Standards Based Instructional Unit

Standards – Based Instructional Unit

Subject: Mathematics June 22, 2010

COURSE: Algebra II GRADE/LEVEL: 11 Topic: Numbers and Operations

Lesson Objective(s):  Identify a real and rational number  Solve problems that involve ordering and comparing subsets  Solve problems that involve proportional relationships, percents, ratios and rates  Use mental arithmetic to calculate perfect square, percentages, and fractions  Use estimation to determine the level of accuracy and analyze the accuracy of results.  Simplify computations or contrast the properties and number systems.

21st Century Graduation Expectation(s): 1.1 Acquiring and applying knowledge and skills within and across the curriculum 1.2 Analyzing and evaluating information 1.3 Applying Technology as a learning tool across all disciplines. 2.1 Working cooperatively and/or independently. 2.2 Applying problem solving strategies. 2.3 Utilizing resources and time effectively. 2.4 Accessing, compiling, interpreting and presenting data and information. 3.1 Making informed life and career decisions. 3.2 Recognizing and respecting the diversity and individuality of others. 3.3 Understanding and accepting the benefits and consequences of his/her behavior. 4.1 Reading widely and critically. 4.2 Writing clearly, concisely and persuasively. 4.4 Mastering technology as a means of communication.

Standards: GSES: Students should: M(N&O)1 Rational Numbers  develop a deeper understanding of very large M(N&O)2 Real Numbers and very small numbers and of various M(N&O)4 Solving Problems reputations of them; M(N&O)6 Mental Computation  compare and contrast the properties of M(N&O)7 Estimation numbers and number systems, including the M(N&O)8 Properties of Numbers rational and real numbers and understand R 3 Breadth of Vocabulary Knowledge complex numbers as solutions to quadratic R 7 Analyzing Informational Text equations that do not have real solutions. W-1 Writing Conventions  understand vectors and matrices as systems W-2 Response to Text that have some of the properties of the real W-8 Informational Writing number system. W-9 Writing Conventions  use number theory arguments to justify relationships involving whole numbers.  Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities .  Develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices.  Develop an understanding of permutations and combinations as counting techniques.  Develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more complicated cases.  Judge the reasonableness of numerical computations and the results.

Reading (Students will…)  use vocabulary strategies to identify context data.  read the text for understanding.  organize information to show understanding.  understand information from the text to answer questions.  organize information to show understanding.

Writing  Students will summarize responses.  Students will formulate responses based on problem solving strategies as well as real-life applications.  Students will reflect on mathematical processes.

Problem Solving  Students will compare and contrast. (Such as families of functions and fit- lines)  Students will utilize a variety of charts.  Students will write number sentence formulas, equations, inequalities, etc.  Students will use models to make predictions.  Students will work backwards.  Students will analyze, evaluate, and interpret data.

Essential Question(s):  How can one analyze and synthesize information from multiple representations?  How can one apply the skills and problem solving strategies to real-life situations?

Content Topics:  Equations and Inequalities  Linear Relations and Functions  Systems of Equations and Functions  Matrices  Quadratic Functions and Relations  Polynomials and Polynomial Functions  Inverses and Radical Functions and Relations  Exponential and Logarithmic Functions and Relations  Rational Functions and Relations  Conic Sections

Student-Centered Instructional Strategies:  Technology  Differentiated instruction  Pre-Assessment

Student-Centered Learning Tasks and Opportunities:  Cooperative learning  Manipulatives  Peer editing

Instructional Resources and Equipment:  Computers  Rulers  Graphing Calculators

Assessment Task(s):  Pre-Assessments  Tests  Class Discussion  Problems of the week  Formative assessments

Rubric(s) for Assessment:

 See attached rubrics for specific lesson plans. Reflection/Comments: Students should be able to summarize the graduation expectations and the GSEs utilized throughout Number and Operations. Standards – Based Instructional Unit

COURSE: Algebra II GRADE/LEVEL: 11 Topic: Geometry and Measurements

Lesson Objective(s):  Utilize distance and mid-point formulas.  Solve problems on and off the coordinate plane.  Determine the effect of changing a scale factor on similar figures.  Utilize units of measure appropriately and consistently when solving problems.  Apply the concepts of congruency by solving problems on or off a coordinate plane involving reflections, translations, and dilations.

