Integrated Beginning Algebra 2 - Skyline Education · Integrated Beginning Algebra 2, Curricular Guide 3 Trademarked Skyline Education, Inc., June 2011 Cannot be reproduced without

Integrated Beginning Algebra 2, Curricular Guide 1

Trademarked Skyline Education, Inc., June 2011

Cannot be reproduced without permission

Integrated Beginning Algebra 2

This course explores beginning Algebraic concepts including: manipulating formulae, identifying

traits of linear and exponential functions, function notation, graphing equations and

inequalities, trend lines, and statistics through algorithmic thinking, logic, and problem-solving

skills. Students will use problem-solving strategies to prepare solutions to authentic situations

involving algebra, geometry, and statistics. Competency (70% or above) in Integrated Beginning

Algebra 1 is a pre-requisite for Integrated Beginning Algebra 2. This course meets one of the

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




Curriculum Binder Sign-in

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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. Any questions, please contact Meghan Dorsett, Director of Curriculum, Instruction, and Assessment, at [email protected], [email protected],

mailto:[email protected]

mailto:[email protected]




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.A-CED.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

HS.A-CED.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constra

HS.A-REI.3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

HS.F-IF.1

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 c

HS.F-IF.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

ETHS-S1C2-01;9-10.RST.3

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.F-BF.1

Write a function that describes a relationship between two quantities.

ETHS-S6C1-03;ETHS-S6C2-03

HS.F-BF.1a

Determine an explicit expression, a recursive process, or steps for calculation from a xcontext.

ETHS-S6C1-03;ETHS-S6C2-03;9-10.RST.7; 11-12.RST.7

HS.F-LE.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

ETHS-S6C1-03;ETHS-S6C2-03;11-12.RST.4; SSHS-S5C5-03






HS.F-LE.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

HS.G-GPE.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

9-10.WHST.1a-1e

HS.N-Q.1

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

HS.N-Q.2 Define appropriate quantities for the purpose of descriptive modeling

HS.N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

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.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers w

9-10.WHST.2f






HS.F-IF.7

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

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 which

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.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

SCHS-S1C2-05;SCHS-S1C3-01;ETHS-S1C2-01;ETHS-S1C3-01;ETHS-S6C2-03






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.S-ID.6c Fit a linear function for a scatter plot that suggests a linear association.

11-12.RST.7

HS.S-ID.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

SCHS-S5C2-01;ETHS-S1C2-01;ETHS-S6C2-03;9-10.RST.4; 9-10.RST.7;9-10.WHST.2f

HS.S-ID.8

Compute (using technology) and interpret the correlation coefficient of a linear fit.

ETHS-S1C2-01;ETHS-S6C2-03;11-12.RST.5;11-12.WHST.2e

HS.S-ID.9 Distinguish between correlation and causation. 9-10.RST.9

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 Solving Multi-Variable Equations

Isolating Y

Solving with Distribution

Week 5 Linear Word Problems

Identifying Rates

Identifying Intercepts

Writing Functions

Week 2 Graphing Basics

Graphing Points

Functions Vs Relations (Function Rule)

Interpreting Graphs (Understanding Axis Labels)

Week 6 Graphing Inequalities

Solving Rules

Graphing Rules

Shading Guidelines

Week 3 Graphing functions

Graphing By Evaluation and T-Charts

Identifying Linear Equations

Graphing by Slope-Intercept

Week 7 Scatter Plots and Trend Lines

Identifying Causation and Correlation

Finding Trend Lines visually

Writing Trend Line Formulae

Week 4 Graphing by Intercepts

Graphing Non-Linear Equations

Writing Linear Equations Based on Graphs

Week 8 Multiple Lines

Parallel and Perpendicular

Multiple Inequalities




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/

Documents

Integrated Beginning Algebra 2 - Skyline Education · Integrated Beginning Algebra 2, Curricular Guide 3 Trademarked Skyline Education, Inc., June 2011 Cannot be reproduced without