VIEWS: 1 PAGES: 38 POSTED ON: 10/1/2012
HSD3 Math Curriculum Assessment Rubrics Algebra II Hamilton School District 3 Hamilton, Montana 1/1/2008 Algebra II Strand: Geometric Reasoning 1. Solving systems of linear inequalities by graphing 2. Solving absolute value inequalities by graphing 3. Solving quadratic inequalities by graphing 4. Graphing relations and determining whether the relation is a function. 5. Identify the range and domain from the graph 6. Identify graphs (x=y ; y x 2 ; y x 3 ; y x ; y x ) 7. Graph logarithmic and exponential functions with and without a graphing calculator Strand: Algebraic and Functional Reasoning 1. Solve systems of linear equations by graphing 2. Solve systems of linear equations by substitution or elimination 3. Solve systems of linear equations by elimination or matrices 4. Solve system of linear inequalities 5. Solve absolute value equations and inequalities 6. Domain and range of functions 7. Composite functions 8. Inverse functions 9. Polynomials; long division 10. Polynomials – Synthetic Division 11. Factoring polynomials 12. Simplifying Radicals 13. Radical equations 14. Simplifying rational exponents 15. Solving equations with rational exponents 16. Operations with rational expressions 17. Addition and subtraction of Complex Numbers 18. Multiplication and division of complex numbers 19. Direct and inverse variations 20. Quadratic formula 21. Completing the square 22. Solving quadratic inequalities 23. Evaluate logarithms 24. Solve equations with logarithms 25. Recognize and Identify properties of logarithms Strand: : Geometric Reasoning Topic: Solving systems of linear inequalities by graphing Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve this system of inequalities by graphing: 3.0 solve a system of inequalities by graphing The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve the following system of inequalities by graphing: 2.0 the student: solves a set of simple inequalities by graphing However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: : Geometric Reasoning Topic: Solving absolute value inequalities by graphing Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Graph : 3.0 solve absolute value inequalities by graphing y 3 2 | x | 4 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Graph: 2.0 the student: solves simple absolute value inequalities by graphing y | x | 2 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: : Geometric Reasoning Topic: Solving quadratic inequalities by graphing Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Graph: 3.0 solve a quadratic inequality by graphing The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Graph: 2.0 the student: y > x2 solves a simple quadratic inequality by graphing However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: : Geometric Reasoning Topic: Graphing relations and determining whether the relation is a function Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Graph and describe if the relation is a function and explain why or 3.0 graph a relation and determine if it is a function why not.. The student exhibits no major errors or omissions. x y2 2 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Draw an example of a graph that is: 2.0 the student: a function recognizes or recalls examples of a graphed function not a function However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: : Geometric Reasoning Topic: Identify the range and domain from the graph Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0 determine the range and domain from a graph Find the domain and range: The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as 2.0 the student: Define the terms domain and range. recognizes or recalls basic terminology such as: o Domain o Range However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: : Geometric Reasoning Topic: Identify graphs (y=x ; y x 2 ; y x 3 ; y x ; y 1x1 ) Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Graph the following functions: 3.0 Graph the following parent functions (y=x ; y x ; y x ; y x; y x ) 2 3 1. Y = x 2 2. Y = x 3 The student exhibits no major errors or omissions. 3. Y = x 4. Y= 5. Y= 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as 2.0 the student: Identify the graphs of the following parent functions (y=x ; recognizes examples of the graphs of parent functions (x=y ; y x ; y x ; y x; y x ) 2 3 y x2 ; y x3; y x ; y 1x1 ) A. B. recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes. C. D. E. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: : Geometric Reasoning Topic: Graph logarithmic and exponential functions Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Graph 3.0 graph logarithmic and exponential functions. 1. y log( x 4) + 2 The student exhibits no major errors or omissions. 2. y 3x 5 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Graph 2.0 the student: 1. y log x graphs simple log and exponential functions 2. x y=2 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 trand: Algebraic and Functional Reasoning Topic: Solve systems of linear equations by graphing Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve and state the solutions. 3.0 solve a system of linear equations by graphing The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve and state the solutions: 2.0 the student: solves a simple system of linear equations by graphing However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Solve systems of linear equations by substitution or elimination Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve by method of choice 3.0 solve a system of linear equations by substitution or elimination The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve by method of choice: 2.0 the student: solves a simple system of linear equations by substitution or elimination However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Solve systems of linear equations by elimination or matrices Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve by method of choice: 3.0 solve a system of linear equations by elimination or matrices The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve by method of choice: 2.0 the student: solves a simple system of linear equations by elimination or matrices However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Solve system of linear inequalities Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Graph and find an ordered pair that satisfies the system 3.0 graph a system of linear inequalities and find a solution that satisfies the system The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Graph and find an ordered pair that satisfies the system: 2.0 the student: o graphs a simple system of linear equations and finds solution y 2x 1 y x 4 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Solve absolute value equations and inequalities Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve: 3.0 solve absolute value equations and inequalities | 9 2 x | 15 The student exhibits no major errors or omissions. 3 | 5 x 8 | 5 6 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve: 2.0 the student: solves simple absolute value equations and inequalities However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Domain and range of functions Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Determine the domain and range of the following functions 3.0 determine domain and range of a given function (e.g., f(x)=3x2-2) f ( x) 3x 2 2 The student exhibits no major errors or omissions. f ( x) x 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Determine the range of the following function. 2.0 the student: determines domain and range of a simple function f(x) = 2x + 1. Given the domain of {-2, 0, 2, 4}, find the range values However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Composite functions Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Let f(x) = 3x-2 and 3.0 find the composite of two functions g ( x) x 2 5 The student exhibits no major errors or omissions. Find f(g(x)) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Let f(x) = 3x and g(x) = x + 1 2.0 the student: Find f(g(x)). finds the composite of simple functions (need example here) recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Inverse functions Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: If f(x) = 7x-5, find the inverse of f(x). 