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Standards – Based Instructional Unit Subject: Mathematics June 2010 COURSE: Topics in Mathematics Topic: Numbers and Operations GRADE/LEVEL: 11-12 Lesson Objective(s): Identify a real number Solve problems that involve proportional relationships, percents, ratios and rates Determine the level of accuracy needed and analyze the accuracy of results. Compare and contrast the 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 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. 4.3 Speaking, listening and interpreting effectively. Standards: Students should: develop a deeper understanding of very large and very small numbers and of various reputations of them; compare and contrast the properties of numbers and number systems, including the rational and real numbers; and understand complex numbers as solutions to quadratic equations that do not have real solutions; understand matrices as systems that have some of the properties of the real-number system; GSES: M(N&O)1 Rational Numbers 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 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 for understanding. Students will organize information to show understanding. Writing Students will summarize responses. Students will formulate responses based on research. (Such as “The Hallway of Lights” common assessment) Problem Solving Students will utilize a chart/Venn diagram Students will write a number sentence/formula Students will use a model Students will work backwards Essential Question(s): Using a mathematical model, how can one analyze and synthesize information from multiple sources, such as in “The Hallway of Lights?” How can one design a mathematical model to inform and solve a practical or abstract situation? Content Topics: Percents Ratios Proportions Logical Reasoning Prime Fractional Operations Divisibility Even/Odd Classifications (counting, whole, integers, etc.) Elements Patterns Counting Techniques Student-Centered Instructional Strategies: Technology Differentiated instruction Pre-Assessment Student-Centered Learning Tasks and Opportunities: Cooperative learning Informal Peer editing Instructional Resources and Equipment: Computers Rulers Calculators Assessment Booklets Performance-based real-world applications Assessment Task(s): Common Tasks Pre-Assessments Tests Class Discussion Rubric(s) for Assessment: See attached rubrics Reflection/Comments: Students should be able to summarize the graduation expectations and the GSEs utilized throughout Number and Operations. Standards – Based Instructional Unit Subject: Mathematics COURSE: Topics in Mathematics Topic: Geometry and Measurements March 2010 GRADE/LEVEL: 11-12 Lesson Objective(s): Utilize geometric properties or theorems involving angles, lines, and polygons. Utilize distance formula. Solve problems on and off the coordinate plane. Determine the effect of changing a scale factor on similar figures. Calculate perimeter, circumference, area, volume, and/or surface area. Utilize units of measure appropriately and consistently when solving problems. 21st Century Graduation Expectation(s): 1.1 Acquiring and applying knowledge and skills within and across the curriculum 1.2 Analyzing and evaluating information 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. 4.2 Writing clearly, concisely and persuasively. Standards: Students should: analyze properties and determine attributes of two and three dimensional objects; use Cartesian coordinates to analyze geometric situations; make decisions about units and scales that are appropriate for problem situations involving measurement; analyze precision, accuracy, and approximate error in measurement situations; understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders; GSES: M(G&M)2 Uses Geometric Properties M(G&M)4 Concepts of Congruency M(G&M)5 Concepts of Similarity M(G&M)6 Two-dimensional Figures M(G&M)7 Uses Units of Measure M(G&M)9 On and off coordinate plane 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 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 for understanding. Students will organize information to show understanding. Writing Students will summarize responses. Students will reflect and support their responses, such as in “A WWI Biplane, A pack mule, and your own two feet…” Problem Solving Students will compare and contrast appropriate units of measure Students will apply the distance formula Students will use a model Students will work backwards Students will observe patterns Essential Question(s): Using a mathematical model, how can one analyze and synthesize information from multiple sources, such as in “A WWI Biplane, A pack mule, and your own two feet…” How can one design a mathematical model to inform and solve a practical or abstract situation? Content Topics: Perimeter Area Properties Circumference Lateral Area Surface Area Volume Isosceles Equilateral Right Pythagorean Theorem Similarity Transformations Parallel Lines Perpendicular lines Student-Centered Instructional Strategies: Technology Differentiated instruction Pre-Assessment Student-Centered Learning Tasks and Opportunities: Cooperative learning Peer editing Instructional Resources and Equipment: Compasses Computers Rulers Calculators Assessment Booklets Web based performance assessments Assessment Task(s): Common Tasks Pre-Assessments Tests Class Discussion Web Based Assessments Rubric(s) for Assessment: 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 Subject: Mathematics June 2010 COURSE: Topics in Mathematics Topic: Functions and Algebra GRADE/LEVEL: 11-12 Lesson Objective(s): Solve problems utilizing pattern Simplify expressions Evaluate expressions Translate problem situations into algebraic expressions Solve problems involving algebraic reasoning Translate problem situations into equations 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: Students should: generalize patterns; use symbolic algebra to represent and explain mathematical relationships; draw reasonable conclusions about a situation being modeled; GSES: M(F&A)1 Patterns M(F&A)3 Algebraic Equations M(F&A)4 Equality M(F&A) 1 Rational Numbers 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 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 for understanding. Students will organize information to show understanding. Writing Students will summarize responses. Students will reflect and support their responses, such as in “The Hungry Hobo…” Problem Solving Students will use the “guess and check” method for solving variables 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 “The Hungry Hobo.” How can one design a mathematical model to inform and solve a practical or abstract situation? Content Topics: Simplification of Algebraic Expressions Substitution of Algebraic Expressions Positive/Negative Exponents Properties of Exponents Solving Multi-Step Equations 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 Calculators Assessment Booklets Web based performance assessments Assessment Task(s): Common Tasks Pre-Assessments Tests Class Discussion Web Based Assessments Rubric(s) for Assessment: 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 COURSE: Topics in Mathematics Topic: Data, Statistics, and Probability June 2010 GRADE/LEVEL: 11-12 Lesson Objective(s): Interpret data from a variety of sources, such as, graphs, tables, charts, bar graphs, pie graphs, etc. Analyze data using measures of central tendency. Represent data using a variety of methods. Utilize counting techniques to determine combinations or permutations. Predict the probability of an event. Decide on most effective method to answer questions regarding data. 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: Students should: understand the meaning of measurement data; identify trends in data; understand the concepts of conditional probability and independent events; understand how to compute the probability of a compound event; GSES: M(DSP)1 Interpretation of Data M(DSP)2 Linear and Nonlinear Functions M(DSP)3 Representation of Data M(DSP)4 Using Counting Techniques 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 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 for understanding. Students will organize information to show understanding. Writing Students will summarize responses. Students will reflect and support their responses, such as in “Who Makes More.” Problem Solving Students will compare and contrast data Students will apply the permutation and combination formulas Students will use a model Students will observe patterns Essential Question(s): Using a mathematical model, how can one analyze and synthesize information from multiple sources, such as in “Who Makes More?” How can one design a mathematical model to inform and solve a practical or abstract situation? Content Topics: Mean Median Mode Range Probability Independent/Dependent Events Permutations/Combinations Circle graphs, Bar Graphs, Venn Diagrams, etc. 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 Calculators Assessment Booklets Web based performance assessments Assessment Task(s): Common Tasks Pre-Assessments Tests Class Discussion Web Based Assessments Rubric(s) for Assessment: See attached rubrics Reflection/Comments: Students should be able to summarize the graduation expectations and the GSEs utilized throughout Data, Statistics, and Probability.