1

Lindblom Mathematics and Science Academy School Year 2017/2018

Advanced Algebra with Trig Syllabus Instructor(s):

Email: Room Office Hours Ms. Parsons aparsons1@cps.edu 326 Tues. 3:15-4pm

Wed. Flex 2 and 3 Fri. 3:15-4pm (Appointment Only)

Ms. Gondim gvgondim@cps.edu 200A Tues/Fri Lunch A-D Wed. Flex 1-3 Tues/Thurs 3:15-4:15

Website: mathparsons.weebly.com

Textbook: Core-Plus Mathematics Course 3 (provided in class when necessary)

Course Description

Advanced Algebra with Trigonometry (AAT) further develops the ideas and techniques

introduced in Algebra I and Geometry. A major goal of this course is for you to develop skills in

manipulating and solving linear, quadratic, exponential, polynomial, rational, and logarithmic

equations. AAT will prepare you to take Pre-Calculus and/or Statistics.

Topics will include: Semester 1 Semester 2

P1: Polynomial Functions P2: Graphing Quadratic Functions P3: Writing Quadratic Functions P4: Solving Quadratic Equations P5: Solving Cubic Equations P6: Simplifying Radical Expressions P7: Defining a Function P8: Domain and Range P9: Function Composition

P1: Simplifying Rational expressions P2: Solving Rational Equations P3: Exponential Growth and Decay P4: Manipulating Logarithm and Exponential Expressions P5: Solving exponential equations P6: Linear Programming P7: Non-Linear Systems of Equations P8: Coordinates on a Circle P9: Unit Circle P10: Sine and Cosine Functions P11: Tangent Functions

Required Course Materials

Math Binder + 8 Dividers will be needed EVERY DAY to take notes and organize class handouts.

Binder checks will occur following each unit for a HOLLs grade.

Writing Utensils: Pencils will be used to complete assignments and quizzes. Colored Pens and

highlighters will be used for note taking and correcting quizzes.

Notebook Paper will be essential for notetaking and completing assignments.

A Scientific Calculator will be used to taking assessments that involves graphing. Students will not

be able to share a calculator on a quiz.

Classroom Folder (Optional) will temporary hold student’s homework and classroom notes when

traveling home.

How will PBL/grades work for this class?

All classes at Lindblom will be following a Proficiency-Based Learning (PBL) model. PBL means

you will have multiple opportunities to demonstrate mastery of new material. PBL recognizes that

2

we all learn at different rates and progress will be different for every student. Our classroom will

honor all types and speeds of mastery. You will have the responsibility to monitoring your own

progress and we will work together on correcting misconceptions you may have. The goal is to

minimize grade stress and place more emphasis on learning.

Your grade in this class will be determined by class assessments. Each Performance Indicator (PI) will be assessed multiple times in class; 2-3 times to be precise. You will be graded on a 1-4 scale. Decimal scores of .4 will be assigned if you have shown sufficient improvement, but did not reach the next level yet. Each student is expected to have MINIMUM of THREE grades for each PI at the end of the semester. After the final version in class, you will be able to complete an outside re-take for potentially a better grade. You must complete both the revisions and re-takes two weeks after you receive your last assessment.

It does not matter WHEN or HOW you cross the finish line, only that you eventually

finish.”

Within each Performance Indicator, the latest assessment will count for more, and the earlier assessments will count for less. Jump rope uses decaying average to calculate your overall grade.

The Calculation of your Final Grade

At the end of each grading period, your final grade will depend on your individual PI scores.

A= All 3s and 4s.

B= All 3s and 4s with no more than two 2’s.

C= All 2s and up with no more than one 1.

D= All 2s and up with two or more 1s

F= All 1s

M=Missing—I have not provided evidence to allow the teacher to assess. This will not affect your

grade in jumprope.

N=Not Revisable—I did not complete the assessment in the time allowed and can no longer revise or

re-take the assessment. This will translate to a 1 in jump rope.

