COURSE NAME: PRE-CALCULUS GRADE: 11,12

Transcription

1 COURSE NAME: PRE-CALCULUS GRADE: 11,12 Prerequisite: ALGEBRA 2 Credits: 5 ABSTRACT The purpose of this full year, five credit course is to prepare students for Calculus at the high school or college level. This course will serve as a comprehensive review of skills previously acquired and to both refine and extend those skills. The study of trigonometry, analytic geometry and elementary functions constitute most of this curriculum. Attention is also given to mathematical rigor, career opportunities, and the attitude with which mathematics must be approached in order to experience success at higher levels. Extensive use is made of graphing calculators and computer laboratory time is assigned. This course is a prerequisite for Calculus. In preparation for the state assessments, students will be given formative and summative assessments throughout the course.

2 STAGE 1: DESIRED RESULTS ESTABLISHED GOALS: (NJ CCCS and/or CCS) CCS F-IF.1-9 F-LE.1-5 F-BF.1-5 CCS F-TF.1-9 CCS N-RN.1-3 N-Q.1-3 N-CN.1-9 Technology st Century Life and Careers A B C D.1-4 MP1-8: 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 Technology st Century Life and Careers A B C D.1-4 MP1-8: 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. Technology st Century Life and Careers A B C D.1-4 MP1-8: 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 2

3 strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 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. strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ENDURING UNDERSTANDINGS: (Students will Understand that...) They can use algebraic and graphing techniques to explain and analyze the general properties and behaviors of functions or relations. They can use functions to model real-world phenomena and solve problems of varying quantities. There are appropriate methods to solve equations and inequalities. 3 Identities are used to evaluate, simplify, and solve trigonometric expressions and equations. The law of cosines and the law of sines can be used to find missing measures. The characteristics of trigonometric and circular functions and their representations are useful in solving realworld problems. There are real-world uses for different types of numbers. Understanding proportions is important for life skills such as reading maps. Understanding the laws of exponents will help them simplify expressions involving numbers raised to powers. There are limitations in using estimation.

4 They can judge the meaning, utility, and reasonableness of the results of symbol manipulations, including technological. It is important to recognize that data can be displayed in different formats. are used in real-life situations, such as cellphone bills. Equations and inequalities are important tools in many different fields. They must use inductive reasoning to form generalizations Connections among the six trigonometric and circular functions are a result of their properties. 4

5 ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) How can algebraic equations be used to solve real-life problems? How do exponential functions model realworld problems and their solutions? How do logarithmic functions model realworld problems and their solutions? How do you graph curves parametrically (by hand and with appropriate technology) How do you successfully eliminate parameters by rewriting parametric equations as a single equation? What is the function of this graph? How do you graph transformations and combinations of transformations for all basic trigonometric functions? Can you solve problems using the fact that trigonometric ratios (sine, cosine, and tangent) stay constant in similar triangles? How do you use the definitions of the six trigonometric ratios as ratios of sides in a right triangle to solve problems about lengths of sides and measures of angles? Can you successfully match a trigonometric equation with its graph? What methods can be used to recognize and extend patterns? How are the different sets of numbers similar and different? How does changing the order of operations affect the results of mathematical expression? How can algebraic equations be used to solve real-life problems? When is estimation an appropriate method? What are the rules for using estimation? Are you able to correctly use summation notation as well as expand and collect expressions in both finite and infinite settings? Can you successfully 5

6 Do you know that the six trigonometric functions can be extended to periodic functions on the real number line? Can you convert from radians to degrees and from degrees to radians? How do you determine the difference made by choice of units for angle measurement when graphing a trigonometric function? How do you find values of inverse trigonometric functions, applying appropriate domain and range restrictions? Can you graph the inverse trigonometric functions and identify their key characteristics? demonstrate an understanding of sequences by representing them recursively and explicitly? Can you use Sigma notation to represent a series? How do you find the sum of a given geometric series (both infinite and finite)? How do you find the sum of a finite arithmetic series? 6

7 Can you graph the six trigonometric functions and identify characteristics such as period, amplitude, phase shift, and asymptotes? How do you determine the appropriate domains for each of the inverse trigonometric functions? Do you know how to use the following trigonometric identities in verifying other identities: Pythagorean, Reciprocal, Quotient, Sum/Difference, Double Angle? Do you know how to use the following trigonometric identities in solving trigonometric equations: Pythagorean, 7

8 Reciprocal, Quotient, Sum/Difference, Double Angle? Can you apply the Pythagorean and Reciprocal Identities to verify identities and solve equations? STAGE 2: ASSESSMENT EVIDENCE PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) Mathematical Practices 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 8 Mathematical Practices 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 Mathematical Practices 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.

