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LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
2 Updated 8/11/15
The following are a list of essential standards for this course and a brief map of where they will be addressed.
Standard Quarter 1 Quarter 2 Quarter 3 Quarter 4
N.RN.1 X
N.RN.2 X
N.Q.1 X X X
N.CN.1-3,7-9 X
A.SSE.1 X X
A.SSE.1a X
A.SSE.1.b X
A.SSE.2-3a X X
A.SSE.3c X
A.APR.2-4, 6-7 X
A.CED.1 X X
A.REI.2,4 X
A.REI.10 X X X
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
3 Updated 8/11/15
Standard Quarter 1 Quarter 2 Quarter 3 Quarter 4
F.IF.1-3,5-6 X
F.IF.4 X X
F.IF.7 X X X
F.IF.7a X
F.IF.7b,c X
F.IF.7e X X
F.IF.8b X
F.BF.1-2 X X
F.BF.3 X
F.BF.4 X
F.BF.5 X
F.LE.1 x X
F.TF.1-4,7-9 X
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
4 Updated 8/11/15
Quarter 1: Unit 1 1A Tables and Patterns 2A Refining Functions 2B Making it Fit: Lagrange and Functions
Learning Goals: Identify and describe specific patterns in input-output tables
Determine whether a linear function matches a table
Use differences to decide what type of function can fit a table
Compare recursive and closed-form rules for functions
Determine what is and isn’t a function
Use function notation and find domain, target and range of a function
Determine if a function has and inverse and find it
Compose functions
Graph piecewise-defined functions
Fit polynomials to a table using Lagrange interpolation
Essential Questions
How can you tell if a relationship is linear, quadratic, or something else?
What is a function?
How can you compose a new function from previous functions?
How can you find a polynomial that fits a table of information?
How can you find the next number in a sequence?
Is it possible for two functions to agree with the same table?
Standards N.Q.1 A.SSE.1 A.CED.1 F.IF 1-3,5-6 F.IF.7 F.BF.1-2 F.BF.4 F.LE.1
Content Objectives Students will be able to: Determine if a relationship is a function from tables, graphs or rules
Determine and find the inverse of a function
Find the domain and range of a function
Graph a piecewise function
Fit polynomials to tables
Use linear combinations of polynomials to determine new polynomials
Find factors of polynomials from their zeros
Tier II Vocabulary Slope, identity, degree, quotient, remainder, integers, rational numbers, real numbers
Tier III Vocabulary Balance point, closed-form definition, cubic function, difference table, factorial function, quadratic function, recursive definition, coefficient, monomial, polynomial, normal form, composite function, domain, range,
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
5 Updated 8/11/15
function, inverse function, identity function, quadratic function, rational expression, Lagrange interpolation
Assessments CIA: 10/26-10/30/15 Data Meeting: 11/9/15
Investigation Reflections; Mid-Chapter Test; End of Unit Test Summative Assessments: Formative Assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME text NOTES Section 2.0 (page 90) is necessary for low-mid level groups and a good review for all levels.
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
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Quarter 2: Unit 2 2C Factors, Roots and Zeros of Functions 2D Advanced Factoring 3A Introduction to Complex Numbers (4A/4B Matrices): See note
Learning Goals/Content Objectives Understand the relationship between roots and factors of polynomials
Divide polynomials by linear polynomials
Discover and use the Remainder Theorem and Factor Theorem
Factor polynomials by; scaling, differences and sums of squares, differences and sums of cubes, grouping, using
quadratic properties for higher order polynomials, and by finding roots.
Write the general form of a function that matches a table
Understand the complex numbers as an extension of the real numbers
Use complex numbers in solving equations
Use complex numbers in multiple step arithmetic with precision
Essential Questions
How are the zeros of polynomial related to its factors? How can you tell if two polynomials are equivalent? Can you use the scaling method to turn non-monic cubics into monic cubics? How do you factor nonmonic quadratics? How do you factor differences and sums of cubes? What is the greatest degree polynomial you need to fit a table with four inputs? What is a complex number? How can you use complex numbers to solve ANY quadratic equation? How do you know that i is not a real number?
