college algebra 2 - ewdayschools.com · 10/8/2012 · college algebra 2, curricular guide 6...

College Algebra 2, Curricular Guide 1

Trademarked Skyline Education, Inc., June 2011

Cannot be reproduced without permission

College Algebra 2

This course explores advanced Algebraic concepts including: Number Sense and Operations,

Estimation, Functions and Relationships, Algebraic Representations, Analysis of Change, Data

Analysis, Function Fitting, and Complex Numbers. Students will use problem-solving strategies

to prepare solutions to authentic situations involving algebra, geometry, and probability

through algorithmic thinking, logic, and problem-solving skills. This course meets one of the

four math requirements for university admission and Arizona State Graduations requirements.




Curriculum Binder Sign-in Please sign and date the page below if you have viewed the contents of this curriculum binder.

PRINT NAME SIGNATURE DATE




An Introduction to Curriculum Mapping and Standards Log Objectives are mapped according to when they should be introduced and when they should be assessed throughout the month (K-4), block (5-8), or course (7-12). A record of when all objectives are introduced and assessed is to be kept through the course map and log, using the month, day, and year introduced. Objectives only have to be reviewed if assessment is not 80% students at 80% mastery. **In some cases, it is not necessary to teach the standards if 80% students are at 80% mastery when pretested. However, if less than 80% students achieve 80% mastery, it is necessary to give instruction and a posttest.** The curriculum is standards-based, and it is the Skyline philosophy to use “Backwards Design” when lesson planning. Backwards Design starts with standards, and from there, an assessment is created in alignment with the standards; next, the instruction for that assessment and those standards is created. Also, all standards addressed for instruction and assessment should be visibly posted in the classroom, along with student-friendly wording of the objectives. Assessments for mastery are to be summative, or cumulative in nature. Formative assessments are generally quick-assessments where the teacher can gauge whether or not student-learning is acquired. Curriculum binders are set up to have a master of each grade or content level, as well as a teacher’s copy, which is to serve as a working document. Teachers may write in the teacher’s binder to log standards, suggest remapping, adjust timing, and so on. The curriculum mapping may be modified or adjusted as necessary for individual students and classes, as well as available resources, within reason. Major changes are to be submitted to the school’s Professional Learning Community, Administration, and the Board.




Suggested Methods of Activity and Instruction Teacher Modeling

Learning Centers

Learning Stations

Anchor Activities

Group Work

Small Group Discussion

Independent Study

Mentor Study

Think/Pair/Share

Total Physical Response

Graphic Organizers

Tiered Assignments

Literature Circles

Experiment

Rigor/Relevance: Quadrant “D” Learning

Drama/Skits/Plays

Arts Integration Projects

Simulations

Data Collection

Lecture

Whole Group Debate

Learning Games

Learning Contracts

Curriculum Compacting

Flexible Pacing

Self-Directed Learning

Problem-Based Learning

Conferencing

Seminars

Real-World Scenarios




Suggested Methods of Assessment FORMATIVE (Grades are not necessarily assigned for all formative assessments)

SUMMATIVE

Quick-write

Quick-draw

Verbal response

Asking questions

Interaction during activities

Pretests

Learning games

Web/Computer-based assessments

Homework/Class Work

Notes

Pop quizzes

Criteria and goal setting

Teacher observations

Self and peer assessment

Student record keeping

Graphic Organizers

Standardized Tests

State Assessments

Student Portfolio

Interdisciplinary projects

Student-Teacher conference narratives

Posttests

District/School/Course/Content tests

Chapter/Unit Tests




Curriculum Mapping and Standards Log

Understanding Look-up Codes.

All the standards follow the state codes for tracking general concepts and topics.