9 OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 9. Independent assignments 10. Written responses 11. Real-world problems 12. Non-routine problems 13. Collaborative problemsolving 14. Write own problems and assessments Pre/Post-assessments Practice HSPA tests Quizzes Unit tests Multiple choice problems Teacher observations Math journals Think-Alouds 9 strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 9. Independent assignments 10. Written responses 11. Real-world problems 12. Non-routine problems 13. Collaborative problemsolving 14. Write own problems and assessments Pre/Post-assessments Practice HSPA tests Quizzes Unit tests Multiple choice problems Teacher observations Math journals Think-Alouds 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 9. Independent assignments 10. Written responses 11. Real-world problems 12. Non-routine problems 13. Collaborative problemsolving 14. Write own problems and assessments Pre/Post-assessments Practice HSPA tests Quizzes Unit tests Multiple choice problems Teacher observations Math journals Think-Alouds Homework

10 Homework Discussions Open-ended problems Homework Discussions Open-ended problems There should be a benchmark at the conclusion of this unit. Discussions Open-ended problems RESOURCES: Pre-calculus textbook (Contemporary Pre-calculus by Hungerford & Shaw Thomson Brooks/Cole, 2009) Online tutorials Educational websites Educational software Research in the Media Center Overhead TI-83 calculator for use by teacher Overhead projector LCD projector Computer/Computer lab availability Pre-calculus textbook (Contemporary Pre-calculus by Hungerford & Shaw Thomson Brooks/Cole, 2009) Online tutorials Educational websites Educational software Research in the Media Center Overhead TI-83 calculator for use by teacher Overhead projector LCD projector Computer/Computer lab availability Pre-calculus textbook (Contemporary Pre-calculus by Hungerford & Shaw Thomson Brooks/Cole, 2009) Online tutorials Educational websites Educational software Research in the Media Center Overhead TI-83 calculator for use by teacher Overhead projector LCD projector Computer/Computer lab availability Graphing Calculator (TI83 10

11 Graphing Calculator (TI83 or equivalent) HSPA resource materials Computer Applications a. Microsoft PowerPoint b. Microsoft Excel Microsoft Word Graphing Calculator (TI83 or equivalent) HSPA resource materials Computer Applications a. Microsoft PowerPoint b. Microsoft Excel Microsoft Word or equivalent) HSPA resource materials Computer Applications a. Microsoft PowerPoint b. Microsoft Excel Microsoft Word STAGE 3: LEARNING PLAN SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) Determine whether a relation represents a function and find the value of a function. Represent functions numerically, algebraically and graphically. Determine the sum, difference, product and Convert between radians and degrees. Find arc length, angular and linear speed, and area of a sector of a circle. Define and evaluate the six trigonometric functions in terms of the lengths of the sides of a Distinguish between a rational and irrational answer Express solutions as approximations Express solutions as numerical expressions Raise number to powers. Assess the amount of error resulting from estimation. 11

12 quotient of functions. Determine the domain and range of functions. Identify the graph of a function and obtain information from the graph of a function. Identify the graph of a function and obtain information from the graph of a function. Determine continuity, increasing-decreasing behavior, local minima and maxima, symmetry, asymptotes and end behavior of a function both graphically and algebraically. Find the average rate of change of a function. Recognize the characteristics of the right triangle, the rotation of a ray in standard position, and a point on a unit circle. Find exact values of trigonometric functions and use the calculator to approximate values. Determine the range, domain, and period of trigonometric functions. Graph the six trigonometric functions, and transformations of these graphs. Apply the concepts of trigonometry to solve real world problems. Find an exact value of an inverse sine, cosine or tangent function. Convert to and from scientific notation, multiply numbers in scientific notation, and solve problems in scientific notation. Understand types of numbers, our numeration system, and the ways they are used and applied in real-world situations. Identify rational and irrational numbers. Order rational and irrational numbers on a number line. Apply ratios, proportions, and percents to a variety of situations. 12

