form?
Unit 5 Summary + Curriculum Alignment
Unit Title
Polynomial Functions
Major Topics
Polynomials, Multiplying Polynomials, Factoring Polynomials, and Finding Real Roots of Polynomial Equations
Description of
Primary
Performance
Task
NOTE: One task
per unit
Common Core A.APR.1 Perform arithmetic operations on polynomials. Understand that polynomials form a system analogous to
Standard(s)
the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add,
Related to Task subtract, and multiply polynomials.
A.APR.3 Understand the relationship between zeros and factors of polynomials. Identify zeros of polynomials
when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by
the polynomial.
A.REI.4b Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square,
the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x-coordinates of the points
where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find
the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
CRS Supporting College Bound FUN 24-27.601 Evaluate polynomial functions, expressed in function notation, at integer values
Skills
Pre-Accelerated FUN 24-27.601 Evaluate polynomial functions, expressed in function notation, at integer values
Honors
FUN 24-27.601 Evaluate polynomial functions, expressed in function notation, at integer values
Industry or
Subject Specific
Standards
Interdisciplinary
Integrations /
Medical, Pascal’s Triangle, Physics, Volume, Fractals, Weather
Thematic
Connections
Connections to
Writing
Framework
Written explanation on how to solve a problem
Graphic organizers
Word problems
Critical Thinking Questions
Assessment
Diagnostic/
PreAssessment
Are You Ready?
Supplementary
Text
Formative
Bell-Ringers, Exit Tickets, Interactive Notebooks, Writing Prompts, Questions and Answers,
Classwork, Group work, Quizzes, Homework, Cornell Notes Summary
Summative
Chapter Test, Ready to Go On, College Entrance Exam, and Performance Task
Description/
Title
Pearson Algebra II
Lexile
Flesch
Reading Ease
Nonfiction, Fiction,
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
How can the properties of the real number system be useful when working with polynomials and rational
expressions?
In what ways can the problem be solved, and why should one method be chosen over another?
Unit Content
Questions
How can you find the degree when there is more than one variable?
What properties of exponents are used to multiply polynomials?
How can you tell whether factoring by grouping will work or not?
Why do you set each factor equal to zero to find the roots?
Unit 6 Summary + Curriculum Alignment
Unit Title
Trigonometry
Major Topics
Right-Angle Trigonometry, The Unit Circle, Inverses of Trigonometric Functions, Applying Trigonometric
Functions, Law of Sines, and Law of Cosines
Description of
Primary
Performance
Task
NOTE: One task
per unit
Common Core
Standard(s)
Related to Task
G.SRT.4 Prove theorems involving similarity. Prove theorems about triangles. Theorems include: a line parallel to
one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved
using triangle similarity.
G.SRT.5 Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
G.SRT.6 Define trigonometric ratios and solve problems involving right triangles. Understand that by similarity,
side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric
ratios for acute angles.
G.SRT.7 Define trigonometric ratios and solve problems involving right triangles. Explain and use the relationship
between the sine and cosine of complementary angles.
G.SRT.11 Apply trigonometry to general triangles. Understand and apply the Law of Sines and the Law of Cosines
to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
CRS Supporting
Skills
College
Bound
FUN 24-27. 602 Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of
given side lengths
Pre-Accelerated FUN 28-32.702 Apply basic trigonometric rations to solve right-triangle problems
Honors
Industry or
Subject Specific
FUN 33-36.802 Use trigonometric concepts and basic identities to solve problems
FUN 33-36.803 Exhibit knowledge of unit circle trigonometry
Standards
Interdisciplinary
Integrations /
Astrometry, Aviation, Indirect Measurement, Geography, Surveying
Thematic
Connections
Connections to
Writing
Framework
Assessment
Supplementary
Text
Written explanation on how to solve a problem
Graphic organizers
Word problems
Critical Thinking Questions
Diagnostic/
PreAssessment
Are You Ready?
Formative
Bell-Ringers, Exit Tickets, Interactive Notebooks, Writing Prompts, Questions and Answers,
Classwork, Group work, Quizzes, Homework, Cornell Notes Summary
Summative
Chapter Test, Ready to Go On, College Entrance Exam, and Performance Task
Description/
Title
Pearson Algebra II
Lexile
Flesch
Reading Ease
Nonfiction, Fiction,
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
How might the features of one figure be useful when solving problems about a similar figure?
Unit Content
Questions
How do you determine which trigonometric function to use?
How can you determine the sign of the trigonometric functions by knowing which quadrant contains the
terminal side of the angle?
How can you use the Triangle Sum Theorem to find the measure of the third angle of the triangle?
What information do you need to solve a triangle by using the Law of Cosines?
Unit 7 Summary + Curriculum Alignment
Unit Title
Exponential and Logarithmic Functions
Major Topics
Exponential Functions, Logarithmic Functions, Properties of Logarithms, Exponential and Logarithmic Equations,
and Natural Base e
Description of
Primary
Performance
Task
NOTE: One task
per unit
Common Core
Standard(s)
Related to Task
F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric
functions, showing period, midline, and amplitude.