Number and Quantity

The Real Number System (N-RN)

Quantities (N-Q)

The Complex Number System (N-CN)

Vector and Matrix Quantities (N-VM)

Algebra

Seeing Structure in Expressions (A-SSE)

Arithmetic with Polynomials and Rational Expressions (A-APR)

Creating Equations (A-CED)

Reasoning with Equations and Inequalities (A-REI)

Functions

Interpreting Functions (F-IF)

Building Functions (F-BF)

Linear, Quadratic, and Exponential Models (F-LE)

Trigonometric Functions (F-TF)

Geometry Congruence (G-CO)

Similarity, Right Triangles, and Trigonometry (G-SRT)

Circles (G-C)

Expressing Geometric Properties with Equations (G-GPE)

Geometric Measurement and Dimension (G-GMD)

Modeling with Geometry (G-MG)

Modeling

Statistics and Probability

Interpreting Categorical and Quantitative Data (S-ID)

Making Inferences and Justifying Conclusions (S-IC)

Conditional Probability and the Rules of Probability (S-CP)

Using Probability to Make Decisions (S-MD)

Contemporary Mathematics

Discrete Mathematics (CM-DM)




Block 1 Block 2 Block 3 Block 4

Lookup Code Descriptor Connections Presented Assessed Presented Assessed Presented Assessed Presented Assessed

HS.M.BS

Modeling Standards are spread through the rest of the standards. Anything that requires composing a organized form of data, graphic, or formula is modeling.

HS.F-IF.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

11-12.RST.7

HS.A-REI.10

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).

HS.F-IF.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep

ETHS-S6C2.03;9-10.RST.7;11-12.RST.7

HS.F-IF.7a

Graph linear and quadratic functions and show intercepts, maxima, and minima.

ETHS-S6C1-03;ETHS-S6C2-03

HS.F-IF.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say whic

ETHS-S6C1-03;ETHS-S6C2-03;9-10.RST.7

HS.F-LE.1

Distinguish between situations that can be modeled with linear functions and with exponential functions.

ETHS-S6C2-03;SSHS-S5C5-03

HS.F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

ETHS-S6C1-03;ETHS-S6C2-03;SSHS-S5C5-03; 11-12.WHST.2e






HS.S-ID.1

Represent data with plots on the real number line (dot plots, histograms, and box plots).

SCHS-S1C1-04;SCHS-S1C2-03; SCHS-S1C2-05;SCHS-S1C4-02;SCHS-S2C1-04;ETHS-S6C2-03;SSHS-S1C1-04;9-10.RST.7

HS.S-ID.6a

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

11-12.RST.7

HS.F-BF.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on

ETHS-S6C2-03;11-12.WHST.2e

HS.N-CN.1

Know there is a complex number i such that i2 =

−1, and every complex number has the form a + bi with a and b real.

HS.N-CN.2

Use the relation i2 = –1 and the commutative,

associative, and distributive properties to add, subtract, and multiply complex numbers. 11-12.RST.4

HS.N-CN.3

. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. 11-12.RST.3






HS.N-CN.4

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. 11-12.RST.3

HS.N-CN.5

Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

HS.N-CN.6 Solve quadratic equations with real coefficients that have complex solutions.

HS.N-CN.7 Extend polynomial identities to the complex numbers.

HS.A-APR.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

HS.A-REI.8

Represent a system of linear equations as a single matrix equation in a vector variable.

ETHS-S6C2-03

HS.A-REI.9

Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using

technology for matrices of dimension 3 3 or greater).

HS.F-IF.7b

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.


HS.F-IF.7c

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.


HS.F-IF.7d

Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.







HS.F-IF.7e

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.


HS.F-BF.4 Find inverse functions. ETHS-S6C2-

03

HS.F-BF.4a

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x

3

or f(x) = (x+1)/(x-1) for x ≠ 1.

HS.F-BF.4b

Verify by composition that one function is the inverse of another.

HS.F-BF.4c

Read values of an inverse function from a graph or a table, given that the function has an inverse.

HS.F-BF.4d

Produce an invertible function from a non-invertible function by restricting the domain.

HS.F-LE.4

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.

ETHS-S6C1-03;ETHS-S6C2-03; 11-12.RST.3

HS.F-TF.4

Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

ETHS-S1C2-01;11-12.WHST.2c

HS.F-TF.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

ETHS-S1C2-01

HS.F-TF.6

Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

ETHS-S1C2-01;11-12.WHST.2e






HS.F-TF.7

Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

ETHS-S1C2-01;11-12.WHST.1a

HS.F-TF.9

Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

11-12.WHST.1a-1e

HS.S-ID.6b

Informally assess the fit of a function by plotting and analyzing residuals.