13 functions Graph piecewise functions. Graph functions using vertical and horizontal shifts, compressions and stretches, and reflections about the x and y-axis. Build and analyze functions. Recognize and graph linear and quadratic functions. Draw and interpret Scatter Diagrams and find the Line of Best Fit. Graph quadratic functions using transformations, symmetry and intercepts. Build quadratic models from verbal descriptions and data. 13 Find an approximate value of an inverse sine, cosine or tangent function. Find the exact value of composite functions. Find the inverse function of a trigonometric function and solve equations involving inverse functions. Know the definitions of the inverse secant, cosecant and cotangent functions and use the calculator to evaluate sec -1 x, csc -1 x, cot -1 x. Use algebra to simplify trigonometric

14 Identify and graph polynomial functions, predict their end behavior and find their real zeros algebraically and graphically. Identify and graph power functions of the form f(x) = ax n. Find the domain and asymptotes of rational functions, and analyze and construct graphs of rational functions. expressions. Use Reciprocal Trigonometric Identities, Quotient Identities, Pythagorean Identities, Co-Function Identities and Odd-Even Identities to simplify trigonometric expressions and solve trigonometric equations. Establish identities. Apply the identities for the cosine, sine and tangent of a difference or sum. Apply the Remainder Theorem, Factor Theorem, theorems for bounds on zeros, and the Apply the Sum and Difference Formulas, Double-angle Formulas, and Half-angle 14

15 Intermediate Value Theorem. Solve polynomial equations. Determine the complex zeros of polynomial equations, and determine the polynomial with the specified zeros. Apply polynomial, power and rational function to real world problems. Formulas. Use trigonometric concepts to solve equations and real world problems. Find the value of trigonometric functions of acute angles using right triangles. Solve right triangles. Solve applied problems. Form composite functions and find their domain. Apply the Law of Sines and Law of Cosines to solve triangles. Determine if a function is one-to-one, and find Find the area of any triangle. 15

16 the inverse of a function Evaluate exponential expressions. Analyze and solve simple harmonic motion problems. Identify and graph exponential and logistic functions. Use exponential growth, decay and regression to model real life problems. Convert equations between logarithmic form and exponential form. Evaluate common and natural logarithms. Graph common and natural logarithmic 16

17 functions. Apply the properties of logarithms to evaluate expressions Solve exponential and logarithmic equations algebraically and graphically. Use exponential and logarithmic equations to solve real life problems CROSS-CURRICULAR / DIFFERENTIATION: (What cross-curricular (e.g. writing, literacy, math, science, history, 21 st century life and careers, technology) learning activities are included in this unit that will help achieve the desired Individual Instruction Plans Current-event problems Manipulatives Tiered Lessons Learning style adaptation R.A.F.T Project Based learning Individual Instruction Plans Current-event problems Manipulatives Tiered Lessons Learning style adaptation R.A.F.T Project Based learning Individual Instruction Plans Current-event problems Manipulatives Tiered Lessons Learning style adaptation R.A.F.T Project Based learning 17

18 results?) (What type of differentiated instruction will be used for ELL, SP.ED. and G&T students?) Compacting Multimedia presentations Open-ended responses Conclusions and analysis of exploratory activities Integrate Technology: 1. Textbook online resources at my.hrw.com (assessments, learning tools) ipad (for above, and YouTube math videos, as appropriate) Compacting Multimedia presentations Open-ended responses Conclusions and analysis of exploratory activities Integrate Technology: 1. Textbook online resources at my.hrw.com (assessments, learning tools) ipad (for above, and YouTube math videos, as appropriate) Compacting Multimedia presentations Open-ended responses Conclusions and analysis of exploratory activities Integrate Technology: 1. Textbook online resources at my.hrw.com (assessments, learning tools) ipad (for above, and YouTube math videos, as appropriate) Special Education: Provide modifications and accommodations as listed in the student s IEP Position student near helping peer or have quick access to teacher Modify or reduce assignments/texts Reduce length of Special Education: Provide modifications and accommodations as listed in the student s IEP Position student near helping peer or have quick access to teacher Modify or reduce assignments/texts Reduce length of Special Education: Provide modifications and accommodations as listed in the student s IEP Position student near helping peer or have quick access to teacher Modify or reduce assignments/texts Reduce length of 18

