Integrated Beginning Algebra 2 - Skyline Education · Integrated Beginning Algebra 2, Curricular...
Transcript of Integrated Beginning Algebra 2 - Skyline Education · Integrated Beginning Algebra 2, Curricular...
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.
Integrated Beginning Algebra 2, Curricular Guide 2
Trademarked Skyline Education, Inc., June 2011
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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
Integrated Beginning Algebra 2, Curricular Guide 3
Trademarked Skyline Education, Inc., June 2011
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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],
Integrated Beginning Algebra 2, Curricular Guide 4
Trademarked Skyline Education, Inc., June 2011
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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
Integrated Beginning Algebra 2, Curricular Guide 5
Trademarked Skyline Education, Inc., June 2011
Cannot be reproduced without permission
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
Integrated Beginning Algebra 2, Curricular Guide 6
Trademarked Skyline Education, Inc., June 2011
Cannot be reproduced without permission
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)
Integrated Beginning Algebra 2, Curricular Guide 7
Trademarked Skyline Education, Inc., June 2011
Cannot be reproduced without permission
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
Integrated Beginning Algebra 2, Curricular Guide 8
Trademarked Skyline Education, Inc., June 2011
Cannot be reproduced without permission
Block 1 Block 2 Block 3 Block 4
Lookup Code Descriptor Connections Presented Assessed Presented Assessed Presented Assessed Presented Assessed
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
Integrated Beginning Algebra 2, Curricular Guide 9
Trademarked Skyline Education, Inc., June 2011
Cannot be reproduced without permission
Block 1 Block 2 Block 3 Block 4
Lookup Code Descriptor Connections Presented Assessed Presented Assessed Presented Assessed Presented Assessed
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
Integrated Beginning Algebra 2, Curricular Guide 10
Trademarked Skyline Education, Inc., June 2011
Cannot be reproduced without permission
Block 1 Block 2 Block 3 Block 4
Lookup Code Descriptor Connections Presented Assessed Presented Assessed Presented Assessed Presented Assessed
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.
Integrated Beginning Algebra 2, Curricular Guide 11
Trademarked Skyline Education, Inc., June 2011
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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
Integrated Beginning Algebra 2, Curricular Guide 12
Trademarked Skyline Education, Inc., June 2011
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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/