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MAT-HS.F-BF.03

MAT-HS Targeted Standards
(F) Concept: Function
(BF) Domain: Building Functions
Cluster: Build new functions from existing functions.

MAT-HS.F-BF.03*   Identify the effect on the graph of replacing f(x) by f(x) + k, f(x + k), k f(x), and f(kx), for specific values of k (both positive and negative); find the value of k given the graphs. Recognize even and odd functions from their graphs.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can experiment to identify, using technology, the transformational effects on the graph of a function f(x) when f(x) is replaced by f(x)+k, k∙f(x), f(kx), and f(x+k) for specific values of k, both positive and negative.
  • I can find the value of k given the graph of a transformed function.
  • I can recognize even and odd functions from their graphs and equations.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. Write three different quadratic functions whose graphs have the line x = 4 as an axis of symmetry but have different y-intercepts.
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  • analyze the transformational effects on the graph of a function.
  • find the value of k given the graph of a transformed function.
  • determine whether a function is even or odd given a graph.
The student exhibits no major errors or omissions.

Describe all the transformations and graph the function.

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall specific terminology, such as:
    • vertical shift
    • horizontal shift
    • compress/amplified
    • stretch/shrink
    • reflection
    • even function
    • odd function
 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 

Given the graph, identify all of the transformations.
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).  
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill.  

Resources

Web

Vocab

  • transformation
  • even functions
  • odd functions

MAT-HS.F-BF.05

MAT-HS Targeted Standards
(F) Concept: Function
(BF) Domain: Building Functions
Cluster: Build new functions from existing functions

MAT-HS.F-BF.05 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Alg II Solve Logarithmic Equations Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.

Describe and correct the error in this work:
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  • solve a logarithmic equation and recognize an extraneous solution.
The student exhibits no major errors or omissions.

Solve the following logarithmic equation and check for extraneous solutions:

log3(x2-30)=log3(x)

  

Solve the following logarithmic equation and check for extraneous solutions:

2log2(x)=log2(4)+log2(x-1)
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall specific terminology such as:
    • Base
    • Logarithm
    • Exponentiate
    • Condense
    • Expand
  • solve simple logarithmic equations.
  • evaluate a logarithmic expression.
  • use properties of logarithms to expand and condense an expression.
 However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

Solve the following logarithmic equation for x:

log10(100)=x
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab

MAT-HS.F-IF.01

MAT-HS Targeted Standards
(F) Concept: Function
(IF) Domain: Interpreting Functions
Cluster: Understand the concept of a function and use function notation.

MAT-HS.F-IF.01 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can use the definition of a function to determine whether a relationship is a function given a table, graph or words.
  • I can identify x as an element of the domain and f(x) as an element in the range given the function f.
  • I can identify that the graph of the function f is the graph of the function y=f(x).

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.

 
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

The student can:

  • understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).


The student exhibits no major errors or omissions.

Is the relation a function (yes or no)? Explain.

a.

b.

 

Identify the domain and range of the relation. Is this relation a function (yes or no)?  Explain.

(-2, 0.5), ( 0,2.5), (4,6.5), (5,2.5)

Graph

f (x) = 2x + 2
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student:
  • Recognize and recall basic vocabulary such as:
    • range
    • domain
    • relation
    • function notation
    • vertical line test
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Find the range of the relation.(4, -2), (-2, 3), (1, -3).

Find the domain of the relation.

(2, 4), (8, 11), (9, 1), (4, 2)

Does the relation pass a vertical line test?

 

  • Identify the domain and range for the given set of ordered pairs.  Is this relation a function?(7,2), (-1,4), (2,-2), (-6,5), (0,0)

 
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web

Vocab

  • function
  • domain
  • range

MAT-HS.F-IF.04

MAT-HS Targeted Standards
(F) Concept: Function
(IF) Domain: Interpreting Functions
Cluster: Interpret functions that arise in applications in terms of the context

MAT-HS.F-IF.04* For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Student Learning Targets:

Knowledge Targets

  • I can identify key features in graphs and tables to include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity for a given function.

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can use correct notation when identifying key features of graphs and tables.

Product Targets

  • I can sketch the graph of a function given its key features.

Alg II Key Features of Graphs Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. Given the graph, identify the intervals where both functions are increasing.

 
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  • identify key features in graphs and tables including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; domain and range; and periodicity for a given function.
  • sketch the graph of a function given its key features.

The student exhibits no major errors or omissions. 

Identify the following from the graph:

x-intercepts:

y-intercepts:

Increasing Intervals:

Decreasing Intervals:

Positive Intervals:

Negative Intervals:

Maximums:

Minimums:

Domain:

Range:

 

Sketch a function that would have an increasing interval from (3,+∞) and a relative minimum at (3,4).
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • Recognize and recall specific terminology such as:
    • intervals
    • intercept (x and y)
    • relative minimum and maximum
    • periodicity
    • end behavior
    • symmetry
    • increasing
    • decreasing
  • use interval notation accurately.