21st Century Graduation Expectation(s): 1.1 Acquiring and applying knowledge and skills within and across the curriculum 1.2 Analyzing and evaluating information 1.3 Applying Technology as a learning tool across all disciplines. 2.1 Working cooperatively and/or independently. 2.2 Applying problem solving strategies. 2.3 Utilizing resources and time effectively. 2.4 Accessing, compiling, interpreting and presenting data and information. 3.3 Understanding and accepting the benefits and consequences of his/her behavior. 4.1 Reading widely and critically. 4.2 Writing clearly, concisely and persuasively. 4.4 Mastering technology as a means of communication.

Standards: GSES: Students should: M(G&M)2 Uses Geometric Properties  analyze properties and determine attributes of M(G&M)4 Concepts of Congruency two and three dimensional objects; M(G&M)5 Concepts of Similarity  use Cartesian coordinates to analyze geometric M(G&M)6 Two-dimensional Figures situations; M(G&M)7 Uses Units of Measure  understand and represent translations, M(G&M)9 On and off coordinate plane reflections, and dilations of objects in the M(F&A) Patterns plane by using sketches, coordinates, vectors, M(F&A) Linear & Nonlinear Functions function notation M(F&A) Algebraic Equations M(F&A) Equality  use various representations to help understand M(N&O)2 Real Numbers the effects of simple transformations and their M(N&O)4 Solving Problems compositions M(N&O)6 Mental Computation  make decisions about units and scales that are M(N&O)7 Estimation appropriate for problem situations involving M(N&O)8 Properties of Numbers measurement; R 10-3 Breadth of Vocabulary Knowledge R 10-7 Analyzing Informational Text W-10-1 Writing Conventions W-10-2 Response to Text W-10-8 Informational Writing W-10-9 Writing Conventions

Reading  The students will use vocabulary strategies to identify context data.  Students will read the text, Problem of the Week, and supplementary materials for understanding.  Students will organize information to show understanding.

Writing  Students will summarize responses.  Students will reflect and support their conjectures and solutions on various types of assessments.  Students will write portfolio reflections.

Problem Solving  Students will compare and contrast.  Students will apply formulas.  Students will use a model.  Students will work backwards.  Students will observe patterns,

Essential Question(s):  Using a mathematical model, how can one apply concepts of the coordinate plane to solve real world problems?  How can one connect solving problems graphically and algebraically?

Content Topics:  Similarity  Coordinate plane  Transformations  Conics  Distance formula  Midpoint formula  Slope formula  Parallel Lines  Perpendicular lines

Student-Centered Instructional Strategies:  Technology  Differentiated instruction  Pre-Assessment

Instructional Resources and Equipment:  Computers  Rulers  Calculators  Possible Web based performance assessments

Assessment Task(s):  Performance based real world applications  Pre-Assessments  Tests, quizzes  Class Discussion  Portfolio  Possible Web Based Assessments

 See attached rubrics Reflection/Comments: Students should be able to summarize the graduation expectations and the GSEs utilized throughout Geometry and Measurements. Standards – Based Instructional Unit

COURSE: Algebra II GRADE/LEVEL: 11 Topic: Functions and Algebra

Lesson Objective(s):  Solve problems utilizing pattern  Simplify expressions  Evaluate expressions  Identify, solve, graph, and analyze functions  Translate problem situations into algebraic expressions  Solve problems involving algebraic reasoning  Translate problem situations into equations  Analyze the behavior of behavior of linear and nonlinear functions  Relationship among functions

Standards: GSES: Students should: M(F&A)1 Patterns  generalize patterns; M(F&A)2 Linear and nonlinear functions and  use symbolic algebra to represent and explain relations mathematical relationships; M(F&A)3 Algebraic Equations  understand functions; operations and M(F&A)4 Equality relationships M(N&O)2 Real Numbers  draw reasonable conclusions about a situation M(N&O)4 Solving Problems being modeled; M(N&O)6 Mental Computation  use technology, such as graphing calculators, M(N&O)7 Estimation to compare and contrast functions M(N&O)8 Properties of Numbers R 10-3 Breadth of Vocabulary Knowledge R 10-7 Analyzing Informational Text W-10-1 Structures of language W-10-2 Response to Text W-10-8 Informational Writing W-10-9 Writing Conventions

Reading  The students will use vocabulary strategies to identify context data.  Students will read the text for understanding.  Students will organize information to show understanding.