11-12.RST.7;11-12.WHST.1b-1c

Practices Applied in all Math Classes

Mathematical Practices (MP)

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.




Suggested Coursework and Pacing Beginning Algebra is a Freshman level course, and has no Honors curriculum. The course is planned as an 8 week course with padded time for review and testing

for midterms and finals.

Week Course Material Week Course Material

Week 1 Review – Functions and Inverses

Graphing Functions

Analyzing Residuals

Week 5 Review – Calculating Square Root

Plotting Square and Cube Root functions

Week 2 Usining Inverses to Solve Trig Functions

Addition and Subtraction formulae for Sin/Cos

Week 6 Complex Numbers

The Complex Plane

Functions with complex numbers

Week 3 Function fitting to data

Domain Restriction to Improve functions

Week 7 Polar Graphing

Understanding the Polar Graph

Converting the polar graph to X,Y

Week 4 Domain Restriction to Invert Functions

Week 8 Graphing functions in Polar coordinates

Suggested Honors Extensions

Satellite Navigation. Design and prove a method for an object with line of sight to a orbital satellite to navigate an area. Explain the effect using Polar

Graphing may have on it.

Spherical Coordinates. Learn/Explain how to track/calculate spherical coordinates.

Data Analysis. Create a series of surveys collecting real data at the school, show the different function fitting techniques and predictions each would

make. Test the results.




Online Resources for Content AZ/ADE Comprehensive Links for AIMS, Standards, Vision, Vocabulary, Rubrics, etc.: http://www.ade.az.gov/K12Literacy/langarts.asp Arizona ELP Information and Standards: http://www.ade.state.az.us/oelas/

Online Resources for Instructional Methods Rigor and Relevance Framework: http://www.leadered.com/rrr.html http://rigor-relevance.com/ http://www.edteck.com/wpa/index.htm www.leadered.com/pdf/Academic_Excellence.pdf 21st Century Leaner: http://www.ala.org/ http://www.p21.org/ http://dpi.wi.gov/cal/iecouncil.html Character Education: http://goodcharacter.com/ http://charactercounts.org/ http://www.ade.state.az.us/charactered/ Bloom’s Taxonomies: http://www.nwlink.com/~Donclark/hrd/bloom.html Multiple Intelligences: http://www.thomasarmstrong.com/multiple_intelligences.htm http://www.infed.org/thinkers/gardner.htm http://literacyworks.org/mi/assessment/findyourstrengths.html Project-based Learning: http://www.edutopia.org/project-based-learning-research http://pblchecklist.4teachers.org/ http://en.wikipedia.org/wiki/Project-based_learning http://www.pbl-online.org/ http://www.bie.org/index.php/site/PBL/overview_pbl/ http://www.edutopia.org/project-based-learning-research Power Point Games: http://jc-schools.net/tutorials/PPT-games/

http://www.ade.az.gov/K12Literacy/langarts.asp

http://www.ade.state.az.us/oelas/

http://www.leadered.com/rrr.html

http://rigor-relevance.com/

http://www.edteck.com/wpa/index.htm

http://www.leadered.com/pdf/Academic_Excellence.pdf

http://www.ala.org/

http://www.p21.org/

http://dpi.wi.gov/cal/iecouncil.html

http://goodcharacter.com/

http://charactercounts.org/

http://www.ade.state.az.us/charactered/

http://www.nwlink.com/~Donclark/hrd/bloom.html

http://www.thomasarmstrong.com/multiple_intelligences.htm

http://www.infed.org/thinkers/gardner.htm

http://literacyworks.org/mi/assessment/findyourstrengths.html

http://www.edutopia.org/project-based-learning-research

http://pblchecklist.4teachers.org/

http://en.wikipedia.org/wiki/Project-based_learning

http://www.pbl-online.org/

http://www.bie.org/index.php/site/PBL/overview_pbl/

http://www.edutopia.org/project-based-learning-research

http://jc-schools.net/tutorials/PPT-games/

college algebra 2 - ewdayschools.com · 10/8/2012 · college algebra 2, curricular guide 6...

Documents