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Write the following in interval notation:

x<3

x>5

x≥10

5<x≤9

For the graph given, the function is increasing from________ to -1 and 3 to _______.

  •  
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).  
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill.  

Resources

Web

Vocab

  • intercepts
  • relative maximum
  • relative minimum
  • end behavior
  • periodicity
  • symmetry

MAT-HS.F-IF.07

MAT-HS Targeted Standards
(F) Concept: Function
(IF) Domain: Interpreting Functions
Cluster: Analyze functions using different representations

MAT-HS.F-IF.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

  • a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
  • c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
  • d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
  • e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
  • f.  Graph f(x)=sin x and f(x)=cos x as representations of periodic phenomena.
  • g.  (+) Graph trigonometric functions, showing period, midline, phase shift and amplitude

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can graph a linear equation.
  • I can manipulate the form of a linear equation.
  • I can identify a linear equation.
  • Given an equation, I can graph a function and label all critical points, e.g. vertex, max or min value, x-intercepts, y-intercepts, slope.
  • I can graph functions expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).
  • I can graph linear functions showing intercepts.
  • I can graph quadratic functions showing intercepts, a maximum or a minimum.
  • I can graph square root, cube root and piecewise-defined functions, including step functions and absolute value functions.
  • I can graph exponential functions, showing intercepts and end behavior. I can graph polynomial functions, identifying zeros when factorable, and show end behavior.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -Student is able to determine and describe intervals where the function is increasing and decreasing using interval notation.
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 The student can:
  • interprets and sketches key features of the linear graph (HS.F-IF.7a1) including:
    • intercepts
    • positive/negative slope
  • interprets and sketches key features of the exponential graph (HS.F-IF.7b2) including:
    • end behavior (growth/decay)
  • interprets and sketches key features of the quadratic graph (HS.F-IF.7e) including:
    • minimum/maximum
    • axis of symmetry
    • intercepts
  • construct simple graphs by hand and use technology for more complicated cases.

The student exhibits no major errors or omissions.

Graph the function and identify the vertex, intercepts, and axis of symmetry.

 y=x2-8x-7

Graph the function and identify the end behavior of the graph.

y=(1/2)x

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:
    • linear equation.
    • quadratic equation.
    • exponential equation.
    • slope
    • intercepts
    • minimum
    • maximum
    • end behavior
    • growth and decay
    • symmetry
    • axis of symmetry
  • only interprets and sketches some of the key features of the graph.
  • can identify if a function is linear, exponential, or quadratic

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Graph the set of points and determine the relationship.  (i.e. linear, exponential, or quadratic)

  (0, 0), (1, 1), (-1, -0.5), (2, 3)
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web

Vocab

  • intercepts
  • maximum
  • minimum
  • square root function
  • cube root function
  • piecewise-defined function
  • step function
  • absolute value function
  • polynomial function
  • zeroes
  • exponential function

MAT-HS.F-IF.07.a

MAT-HS Targeted Standards
(F) Concept: Function
(IF) Domain: Interpreting Functions
Cluster: Analyze functions using different representations

MAT-HS.F-IF.07* Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

  • Graph linear functions and show intercepts, maxima, and minima where appropriate.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can graph a linear equation and show intercepts. (HS.F-IF.7.a)

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -Student is able to determine and describe intervals where the function is increasing and decreasing using interval notation.
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  • interpret and sketch key features of the linear graph (HS.F-IF.7a1) including:
    • intercepts
    • positive/negative slope
  • construct simple graphs by hand and use technology for more complicated cases.

The student exhibits no major errors or omissions.

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:
    • linear equation.
    • quadratic equation.
    • exponential equation.
    • slope
    • intercepts
  • only interprets and sketches some of the key features of the graph.
  • can identify if a function is linear, exponential, or quadratic

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Alg II Graph Quadratic Functions Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)		 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. The graph of  f(x)=ax2+c is shown Points A and B are the same distance from the vertex of the graph of f.  Which point is closer to the vertex of the graph of  f as c increases? Explain your reasoning.

 
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)
 The student can:
  • graph quadratic functions in any form expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).

The student exhibits no major errors or omissions.		 Graph the following equations and identify all the key features including:  vertex, x-intercepts, y-intercepts, increasing interval, decreasing interval, maximums, minimums, axis of symmetry,  end behaviors, domain and range.

  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:
    • quadratic function
    • vertex
    • x- intercepts
    • y- intercepts
    • zeros
    • solutions
    • roots
    • intervals
    • minimum/maximum values
    • axis of symmetry
    • domain
    • range

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Given a graph,  identify all the key features including: vertex,x-intercepts, y-intercepts, increasing interval, decreasing interval, maximums, minimums, axis of symmetry, end behaviors, domain and range.    
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).  
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill.  