Notes on absences: If you are absent, do NOT wait until the next class session to check in! Check web site and google classroom to stay informed about class lessons, view class notes, and assigned homework. You have a two-week window to make up an assessment. If the Missing assignment is not made up within this time, you will receive a score of N =1.

3

Advanced Algebra with Trigonometry Performance Indicators Rubric Semester One

Scoring Criteria

“1” – Emerging I have demonstrated the most

basic knowledge/skills relevant to this standard.

“2” – Developing I have demonstrated relevant

knowledge/skills, but have not yet demonstrated convincing evidence of fully

meeting the standard.

“3” – Achieving I have demonstrated that I have the knowledge/skills

defined in the standard.

“4” – Excelling I have demonstrated the knowledge/skills

defined by the standard with a high level of understanding/ability as defined by the

discipline.

Performance Indicators 1

2

Level 1, plus....

3

Level 2, plus...

4

Level 3, plus...

P1 Add, subtract, multiply, and divide polynomials and functions; determine appropriate operation(s) for given situations.

I can identify the degree and leading coefficient of a polynomial and classify polynomials by type (linear / quadratic / cubic) and number of terms (monomial / binomial / trinomial).

I can add and subtract polynomials and write the result in standard polynomial form.

I can multiply and divide polynomials and write the result in standard polynomial form.

I can determine and apply the appropriate arithmetic operation(s) for a given situation.

P2 Graph a parabola given a quadratic function in vertex, factored, and standard forms.

I can determine the form of a quadratic function (standard, factored, and vertex).

I can identify critical points on a parabola associated with a given function form.

I can graph a parabola given a quadratic function in vertex, factored, and standard forms and label the critical attributes.

I can compare multiple quadratic functions presented in the same form and describe how the graphs are related to one another.

P3 Write the quadratic function for a parabola given a graph or function parameters.

I can identify the vertex, zeros, and y-intercept of a parabola from a graph.

I can select the appropriate form of the quadratic function to model a parabola and substitute the available parameters.

▪ I can write a quadratic function for a parabola given a graph or function parameters.

▪ I can write the equation for the axis of symmetry.

I can compare multiple parabolas (either graphs or critical attributes) and describe how the quadratic functions are related to one another.

P4 Solve quadratic equations by factoring, using the quadratic formula and graphing.

▪ I can write the quadratic formula.

▪ Given the discriminant, I can identify the number and types of solutions.

▪ I can calculate the discriminant for a quadratic equation.

▪ I can apply the zero product property to find the solutions to a quadratic equation presented in factored form.

▪ I can apply the zero product property to find the solutions to a quadratic equation presented in standard form.

▪ I can solve a quadratic equation that cannot be factored by graphing or using the quadratic formula.

I can apply my understanding of quadratic functions to answer questions about and solve real-world problems.

4

P5 Solving Cubic Equations by factoring and using cubic formula

I can identify the number of real and complex solution given a cubic in factored form and or given a graph

I can factor a quadratic equation by grouping,

Then apply the zero-product property to find the solutions to a quadratic equation presented in factored form.

I can factor a cubic equation by grouping and taking out the GCF. Afterwards, apply the zero-product property to find all real solutions to a cubic equation once presented in factored form.

I can factor a cubic equation by grouping and apply the zero-product property to find all real and complex solutions to a cubic equation once presented in factored form

P6 Simplifying Radical Expressions

I can simply radical expressions (square roots) that includes numbers.

I can simplify radical expressions (square and cube roots) that includes both numbers and variables.

I can multiply/divide radical expressions, then simplify.

I can add/subtract radical expressions (square roots), then simplify.

I can add/subtract radical expressions (square roots and cube roots), then simplify.

P7 Distinguish between relationships that are functions and those that are not.

I can give the definition of a function and identify the independent and dependent variables from a graph or table.

I can explain whether relationships are / are not functions by evaluating tables and graphs.

I can explain whether relationships are / are not functions by evaluating algebraic representations and real-world situations.

I can compare relations and functions by providing example tables, graphs, algebraic representations, and real-world situations.

P8 Identify the theoretical and practical domain and range of a function.

I can define domain and range and describe the difference between practical and theoretical domain and range.