3.0 find the inverse of a function The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Find the inverses of the following functions: 2.0 the student: f(x) = x + 2 finds the inverse of a simple function (need example here) f(x) = 3x However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Polynomial long division Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Divide 3.0 perform long division with polynomials (15 x 2 8 x 12 ) (3x 1) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Divide: 2.0 the student: (15x2 – 9x + 12) ÷ 3x performs simple long division with polynomials However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Polynomials – Synthetic Division Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Divide using synthetic division 3.0 perform synthetic division with polynomials 5 2 (t -3t -20) ÷ (t- 2) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Divide using synthetic division: 2.0 the student: performs simple synthetic division x 3 4 x 2 3x 5) ( x 4) However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Factoring polynomial Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Factor and simplify 3.0 factor polynomials 6c 2 13c 6 The student exhibits no major errors or omissions. 3x 2 27 y 2 x 2 4x 3 x 2 x 12 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Factor and simplify: 2.0 the student: c2 + 4c + 4 factors simple polynomials x2 – 81 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Simplifying Radicals Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Simplify 3.0 simplify radicals 180x 2 The student exhibits no major errors or omissions. 5 32x15 y 20 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Simplify: 2.0 the student: recognizes or recalls the rules to simplifying radicals However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Radical equations Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve 3.0 solve equations that contain radicals 10 x 3 x 1 The student exhibits no major errors or omissions. x2 x2 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as 2.0 the student: solves simple equations using radicals (need example here) = However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Simplifying rational exponents Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Simplify 3.0 simplify rational exponents The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Simplify: 2.0 the student: recognizes or recalls the rules to simplifying rational exponents However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Solving equations with rational exponents Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will : Solve 3.0 solve equations with rational exponents =192 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve: 2.0 the student: = 64 solves simple equations with rational exponents However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Operations of radical expressions Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Perform the indicated operation 3.0 perform operations with rational expressions 2x 7 The student exhibits no major errors or omissions. 2 x 1 3x 1 x 2 2 x 15 x 2 9 ( x 2) 2x 4 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and Perform the indicated operation: 2.0 processes as the student: + simplifies rational expressions However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Addition and Subtraction of Complex Numbers Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Perform the indicated operation 3.0 add and subtract complex numbers (6 4i) (1 3i) The student exhibits no major errors or omissions. (3 2i) (5 4i) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and Perform the indicated operation 2.0 processes as the student: 6i + 4i adds or subtracts imaginary numbers (e.g., 6i + 4i) 17i – 4i + 6i However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Multiplication and division of complex numbers Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Perform the indicated operations 3.0 multiply and divide complex numbers (4 4i )(6 i ) The student exhibits no major errors or omissions. 5i 2 4i 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and Perform the indicated operations 2.0 processes as the student: (4i)(7i) multiplies and divides imaginary numbers (e.g., (6i)(4i)) 5i(6i – 2) recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Direct and inverse variations Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve 3.0 solve direct and inverse variation problems 1. The perimeter P of a regular dodecagon varies directly as the side lengths, and p=18in when s=1.5in. Find s when P The student exhibits no major errors or omissions. =75 inches. 2. If y varies inversely as x and y=5 when x=10, find y when x=2. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as State whether each equation represents a direct, joint, or inverse 2.0 the student: variation: solves simple direct and inverse variation problems ab = 20 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 5bh 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Quadratic formula Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve using the quadratic formula. 3.0 solve quadratic equations using the quadratic formula x 2 16 x 4 0 The student exhibits no major errors or omissions. 3x 2 2 x 5 0 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve using the quadratic formula. 2.0 the student: solves simple equations using the quadratic formula However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Completing the square Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve by completing the square. 3.0 solve equations by completing the square x 2 9 x 20 0 The student exhibits no major errors or omissions. 2 x 2 8 x 12 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve by completing the square 2.0 the student: x 2 8x 20 0 solves simple equations by completing the square =9 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Solving quadratic inequalities Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve algebraically 3.0 solve quadratic inequalities The student exhibits no major errors or omissions. 2 2x + 3x > 5 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve algebraically 2.0 the student: solves simple quadratic inequalities x2 x 6 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Evaluate logarithms Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Evaluate 3.0 evaluate logarithms log 4 256 The student exhibits no major errors or omissions. log 2 1 8 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Evaluate 2.0 the student: log2 16 converts expressions between exponents and logarithms log3 27 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Solve equations with logarithms Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve 3.0 solve equations with logarithms 3 log 5 x 12 The student exhibits no major errors or omissions. 4 x 8 264 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as Solve: 2.0 the student: log4 x = solves simple equations with logarithms 3x = 243 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Recognize and Identify properties of logarithms Class: Algebra II Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will : Rewrite as the log of a single number. 3.0 simplify expressions using properties of logarithms 3(log 5 + log 6) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and Rewrite as a log of a single number. 2.0 processes as the student: recognizes or recalls accurate statements about the properties or rules of log 6 log 4 logarithms log 10 log 2 However, the student exhibits major errors or omissions regarding the more 3 log 7 complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0