Resources

Web

Vocab

  • intercepts
  • maximum
  • minimum
  • square root function
  • cube root function
  • piecewise-defined function
  • step function
  • absolute value function
  • polynomial function
  • zeroes
  • exponential function

MAT-HS.F-IF.07.b

MAT-HS Targeted Standards
(F) Concept: Function
(IF) Domain: Interpreting Functions
Cluster: Analyze functions using different representations

MAT-HS.F-IF.07* Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

  • a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
  • c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
  • d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
  • e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
  • f.  Graph f(x)=sin x and f(x)=cos x as representations of periodic phenomena.
  • g.  (+) Graph trigonometric functions, showing period, midline, phase shift and amplitude

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Alg II Graph Square Root Functions Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)		 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. Graph the following function:  

 

 

 

 
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)
 The student can:
  •  graph square root functions symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).
The student exhibits no major errors or omissions.		  Graph the following equations and identify all the key features including:x-intercepts, y-intercepts, increasing interval, decreasing interval, maximums, minimums, domain and range.  

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:

    • radical

    • index

    • radicand

    • perfect squares

    • x-intercepts

    • y-intercepts

    • increasing intervals

    • decreasing intervals

    • maximums

    • minimums

    • domain

    • range

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

Given the graph, identify all the key features including: x-intercepts, y-intercepts, increasing interval, decreasing interval, maximums, minimums, domain and range.  

 
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)		 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).  
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill.  

Alg II Graph Cube Root Functions Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. Explain why your graph of begin mathsize 12px style g left parenthesis x right parenthesis space equals space cube root of x end style is in both the first and third quadrants? 
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  • graph cube root functions expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).
The student exhibits no major errors or omissions.		  
Graph the following equations and identify all the key features including: x-intercepts, y-intercepts, increasing interval, decreasing interval, inflection point, domain and range.  
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:

    • index

    • radicand

    • radical

    • perfect cubes

    • x-intercepts

    • y-intercepts

    • increasing intervals

    • decreasing intervals

    • inflection point

    • domain

    • range


However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

Given the graph, identify all the key features including:

x-intercepts, y-intercepts, increasing interval, decreasing interval, inflection point, domain and range.  
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).  
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill.  

Alg II Graph Piecewise Functions Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)		 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.

 

Write the equation of the following piecewise graph and determine the domain and range of the following graph.

 

  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)
 The student can:
  • graph step functions expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).
  • graph piecewise functions expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).              

The student exhibits no major errors or omissions.		 Graph the following equations and identify all the key features including: increasing interval, decreasing interval, discontinuity, continuity, domain and range.  

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)		 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:

    • decreasing intervals

    • increasing intervals

    • discontinuity

    • continuity

    • domain

    • range


However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

Given the graph, identify all the key features including: increasing interval, decreasing interval, discontinuity, continuity, domain and range.   
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)		 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Alg II Graph Absolute Value Functions Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)		 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. Graph the following function and explain why the graph looks as it does:

 
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)
 The student can:

  • graph absolute value functions expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).


The student exhibits no major errors or omissions.		  Graph the following equations and identify all the key features including: vertex, x-intercepts, y-intercepts, increasing interval, decreasing interval, maximums, minimums, domain and range.  

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)		 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:

    • absolute value

    • vertex

    • x-intercepts

    • y-intercepts

    • intervals (increasing and decreasing)

    • maximums

    • minimums

    • domain

    • range


However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
Given the graph, identify all the key features including: vertex,x-intercepts, y-intercepts, increasing interval, decreasing interval, maximums, minimums, domain and range.  

 
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)		 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).  
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill.  

Resources

Web

Vocab

 

MAT-HS.F-IF.07.c

MAT-HS Targeted Standards
(F) Concept: Function
(IF) Domain: Interpreting Functions
Cluster: Analyze functions using different representations

MAT-HS.F-IF.07* Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

  • a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
  • c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
  • d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
  • e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
  • f.  Graph f(x)=sin x and f(x)=cos x as representations of periodic phenomena.
  • g.  (+) Graph trigonometric functions, showing period, midline, phase shift and amplitude

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Alg II Graph Polynomial Functions Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)		 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. Compare and contrast the two polynomial functions key features.

 
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  • graph polynomial functions expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).
  • identify zeros of a polynomial function when factorable and show end behavior.

 
The student exhibits no major errors or omissions.

 

Graph the following equations and identify all the key features including:x-intercepts, y-intercepts, increasing interval, decreasing interval, maximums, minimums, end behaviors, domain and range.  