▪ I can determine a function’s domain and range from a graph or table.

▪ I can identify whether a function’s practical domain / range are continuous or discrete.

I can determine theoretical and practical domain and range for a function which models a real-world situation.

I can determine domain and range of a function expressed algebraically.

P9 Compose two or more functions using symbolic representations, graphs or tables.

I can evaluate a composition of two functions using graphs, tables or symbolic representations with integer inputs and no undefined values.

I can evaluate a composition of two functions with basic symbolic inputs.

I can evaluate a composition of three or more functions using graphs, tables or symbolic representations including undefined values.

▪ I can apply the concept of function composition to real life situations.

▪ I can explain using examples when composition of functions is / is not commutative.

5

Performance Indicators 1

2

Level 1, plus....

3

Level 2, plus...

4

Level 3, plus...

P1 Simplify rational expressions, including those involving addition, subtraction, multiplication, and division.

I can simplify a rational expression by factoring the numerator and denominator and identify values for which the expression is undefined.

I can add and subtract rational expressions with common denominators and simplify the result, including identifying values for which the expression is undefined.

I can multiply and divide rational expressions and simplify the result, including identifying values for which the expression is undefined.

I can add and subtract rational expressions with unlike denominators and simplify the result, including identifying values for which the expression is undefined.

P2 Solve equations involving rational expressions; model problem situations using rational functions.

I can identify the Least Common Denominator before solving rational equations.

I can solve a rational equation with a common denominator and identify extraneous solutions.

I can solve a rational equation with unlike denominators, and check for and identify extraneous solutions.

I can set up and use a rational equation to model a real-life situation.

P3 Model exponential growth and decay situations using graphs, tables, and equations.

I can distinguish between exponential growth and decay situations and determine the starting value and common multiplier (growth rate) for exponential functions by looking at an equation.

▪ I can determine an exponential function rule by looking at a table or graph.

▪ I can graph exponential functions including starting value, sufficient plotted points, and asymptote.

I can create exponential functions to model real-world growth and decay situations and answer questions using those functions.

I can model compounding interest using the appropriate exponential model, including annual, periodic, and continuous compounding (with e).

P5 Solve exponential equations using logarithms, including natural and common logs as appropriate.

I can convert between exponential and logarithmic forms.

I can solve simple equations involving exponents and logarithms.

I can solve complex equations involving exponents and logarithms.

I can use logarithms to answer questions about situations modeled with exponential functions.

P4 Manipulate logarithmic expressions using properties of logarithms including addition, subtraction, and exponents.

I can use change of base formula to evaluate logarithms with bases other than 10 and e and appropriately round answers as directed.

I can apply the properties of logarithms to manipulate logarithmic expressions with 2 terms.

I can apply the properties of logarithms to manipulate, expand, and condense logarithmic expressions with more than 2 terms.

I can create equivalent logarithmic expressions that demonstrate the properties of logarithms.

6

P6 Solve non-linear systems that result in quadratic equations.

I can give the solution to a non-linear system when given a graph of the functions.

I can solve non-linear systems (one quadratic and one linear) that result in quadratic equations.

I can set up and solve a real-world problem that involves a non-linear system of equations.

I can set up and solve a real-world problem that involves an inequality relationship between non-linear functions and interpret my solutions.

P7 Model and solve real world problems using linear programming.

I can model, graph, and solve problems using a two-variable inequality.

I can model, graph, and solve problems using a system of two-variable inequalities.

I can model and solve a real-world problem using linear programming.

I can model and solve a real-world problem using linear programming, including interpreting non-integer solutions.

P8 Determine the coordinates of points on a circle using angle measure and the equation of a circle.

▪ I can determine the coordinates of points on a circle located on the axes.

▪ I can write the equation of a circle centered at the origin with radius 𝑟.

▪ I can determine the radius of a circle given the equation.

I can determine the coordinates of points on a circle in the first quadrant given the radius and / or angle measure.

I can determine the coordinates of any points on a circle given the radius and / or angle measure.

