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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.02

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.02 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Student Learning Targets:

Knowledge Targets

  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can evaluate functions for inputs in their domains.
  • I can interpret statements that use function notation in terms of a context in which they are used.
  • I can use f(x) notation when a relation is determined to be a function.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught

  • If f(x) = –5x + 11 and f(n) = 21, what is the value of n? Explain.

  • Each set of ordered pairs represents a function. Write a rule that represents the function:

    • (-2, 10/9), (-1, 4/3), (0,2),(1,4)(2,10)

  • If f(x) = -3x+7 and g(x) =-7x +3, what is h(x) if h(x)=f(g(x))?
  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 use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.


The student exhibits no major errors or omissions.

  • What is f(–5) for the function f(x) = –9x – 3?

  • Find the range of each function for the given domain.          f(x) = x3 + 1; {–2, –1, 0, 1, 2}

  • In the formula d(t) = rt, explain what r represents, what t represents, and what d(t) represents.

  • How can it be determined if a relation is a 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 use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Recognize and recall basic vocabulary such as:

  • Domain

  • Range

  • Function vs. Relation

  • Function Notation



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

  • Find the range of the function for the given domain.            

  •  f (x) = –2x + 1; {–2, 0, 2, 4, 6}  

  • Evaluate f(x) = 2x +3 for x = 6
  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, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. -
  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 notation

MAT-HS.F-IF.03

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.03 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

Student Learning Targets:

Knowledge Targets

  • I can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

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 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 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  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 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  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

  • recursive
  • integers

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.05

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.05 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can solve a linear system (substitution, linear combination, graphically).
  • I can write a linear system.
  • I can identify the number of solutions of a linear system.
  • I can identify the most efficient method to solve a system.
  • I can check the solution of the system.
  • I can graph a linear equation.
  • I can manipulate the form of a linear equation.
  • I can identify a linear equation.
  • I can interpret a graph to determine the appropriate numerical domain being described.

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. -
  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 Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  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 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  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

MAT-HS.F-IF.06

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.06 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can estimate the average rate of change over a specified interval of a function from its graph.

Skills (Performance) Targets

  • I can calculate and interpret the average rate of change of a function presented symbolically or as a table.

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. -
  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 Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  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 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  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

  • rate of change
  • interval

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.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

MAT-HS.F-IF.07.f

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 
  • I can 

Product Targets

  • I can
  • I can

Alg II Graph Sine and Cosine 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 equation for the graph in the form y = A sin ( Bx + C ). Write an equation for the same graph in the form y = A cos( Bx+C).

  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 trigonometric 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, maximums, minimums, domain and range, amplitude, increment, period, midline. f(x) = asinx

 

 
  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:

    • trigonometric function

    • amplitude

    • increment

    • period

    • midline

    • 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, maximums, minimums, domain and range, amplitude, increment, period,and midline.

 
  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.g

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 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:
  •  

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 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 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.08

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

MAT-HS.F-IF.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

  • a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
  • b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

Student Learning Targets:

Knowledge Targets

  • I can recall the order of operations.
  • I can understand and identify a power and its parts (base and exponent).
  • I can recognize the properties of exponents (i.e. product of powers, power of a power, power of a product).
  • I can recognize a zero or negative exponent.
  • I can identify a radical.
  • I can identify if a radical expression is in simplest form.
  • I can recognize the properties of radicals, i.e., product, quotient, and sum of radicals.
  • I can identify perfect squares.
  • I can define a logarithm.
  • I can recall properties of logarithms and exponents.
  • I can recognize common logarithms and natural logarithms.
  • I can identify an asymptote.
  • I can recall the change of base formula.

Reasoning Targets

  • I can analyze an algebraic expression.
  • I can decide what to do next based on my knowledge of the order of operations.
  • I can distinguish the difference of when to use each property of radicals.
  • I can evaluate the properties of radicals.
  • I can apply the distributive property.
  • I can analyze what type of factoring technique that should be used for a given expression. (i.e. factor trinomials, factor difference of squares, factor sum and difference of cubes, factor by grouping, factor out the greatest common factor)
  • I can combine like terms in an expression or equation.
  • I can convert from a logarithm to exponential expressions.
  • I can identify an asymptote.
  • I can expand and condense logarithms.
  • I can evaluate logarithms and exponential expressions.
  • I can distinguish between a natural log and common log.