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:

  • recognize and recall basic terminology, such as:

    • Intervals
    • Increasing
    • Decreasing
    • Minimum
    • Maximum
    • End behavior
    • Terms
    • Factors
    • Lead Coefficient
    • Constant
    • Degree
    • Cubic
    • Quartic
    • Polynomial
    • Domain
    • Range           

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
Given the graph, identify all the key features including: x-intercepts, y-intercepts, increasing interval, decreasing interval, maximums, minimums, end behaviors, domain and range.   
 
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web

Vocab

 

MAT-HS.F-IF.07.d

MAT-HS Targeted Standards
(F) Concept: Function
(IF) Domain: Interpreting Functions
Cluster: Analyze functions using different representations

MAT-HS.F-IF.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

  • a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
  • c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
  • d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
  • e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
  • f.  Graph f(x)=sin x and f(x)=cos x as representations of periodic phenomena.
  • g.  (+) Graph trigonometric functions, showing period, midline, phase shift and amplitude

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity

4.0

(advanced proficient)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -Student is able to determine and describe intervals where the function is increasing and decreasing using interval notation.
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  •  

The student exhibits no major errors or omissions.

 

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(developing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(novice)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

 

Resources

Web

Vocab

 

MAT-HS.F-IF.07.e

MAT-HS Targeted Standards
(F) Concept: Function
(IF) Domain: Interpreting Functions
Cluster: Analyze functions using different representations

MAT-HS.F-IF.07* Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

    • a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
    • b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
    • c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
    • d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
    • e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
    • f.  Graph f(x)=sin x and f(x)=cos x as representations of periodic phenomena.
    • g.  (+) Graph trigonometric functions, showing period, midline, phase shift and amplitude

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • Given an equation, I can graph a function and label all critical points, e.g. vertex, max or min value, x-intercepts, y-intercepts, slope.
  • I can graph functions expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).
  • I can graph exponential functions, showing intercepts and end behavior. 

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -Student is able to determine and describe intervals where the function is increasing and decreasing using interval notation.
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 The student can:
  • interprets and sketches key features of the linear graph (HS.F-IF.7a1) including:
    • intercepts
    • positive/negative slope
  • interprets and sketches key features of the exponential graph (HS.F-IF.7b2) including:
    • end behavior (growth/decay)
  • interprets and sketches key features of the quadratic graph (HS.F-IF.7e) including:
    • minimum/maximum
    • axis of symmetry
    • intercepts
  • construct simple graphs by hand and use technology for more complicated cases.

The student exhibits no major errors or omissions.

Graph the function and identify the vertex, intercepts, and axis of symmetry.

 y=x2-8x-7

Graph the function and identify the end behavior of the graph.

y=(1/2)x

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:
    • linear equation.
    • quadratic equation.
    • exponential equation.
    • slope
    • intercepts
    • minimum
    • maximum
    • end behavior
    • growth and decay
    • symmetry
    • axis of symmetry
  • only interprets and sketches some of the key features of the graph.
  • can identify if a function is linear, exponential, or quadratic

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Graph the set of points and determine the relationship.  (i.e. linear, exponential, or quadratic)

  (0, 0), (1, 1), (-1, -0.5), (2, 3)
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Alg II Graph Exponential Functions Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. Write an exponential function whose graph lies between the graphs of y=(0.5)x and y=(0.25)x+3
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  • graph functions expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).
  • graph exponential functions, showing intercepts and end behavior (asymptote).

The student exhibits no major errors or omissions.		 Graph the following equations and identify all the key features including: x-intercepts, y-intercepts, increasing interval, decreasing interval, domain, range and asymptote.

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:
    • x-intercepts
    • y-intercepts
    • intervals (decreasing and increasing)
    • asymptote
    • domain
    • range

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Given the graph, identify all the key features including: x-intercepts, y-intercepts, increasing interval, decreasing interval, domain and range and asymptote.
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).  
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill.  

Alg II Graph Logarithmic Functions Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. Once a hurricane reaches land, the wind speed s (in knots) within the hurricane is related to the time t (in hours) the hurricane remains over land.  For one particular hurricane, this relationship can be modeled  by the equation y= -57.1 log t +121. Graph the equation and analyze the graph to determine how long the hurricane must be over land for winds speeds to become about 80 knots. 
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:

  • Graph logarithmic functions expressed symbolically and show key features of the graph (graph simple cases by hand and use technology to show more complicated cases).


The student exhibits no major errors or omissions.

Graph the following equation and identify all the key features including: increasing interval, decreasing interval, asymptote, domain and range.  

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall basic terminology, such as:
    • logarithm
    • base
    • exponent
    • intervals (increasing and decreasing)
    • asymptote
    • domain
    • range

    However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

Given the graph, identify all the key features including the asymptote, increasing and decreasing intervals, domain, and range.  
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).  
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill.  

Resources

Web

Vocab

  • intercepts
  • maximum
  • asymptote
  • minimum
  • exponential function

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