Writing  Students will summarize responses.  Students will reflect and support their responses, such as performance based/real world applications.  Students will write portfolio reflections.

Problem Solving  Students will use the “guess and check” method for solving variables.  Students will use a model.  Students will work backwards.  Students will observe patterns.  Students will formulate a number sentence from a given situation.

Essential Question(s):  Using a mathematical model, how can one analyze and synthesize information from multiple sources, such as in real world/performance base applications?  How can one design a mathematical model to inform and solve a practical or abstract situation?

Content Topics:  Equations and Inequalities  Linear relations and functions  Matrices  Functions: Linear, quadratic, polynomial  Properties of Exponents  Radical functions and relations  Rational functions and relations  Conic sections

Student-Centered Instructional Strategies:  Technology  Differentiated instruction  Pre-Assessment  Post-Assessment and reflection

Instructional Resources and Equipment:  Computers  Rulers  Calculators  Possible Web based performance assessments

Assessment Task(s):  Performance based real world applications  Pre-Assessments  Tests, quizzes  Class Discussion  Web Based Assessments  Reflections

 See attached rubrics Reflection/Comments: Students should be able to summarize the graduation expectations and the GSEs utilized throughout Functions and Algebra.

Standards – Based Instructional Unit

Subject: Mathematics August 31, 2009

COURSE: Algebra II GRADE/LEVEL: 11 Topic: Data, Statistics, and Probability

Lesson Objective(s):  Interpret data from a variety of sources, such as, graphs, tables, charts, bar graphs, pie graphs, etc.  Represent data using a variety of methods.  Decide on most effective method to answer questions regarding data.

Standards: GSES: Students should: M(DSP)1 Interpretation of Data  understand the meaning of measurement data; M(DSP)2 Linear and Nonlinear Functions  identify trends in data; M(DSP)3 Representation of Data  understand fit-lines and lines of regression M(DSP)5 Solving Problems M(DSP)6 Response to Question M(N&O)2 Real Numbers M(N&O)4 Solving Problems M(N&O)6 Mental Computation M(N&O)7 Estimation M(N&O)8 Properties of Numbers R 10-3 Breadth of Vocabulary Knowledge R 10-7 Analyzing Informational Text W-10-1 Structures of Language W-10-2 Response to Text W-10-8 Informational Writing W-10-9 Writing Conventions

Reading  The students will use vocabulary strategies to identify context data.  Students will read the text for understanding.  Students will organize and present information to show understanding. Writing  Students will summarize responses.  Students will reflect and support their responses

Problem Solving  Students will compare and contrast data.  Students will interpret graphs.  Students will observe patterns.  Students will use a model  Students will use a variety of graphs to model data.

Essential Question(s):  Using a mathematical model, how can one analyze and synthesize information from multiple sources, such as in performance based real world problems?  How can one design a mathematical model to inform and solve a practical or abstract situation?

Content Topics:  Linear and non-linear functions and their graphs  Quadratic models

Student-Centered Instructional Strategies:  Technology  Differentiated instruction  Post-Assessment and reflection

Student-Centered Learning Tasks and Opportunities:  Cooperative learning  Manipulatives  Peer editing  Informal oral presentations

Instructional Resources and Equipment:  Computers  Rulers  Calculators  Supplemental materials Assessment Task(s):  Performance based real world applications  Tests, quizzes  Class Discussion  Reflections

 See attached rubrics Reflection/Comments: Students should be able to summarize the graduation expectations and the GSEs utilized throughout Data, Statistics, and Probability.