19 assignment for different mode of delivery Increase one-to-one time Utilize working contract between you and student at risk Prioritize tasks Provide manipulatives Use graphic organizers Use interactive math journals Use online resources for skill building Provide teacher notes Use collaborative grouping strategies such as small groups Use online resources assignment for different mode of delivery Increase one-to-one time Utilize working contract between you and student at risk Prioritize tasks Provide manipulatives Use graphic organizers Use interactive math journals Use online resources for skill building Provide teacher notes Use collaborative grouping strategies such as small groups Use online resources assignment for different mode of delivery Increase one-to-one time Utilize working contract between you and student at risk Prioritize tasks Provide manipulatives Use graphic organizers Use interactive math journals Use online resources for skill building Provide teacher notes Use collaborative grouping strategies such as small groups Use online resources ELL: Place student next to same-language speaker, if possible ELL: Place student next to same-language speaker, if possible ELL: Place student next to samelanguage speaker, if possible 19

20 Provide text to speech for math problems Use of translation dictionary or software Implement strategy groups Confer frequently Provide graphic organizers Modification plan Adapt a strategyadjusting strategy for ELL: om/content/esl/adaptstrat. cfm *ELL Students- Instruction will be based on language proficiency. At Risk: Tiered interventions following RtI framework Rtl Intervention Bank 20 Provide text to speech for math problems Use of translation dictionary or software Implement strategy groups Confer frequently Provide graphic organizers Modification plan Adapt a strategyadjusting strategy for ELL: om/content/esl/adaptstrat. cfm *ELL Students- Instruction will be based on language proficiency. At Risk: Tiered interventions following RtI framework Rtl Intervention Bank Provide text to speech for math problems Use of translation dictionary or software Implement strategy groups Confer frequently Provide graphic organizers Modification plan Adapt a strategy-adjusting strategy for ELL: m/content/esl/adaptstrat.cf m *ELL Students- Instruction will be based on language proficiency. At Risk: Tiered interventions following RtI framework Rtl Intervention Bank Use additional practice and textbook RTI resources

21 Use additional practice and textbook RTI resources Utilize online resources such as or Gifted: Process should be modified: higher-orderthinking skills, openended thinking, discovery Utilize project-based learning for greater depth of knowledge Utilize exploratory connections to higher grade concepts Contents should be modified: abstraction, complexity, variety, organization 21 Use additional practice and textbook RTI resources Utilize online resources such as or Gifted: Process should be modified: higher-orderthinking skills, openended thinking, discovery Utilize project-based learning for greater depth of knowledge Utilize exploratory connections to higher grade concepts Contents should be modified: abstraction, complexity, variety, organization Utilize online resources such as or Gifted: Process should be modified: higher-order-thinking skills, open-ended thinking, discovery Utilize project-based learning for greater depth of knowledge Utilize exploratory connections to higher grade concepts Contents should be modified: abstraction, complexity, variety, organization Products should be modified: real-world problems, audiences, deadlines, evaluation,

22 Products should be modified: real-world problems, audiences, deadlines, evaluation, transformations Learning environments should be modified: student-centered learning, independence, openness, complexity, groups varied Use of web based resources such as geogebra.org Products should be modified: real-world problems, audiences, deadlines, evaluation, transformations Learning environments should be modified: student-centered learning, independence, openness, complexity, groups varied Use of web based resources such as geogebra.org transformations Learning environments should be modified: student-centered learning, independence, openness, complexity, groups varied Use of web based resources such as geogebra.org 22

23 UNIT: 4 Vectors and Matrices (May, 30) UNIT: 5 Algebra STAGE 1: DESIRED RESULTS ESTABLISHED GOALS: (NJ CCCS and/or CCS) CCS N-VM.1-12 A-REI.5-12 Technology st Century Life and Careers A B C D.1-4 MP1-8: 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. 23 CCS A-SSE.1-4 A-APR.1-7 A-CED.1-4 A-REI.1-4 Technology st Century Life and Careers A B C D.1-4 MP1-8: 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.

24 UNIT: 4 Vectors and Matrices (May, 30) UNIT: 5 Algebra 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ENDURING UNDERSTANDINGS: (Students will Understand that...) Vectors are added and multiplied and this helps with mathematical calculations for engineering and physics. Linear and nonlinear systems of equations and inequalities symbolically and graphically and performs operations on matrices If the determinant of a matrix is zero, then the inverse of the matrix does not exist. Large systems of linear 24 Performs operations on expressions containing complex numbers, rational exponents and complex fractions Recognizes classes of functions including linear, polynomial, absolute value, step, rational, and exponential from multiple representations such as graphical, tabular, and symbolic and converts between these representations