F.LE.4 Construct and compare linear, quadratic, and exponential models and solve problems. For exponential
models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10,
or e; evaluate the logarithm using technology.
A.REI.11
CC.9-12.A.REI.11 Represent and solve equations and inequalities graphically. Explain why the x-coordinates of the
points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x);
find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.
CRS Supporting
Skills
College
Bound
NCP 33-36.801 Draw conclusions based on number concepts, algebraic concepts, and/or
relationships between expressions and numbers
NCP 33-36.802 Exhibit knowledge of logarithms and geometric sequences
Pre-Accelerated NCP 33-36.801 Draw conclusions based on number concepts, algebraic concepts, and/or
relationships between expressions and numbers
NCP 33-36.802 Exhibit knowledge of logarithms and geometric sequences
Honors
NCP 33-36.801 Draw conclusions based on number concepts, algebraic concepts, and/or
relationships between expressions and numbers
NCP 33-36.802 Exhibit knowledge of logarithms and geometric sequences
Industry or
Subject Specific
Standards
Interdisciplinary
Integrations /
Half-Life, Bacteria Growth, Population Growth, Interest Income
Thematic
Connections
Connections to
Writing
Framework
Assessment
Supplementary
Text
Written explanation on how to solve a problem
Graphic organizers
Word problems
Critical Thinking Questions
Diagnostic/
PreAssessment
Are You Ready?
Formative
Bell-Ringers, Exit Tickets, Interactive Notebooks, Writing Prompts, Questions and Answers,
Classwork, Group work, Quizzes, Homework, Cornell Notes Summary
Summative
Chapter Test, Ready to Go On, College Entrance Exam, and Performance Task
Description/
Title
Pearson Algebra II
Nonfiction, Fiction,
Informational
Lexile
Flesch
Reading Ease
Flesch-Kincaid Reading Level
Framing Questions
Essential
Question(s)
In what ways can the problem be solved, and why should one method be chosen over another?
How can the relationship between quantities best be represented?
When does a function best model a situation?
Unit Content
Questions
How can you differentiate between exponential growth and exponential decay?
What questions can you ask yourself to evaluate the logarithmic expressions?
Why would you want to change the base of a logarithm?
How can you tell when you can write both sides using the same base?
How does the graph f(x) = ex compare to the graphs g(x) = 2x and h(x) 3e?
Unit 8 Summary + Curriculum Alignment
Unit Title
Rational and Radical Functions
Major Topics
Variation Functions, Multiply and Dividing Rational Expressions, Adding and Subtracting Rational Expressions, and
Radical Expressions and Rational Exponents
Description of
Primary
Performance
Task
NOTE: One task
per unit
Common Core
Standard(s)
Related to Task
N.Q.2 Reason quantitatively and use units to solve problems. Define appropriate quantities for the purpose of
descriptive modeling.
A.CED.1 Create equations that describe numbers or relationship. Create equations and inequalities in one variable
and use them to solve problems. Include equations arising from linear and quadratic functions, and simple
rational and exponential functions.
CRS Supporting
Skills
College
Bound
NCP 28-32.704 Apply rules of exponents
NCP 33-36.801 Draw conclusions based on number concepts, algebraic concepts, and/or
relationships between expressions and numbers
Pre-Accelerated NCP 28-32.704 Apply rules of exponents
NCP 33-36.801 Draw conclusions based on number concepts, algebraic concepts, and/or
relationships between expressions and numbers
Honors
NCP 28-32.704 Apply rules of exponents
NCP 33-36.801 Draw conclusions based on number concepts, algebraic concepts, and/or
relationships between expressions and numbers
Industry or
Subject Specific
Standards
Interdisciplinary
Integrations /
Architecture, Transportation
Thematic
Connections
Connections to
Writing
Framework
Assessment
Supplementary
Text
Written explanation on how to solve a problem
Graphic organizers
Word problems
Critical Thinking Questions
Diagnostic/
PreAssessment
Are You Ready?
Formative
Bell-Ringers, Exit Tickets, Interactive Notebooks, Writing Prompts, Questions and Answers,
Classwork, Group work, Quizzes, Homework, Cornell Notes Summary
Summative
Chapter Test, Ready to Go On, College Entrance Exam, and Performance Task
Description/
Title
Pearson Algebra II
Lexile
Flesch
Reading Ease
Nonfiction, Fiction,
Informational
Flesch-Kincaid Reading Level
Framing Questions
Essential
How can algebra describe the relationship between sets of numbers?
Question(s)
In what ways can the choice of units, quantities, and levels of accuracy impact the solution?
Unit Content
Questions
Why should you factor the numerator and the denominator before you multiply?
If two polynomials have a common factor, which power of the factor do you use in the LCM?
Why can one of the solutions of the rational equation be eliminated”