I can use my understanding of circles to answer questions beyond those explicitly covered in class .

P9 Label the angles and coordinates on the unit circle, determine values of trig ratios, and give coterminal angles in degrees and radians.

I can draw and label angles using degrees.

I can draw and label angles using radians and convert between degrees and radians.

I can give coterminal angles in degrees.

I can give coterminal angles in radians.

I can label the coordinates on the unit circle and give sine / cosine values for angles on the unit circle.

I can give tangent values using the unit circle.

I can give the unit circle coordinates and sine / cosine values of coterminal angles.

P10 Graph sine and cosine functions in radians and degrees using key parameters. Write sine and cosine functions for given graphs using key parameters.

I can graph the sine and cosine parent functions and identify the following key characteristics: ▪ Amplitude ▪ Midline ▪ Min / max values ▪ “Start” value ▪ Period ▪ Pattern of critical points

I can identify key characteristics of transformed sine / cosine functions (including matching graphs and equations) and graph sine / cosine functions involving up to two transformations (excluding period changes).

I can graph sine / cosine functions involving more than two transformations (including period changes OR phase shifts).

I can write a single function rule to model a given graph of a transformed sine / cosine function (including period changes OR phase shifts).

I can graph sine / cosine functions involving more than two transformations (including period changes AND phase shifts combined). I can write multiple function rules to model a given graph of a transformed sine / cosine function (including period changes).

7

P11 Graph tangent functions in radians and degrees using key parameters. Write sine and cosine functions for given graphs using key parameters.

I can graph the tangent parent function and identify the following: ▪ Period ▪ Vertical asymptotes ▪ Midline ▪ “Start” value ▪ Pattern of critical points

I can identify key characteristics of transformed tangent functions (including matching graphs and equations) and graph tangent functions involving up to two transformations (excluding period changes).

I can graph tangent functions involving more than two transformations (excluding period changes)

I can write a single function rule to model a given graph of a transformed tangent function (excluding period changes).

I can graph tangent functions involving more than two transformations (including period changes)

I can write multiple function rules to model a given graph of a transformed tangent function (including period changes).

HOLLs (Habits of Lifelong Learners) In addition to academic performance, all classes will also be monitoring and tracking student’s performance and progress on non-academic traits. The HOLLs

traits that will be monitored this year will be:

HOLL Standard 1: Student shows a commitment to Intellectual Growth

Performance Indicator: Demonstrate self-awareness and metacognition in order to develop one’s strengths and weaknesses as a student.

Emerging: I need guidance to identify my strengths and weaknesses as a student.

Developing: I can identify my strengths and weaknesses as a student.

Achieving: I can use self-awareness and metacognition to identify and develop my strengths and weaknesses as a student.

Excelling: I take initiative to find additional ways to challenge myself and continually develop my strengths and weaknesses as a student.

Forms of evidence: Student completes revisions for quizzes/tests and takes initiative to complete additional practice before reassessments. Conferences with Ms. Parsons (as needed or requested). Participation in flex tutoring sessions

HOLL Standard 2: Student shows a commitment to Social Growth

Performance Indicator: Collaborate effectively and respectfully with peers.

Emerging: I struggle to collaborate with peers and may disrupt group work.

Developing: I can work collaboratively with peers when assigned a specific role.

Achieving: I can collaborate effectively and respectfully with peers.

Excelling: I take a leadership role to actively engage with classroom members. I provide a model of respectfulness by supporting my peers and/or seeking out and incorporating the perspectives of others.

Forms of evidence: Group work Rubric to evaluate group collaboration and willingness to get to know and work with peers. Respectfulness and participation in class discussions.

HOLL Domain 3: Student shows a commitment to Personal Responsibility

Performance Indicator: Complete necessary preparatory/practice tasks.

Emerging: I struggle to complete necessary preparatory/ practice tasks.

Developing: I sometimes complete necessary preparatory/ practice tasks.

Achieving: I complete necessary preparatory/ practice tasks.

Excelling: I thoroughly complete necessary preparatory/ practice tasks and independently seeks enrichment opportunities that challenge me.

8