25 UNIT: 4 Vectors and Matrices (May, 30) equations can be solved using technology UNIT: 5 Algebra Performs operations on and finds solutions for various types of functions including linear, polynomial, absolute value, and rational Solves linear and nonlinear systems of equations and inequalities symbolically and graphically Uses the language of mathematics to express ideas precisely through reasoning, representations, and communication 25

26 ESSENTIAL QUESTIONS: (What provocative questions will foster inquiry, understanding, and transfer of learning?) UNIT: 4 Vectors and Matrices (May, 30) Can you multiply a vector by a scalar both algebraically and graphically? Can you add vectors both algebraically and graphically? Can you calculate magnitude and direction of a vector? Can you calculate and interpret the dot product of two vectors? Do you understand that vectors are determined by the coordinates of their initial and terminal points, or by their components? Can you use vectors to model velocity and direction to solve problems? 26 UNIT: 5 Algebra What is the next number in the pattern? How can we use patterns to solve problems? What is a limit? What is the formula for the nth term? What is the difference between a function and a relation? What is the domain and range of a function? What is the maximum? Minimum? What does the solution of a system mean? What is the equation of this graph? What will the graph of this equation look like? Why can t we add x3 and X2? What is (a + b)(a b)?

27 UNIT: 4 Vectors and Matrices (May, 30) UNIT: 5 Algebra What is it called? What is the solution of the equation? System? STAGE 2: ASSESSMENT EVIDENCE PERFORMANCE TASKS: (Through what authentic performance tasks will students demonstrate the desired understandings?) (By what criteria will performances of understanding be judged?) Mathematical Practices 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. 27 Mathematical Practices 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.

28 OTHER EVIDENCE: (Through what other evidence (e.g. quizzes, tests, academic prompts, observations, homework, journals) will students demonstrate achievement of the desired results?) (How will students self-assess their learning?) UNIT: 4 Vectors and Matrices (May, 30) 8. Look for and express regularity in repeated reasoning. 9. Independent assignments 10. Written responses 11. Real-world problems 12. Non-routine problems 13. Collaborative problemsolving 14. Write own problems and assessments Pre/Post-assessments Practice HSPA tests Quizzes Unit tests Multiple choice problems Teacher observations Math journals Think-Alouds Homework Discussions Open-ended problems 28 UNIT: 5 Algebra 8. Look for and express regularity in repeated reasoning. 9. Independent assignments 10. Written responses 11. Real-world problems 12. Non-routine problems 13. Collaborative problemsolving 14. Write own problems and assessments Pre/Post-assessments Practice HSPA tests Quizzes Unit tests Multiple choice problems Teacher observations Math journals Think-Alouds Homework Discussions Open-ended problems There should be a

29 UNIT: 4 Vectors and Matrices (May, 30) UNIT: 5 Algebra RESOURCES: Pre-calculus textbook (Contemporary Precalculus by Hungerford & Shaw Thomson Brooks/Cole, 2009) Online tutorials Educational websites Educational software Research in the Media Center Overhead TI-83 calculator for use by teacher Overhead projector LCD projector Computer/Computer lab availability Graphing Calculator (TI83 or equivalent) HSPA resource materials benchmark at the conclusion of this unit Pre-calculus textbook (Contemporary Precalculus by Hungerford & Shaw Thomson Brooks/Cole, 2009) Online tutorials Educational websites Educational software Research in the Media Center Overhead TI-83 calculator for use by teacher Overhead projector LCD projector Computer/Computer lab availability Graphing Calculator (TI83 or equivalent) HSPA resource materials 29

30 UNIT: 4 Vectors and Matrices (May, 30) Computer Applications a. Microsoft PowerPoint b. Microsoft Excel Microsoft Word UNIT: 5 Algebra Computer Applications a. Microsoft PowerPoint b. Microsoft Excel Microsoft Word STAGE 3: LEARNING PLAN SKILLS AND TOPICS: (What specific activities will students do and what skills will students know as a result of the unit?) Convert points and equations from polar to rectangular form and vice versa. Transform equations from polar to rectangular form. Graph polar equations and determine the maximum r-value and the symmetry of the equation s graph. Represent complex numbers in trigonometric form and perform 30 Use iterative and recursive patterns and processes to model a variety of practical situations and solve problems. Show the relationship between equations and Use various types of functions to represent Solve word problems that functions. Add, subtract, multiply, and divide polynomials and monomials.