Standards N.CN.1-3,7-9 A.SSE.1-3A A.APR.2-4,6-7 A.REI.2,4 A.REI.10
Content Objectives Students will be able to: - Describe the relationship between roots and factors of a polynomial - Describe and use the Remainder Theorem and the Factor Theorem - Find the number of values that must be checked to determine if two functions are equivalent and determine if they are. - Describe the method for scaling a polynomial in order to factor it. - Determine if a product of two polynomials can be written as the sum or difference of cubes. - Compare higher order polynomials to quadratic or cubic expressions and factor them using known properties. - Use polynomial factoring to solve equations and describe the method in steps. - From a table, write the general form of a function and describe the method for doing so - Use division to factor polynomials
Tier II Vocabulary Zeros, intercept, relationship, property, extension, root, factor, function,
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
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Tier III Vocabulary Difference of cubes, sum of cubes, quadratic formula, the rational numbers, irrational numbers, natural numbers, i, complex numbers, fundamental theorem of Algebra, conjugate,
Assessments Midterms: 1/19-1/22/16 Data Meeting: 2/1/16
Investigation Reflections; Mid-Chapter Test; End of Unit Test Summative Assessments: Formative Assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME text NOTES Student ability and level of class will determine how quickly you can move through 2c and 2d, some classes
really struggle with any factoring and need to have this concept concrete before tackling the factoring skills involving nonmonic quadratics. The project on page 200 (Heron’s Formula) is a great writing project within the math curriculum. Notice that we skip 3C, many students have seen magnitude and direction in physics, if time allows introducing graphing on the coordinate plane could be a nice mini lesson if you need a filler class.
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
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Quarter 2A: (Or another time during the school year) Extension Work: To be used when time allows. **Honors Classes (4A/4B Matrices): See note
Learning Goals:
Solve systems that include three equations and three variables
Translate system of equations into matrices and vice versa
Use Gaussian Elimination to solve a system of equations
Compute sums, difference, dot products, products, and inverses of matrices
Interpret and solve problems using matrix calculations
Communicate and prove results about matrices, including the ideas of rows and columns and indices
Compute sums, differences, dot products, products, and inverses of matrices
Interpret and solve problems using matrix calculations
Essential Questions
How can you write a system of equations as a matrix? Why is it possible to solve systems of linear equations in matrix form? How can you find the values of 3 variables in a system of three equations? What is the dot product? How can you represent matrix multiplication using dot products? What are some special cases of matrices that have products that are commutative?
Standards A.REI.6-8 N.VM.6-12 S.IC.3-4
Content Objectives Students will be able to: - Describe how to write a matrix form of a system of equations.
- Compare solutions for systems of three variables and determine if they are correct.
- Describe and apply the process of Gaussian Elimination and apply it both by hand and with technology.
- Compute sums, differences, dot products, products and inverses of matrices, and compare the steps to other
mathematical operations.
- Use matrices to solve real world systems of equations and determine if the solution is viable.
- Find the inverse of matrices and compare them to the inverses of other mathematical operations.
Tier II Vocabulary Dimension, elimination, substitution, linear combination, inverse, Tier III Vocabulary Matrix, row-reduced echelon form, Gaussian Elimination, determinant, dot product, identity matrix, zero
matrix, scalar multiplication,
Assessments Midterms: 1/19-1/22/16
Investigation Reflections; Mid-Chapter Test; End of Unit Test Summative Assessments: Formative Assessments:
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
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Data Meeting: 2/1/16
Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME text NOTES
This entire section has been skipped in the past, but it is the only time students will have an experience with matrices during high school. This is a great section to use with a fast moving class before the Winter break, or even later in the school year if you run into a scheduling issue. It has been used in classes that are moving quickly during a particular Term and don’t want to teach material from the next term until after the common assessment.
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
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Quarter 3 : Unit 3 5A Exponent Review 5B Exponential Functions and It’s Inverse 5C Formal Introduction of Logarithms
Learning Goals:
Evaluate expressions involving exponents, including zero, negative and rational numbers
Find missing terms in geometric sequences
Create expressions that match geometric sequences
Identify identities from specific examples
Graph an exponential function
Determine the equation of an exponential function given two points on the graph
Use approximation to evaluate exponential functions
Evaluate logarithms of any base using a calculator
Use logarithms to solve exponential equations
Graph logarithmic functions
Essential Questions
What is the fundamental law of exponents and what are some of its corollaries? How to you extend the law of exponents to define zero, negative, and rational exponents? How do you simplify expressions with exponents that are zero, negative or rational? How do the laws of exponents apply to functions? What must an exponential function have an inverse function? How can you find the compounded interest of an investment using exponents? What is a logarithm and why is it necessary? What is a logarithmic scale and when do you use it? How can you determine the number of years it will take to double your investment?
