HSD3 Math Curriculum Assessment Rubrics - Hamilton School District #3 by 7xS3ef

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									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.
                                                                                                      x2  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
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.                                     5i
                                                                                               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

								
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