31 CROSS-CURRICULAR: (What cross-curricular (e.g. writing, literacy, math, science, history, 21 st century life and careers, technology) learning activities are included in this unit that will help achieve the desired results?) UNIT: 4 Vectors and Matrices (May, 30) operations on them. Use De Moivre s Theorem Perform operations with vectors and use vectors to solve real world problems. Find dot products and projections of vectors and apply to real world problems. Add and subtract matrices. Organize and interpret data in matrices. Individual Instruction Plans Current-event problems Manipulatives Tiered Lessons Learning style adaptation R.A.F.T Project Based learning Compacting 31 UNIT: 5 Algebra Solve equations and inequalities Solve equations and inequalities with variables on both sides of the equal sign. Judge the meaning, utility, and reasonableness of the results of symbol manipulation, including technological. Individual Instruction Plans Current-event problems Manipulatives Tiered Lessons Learning style adaptation R.A.F.T Project Based learning Compacting

32 UNIT: 4 Vectors and Matrices (May, 30) Multimedia presentations Open-ended responses Conclusions and analysis of exploratory activities Integrate Technology: 1. Textbook online resources at my.hrw.com (assessments, learning tools) ipad (for above, and YouTube math videos, as appropriate) Special Education: Provide modifications and accommodations as listed in the student s IEP Position student near helping peer or have quick access to teacher Modify or reduce assignments/texts Reduce length of assignment for different 32 UNIT: 5 Algebra Multimedia presentations Open-ended responses Conclusions and analysis of exploratory activities Integrate Technology: 1. Textbook online resources at my.hrw.com (assessments, learning tools) ipad (for above, and YouTube math videos, as appropriate) Special Education: Provide modifications and accommodations as listed in the student s IEP Position student near helping peer or have quick access to teacher Modify or reduce assignments/texts Reduce length of assignment for different

33 UNIT: 4 Vectors and Matrices (May, 30) mode of delivery Increase one-to-one time Utilize working contract between you and student at risk Prioritize tasks Provide manipulatives Use graphic organizers Use interactive math journals Use online resources for skill building Provide teacher notes Use collaborative grouping strategies such as small groups Use online resources ELL: Place student next to same-language speaker, if possible Provide text to speech for 33 UNIT: 5 Algebra mode of delivery Increase one-to-one time Utilize working contract between you and student at risk Prioritize tasks Provide manipulatives Use graphic organizers Use interactive math journals Use online resources for skill building Provide teacher notes Use collaborative grouping strategies such as small groups Use online resources ELL: Place student next to same-language speaker, if possible Provide text to speech for

34 UNIT: 4 Vectors and Matrices (May, 30) math problems Use of translation dictionary or software Implement strategy groups Confer frequently Provide graphic organizers Modification plan Adapt a strategyadjusting strategy for ELL: om/content/esl/adaptstrat. cfm *ELL Students- Instruction will be based on language proficiency. At Risk: Tiered interventions following RtI framework Rtl Intervention Bank Use additional practice 34 UNIT: 5 Algebra math problems Use of translation dictionary or software Implement strategy groups Confer frequently Provide graphic organizers Modification plan Adapt a strategyadjusting strategy for ELL: om/content/esl/adaptstrat. cfm *ELL Students- Instruction will be based on language proficiency. At Risk: Tiered interventions following RtI framework Rtl Intervention Bank Use additional practice

35 UNIT: 4 Vectors and Matrices (May, 30) and textbook RTI resources Utilize online resources such as or Gifted: Process should be modified: higher-orderthinking skills, openended thinking, discovery Utilize project-based learning for greater depth of knowledge Utilize exploratory connections to higher grade concepts Contents should be modified: abstraction, complexity, variety, organization Products should be 35 UNIT: 5 Algebra and textbook RTI resources Utilize online resources such as or Gifted: Process should be modified: higher-orderthinking skills, openended thinking, discovery Utilize project-based learning for greater depth of knowledge Utilize exploratory connections to higher grade concepts Contents should be modified: abstraction, complexity, variety, organization Products should be

36 UNIT: 4 Vectors and Matrices (May, 30) modified: real-world problems, audiences, deadlines, evaluation, transformations Learning environments should be modified: student-centered learning, independence, openness, complexity, groups varied Use of web based resources such as geogebra.org UNIT: 5 Algebra modified: real-world problems, audiences, deadlines, evaluation, transformations Learning environments should be modified: student-centered learning, independence, openness, complexity, groups varied Use of web based resources such as geogebra.org 36