Standards N.RN.1,2 N.Q.1 A.SSE.1 A.SSE.2-3 A.CED.1 A.REI.10 F.IF.4,7,8 F.BF.5 F.LE1
Content Objectives Students will be able to: - Show proficiency when working with exponents and relate them to other math operations - Describe how to solve equations that involve exponents - Describe why any value with a zero exponent is equal to one. - Compare and contrast positive and negative exponents - Interpret expressions by missing terms in a geometric sequence. - Compare rational exponents to previous knowledge and solve equations involving rational exponents - Convert rational exponents between exponential form and radical form and provide evidence of why it
works - Describe how to find the equation of an exponential function from two points on a graph. - Compare functions that are strictly increasing or strictly decreasing.
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
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- Determine the close formed exponential function that matches a table of values and describe how to replicate the process.
- Extend the laws of exponents to include all real-number exponents and express the laws as function equations.
- Describe how to estimate the inverse of the equation .
- Describe how to use a calculator to find the logarithm of any base. - Graph logarithmic functions and compare them to the graphs of exponential functions. - Graph functions using the logarithmic scale and compare to a standard logarithmic graph
Tier II Vocabulary Base, exponent, increasing, decreasing
Tier III Vocabulary Laws of exponents, product model, negative exponent, zero exponent, arithmetic sequence, geometric sequence, rational exponent, real nth root, extension by continuity, closed-form definition, exponential decay/growth, recursive definition, functional equation, monotonic, chane-of-base rule, common logarithm, logarithmic function, linear scale, log-log graph paper, logarithmic scale, semilog graph paper
Assessments CIA: 4/4-4/8/16 Data Meeting: 4/25/16
Investigation Reflections; Mid-Chapter Test; End of Unit Test Summative Assessments: Formative Assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME text NOTES Students have already seen these functions with tables during 1A, they might be familiar with them but will
need specific reminders about exponent rules.
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
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Quarter 4: Unit 4 6A Transforming Basic Graphs 8.00 Right Triangle Trig (review) 8A Trigonometric Functions 8B
Learning Goals:
sketch the graphs of basic equations
describe the effects of translations on the basic graphs in words and algebraically
describe the effect of scaling an axis on the graphs and algebraically
compose transformations and sketch their effect
use right triangle trigonometry to find the coordinates on the unit circle
evaluate sine, cosine, and tangent functions for any angle
solve equations involving trigonometric functions
Sketch the graphs of sine, cosine, and tangent
Use trigonometric graphs to solve problems
Use proofs involving trigonometric identities
Essential Questions
How are quadratic graphs related? How does the graph of a circle change when simple operations change the variable? How can you determine what a graph looks like simply by looking at an equation? What effect do simple mathematical operations have on basic graphs? How can you extend the definitions of sine, cosine, and tangent to any angle, not just acute angles? If an angle is in Quadrant, IV, what can you say about the sign of its sine, cosine, and tangent? What is the relationship between the equation of the unit circle and the Pythagorean Identity? What do the graphs of the sine and cosine functions look like? Why does the tangent function have a period of 180 degrees? What is a simple rule for finding the value of ?
Standards N.Q.1 A.REI.10 F.IF.4,7 F.BF.3 F.TF.1-4,7-9
Content Objectives Students will be able to: -Describe and compare the basic graphs of equations/ -Describe the effect of a translation of one of the basic graphs. -Describe the effect of a translation on the equation of a basic graph. -Compose transformation and sketch the effect of compositions and describe in words how the graph changes. - Complete scale transformations no the axis of a basic graph. - Complete Reflections of basic graphs over axis. - Describe how to use right triangle trigonometry to find the coordinates of any angle on the unit circle. - Compare the sine, cosine, and tangent of angles and describe their relationship.
LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016
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-Use trigonometric functions to solve equations and explain how it compares with other equations. - Describe the similarities of sine and cosine’s graphs. - Compare sine, cosine, and tangent. - Describe how to use the graph of trigonometric functions to solve problems. - Prove trigonometric identities.
Tier II Vocabulary Solutions, acute, origin, relationship
Tier III Vocabulary Even function, odd function, unit circle, sine, cosine, tangent, standard position, trigonometric equations, discontinuity, period
Assessments Finals: 6/7-6/10/16*
Summative Assessments: Formative Assessments: Common Prompts: Rubrics: Grading:
21st Century Learning Expectations
Academic: Effective communication, evaluate information, solve problems, collaborate, support claims, use technology Social: Act with persistence when facing challenging tasks, responsible and respectful behavior, goal setting Civic: Utilize networking skills and engage inclusively with others
RETELL Strategies
7-step Vocab; posted word walls; Think Aloud; Partner Reading; Write Around
Texts/Resources CME text NOTES Students must have concrete knowledge of trigonometry and the unit circle in degrees. Pre-Calculus start with a
similar exploration using radians. Strong classes can use 8.00 as a quick review, other classes may need a few days on it. *Dates may be adjusted according to inclement weather cancellations