Lawrence High School ALGEBRA II Curriculum Map · 2017-03-22 · LAWRENCE HIGH SCHOOL ALGEBRA II...

LAWRENCE HIGH SCHOOL ALGEBRA II CURRICULUM MAP 2015-2016

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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


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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


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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,


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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.


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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,


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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




RETELL Strategies


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.


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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:


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Data Meeting: 2/1/16

Common Prompts: Rubrics: Grading:



RETELL Strategies


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.


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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.


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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




RETELL Strategies


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.


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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.


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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:



RETELL Strategies


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

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Lawrence High School ALGEBRA II Curriculum Map · 2017-03-22 · LAWRENCE HIGH SCHOOL ALGEBRA II...

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