Skills (Performance) Targets

  • I can simplify an algebraic expression.
  • I can apply factor using perfect square.
  • I can do prime factorization.
  • I can rationalize a denominator.
  • I can simplify a polynomial expression.
  • I can multiply polynomials.
  • I can justify the steps taken in manipulating an expression.
  • I can complete all necessary steps in order to simplify the expression.
  • I can distribute and factor an expression.
  • I can solve for (isolate) a specific variable.
  • I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.).
  • I can check the solution.
  • I can set a polynomial equal to zero and solve by factoring, quadratic formula, graphing, linear combinations, and substitution.
  • I can solve for (isolate) a specific variable.
  • I can write a linear system.
  • I can perform transformations that produce equivalent equations (e.g., adding the same amount to both sides of the equation, etc.)
  • I can check the solution.
  • I can solve a quadratic.
  • I can multiply and factor polynomials.
  • I can solve a linear inequality.
  • I can graph a linear inequality.
  • I can solve a system of linear inequalities.
  • I can graph a system of linear inequalities.
  • I can check the solution of the system.
  • I can solve a linear system (substitution, linear combination, graphically).
  • I can write a linear system.
  • I can identify the number of solutions of a linear system.
  • I can identify the most efficient method to solve a system.
  • I can check the solution of the system.
  • I can apply basic properties of exponents and logarithms to rewrite algebraic expressions.
  • I can graph logarithmic and exponential functions.
  • I can solve logarithmic and exponential equations.
  • I can apply the change of base formula to evaluate a logarithmic expression.
  • I can graph and determine the equation of an asymptote.
  • I can write a function in equivalent forms (eg. factored vs. general form) to show different properties of the function.
  • I can explain different properties of a function that are revealed by writing a function in equivalent forms.
  • I can use the process of factoring and completing the square in a quadratic function to show zeros, a maximum or minimum, and symmetry of the graph, and interpret these in terms of a real-world situation.
  • I can use the properties of exponents to interpret exponential functions as growth or decay.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught -
  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:

  • Write a function in equivalent forms (eg. factored vs. general form) to show different properties of the function

  • Explain different properties of a function that are revealed by writing a function in equivalent forms

  • Use the process of factoring and completing the square in a quadratic function to show zeros, a maximum or minimum, and symmetry of the graph, and interpret these in terms of a real-world situation

  • Use the properties of exponents to interpret exponential functions as growth or decay


The student exhibits no major errors or omissions.

Given f(x)=x2-5x-6:

  1. Rewrite the function in factored form to find the zeros.   

  2. Find the x value of the maximum or minimum and state if a maximum or minimum occurs at that x value.
  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:

  • recognizes and recalls specific terminology, such as

    • exponential growth

    • exponential decay



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 With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. -
  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).

Alg II Equivalent Quadratic Expressions 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 graph in the three forms.  If you cannot write the function in one of the forms, explain why.

 
  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:
  • explain the different properties of a function that are revealed by writing a function in equivalent forms.
  • write a function in equivalent forms (factored vs. general form) to show different properties of the function.

The student exhibits no major errors or omissions.

Rewrite the following equation of the parabola in vertex form.  Identify the minimum/maximum value.

f(x)=2x2+16x+10

 

Rewrite the following equation of the parabola in standard form and find the vertex.f(x)=2(2x-1)(x+9) 

Explain the advantages of each form of a quadratic 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:

  • identify the different forms of functions (eg. Factored vs. general form) that show different properties of the function.
  • recognize and recall basic terminology, such as:
    • factor
    • intercept
    • vertex
    • complete the square
    • standard form
    • parabola

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

 Label each of the following functions with the quadratic form it represents.

  1. f(x)=2x2+5x+9
  2. q(x)=3(2x+5)(x-2)
   3. g(x)=4(x-3)2+6
  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

  • exponential growth
  • exponential decay

MAT-HS.F-IF.09

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

MAT-HS.F-IF.09* Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).


Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can 

Skills (Performance) Targets

  • I can compare the key features of two functions that are represented in different ways.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught

Given the function, y = 3x + 2 create the following:

  • A graph that is increasing at the same rate.

  • A table that is increasing at a lesser rate

  • A verbal description that is increasing at a greater rate.

Graph 2x + 3y = 6, 2x + 3y = 12, and 2x + 3y = 18 in the same coordinate plane.

. How are the lines from part (a) related?

. As C increases, what happens to the graph of 2x + 3y = C

 
  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:

  • compare properties of two functions each represented in a different way:

    • algebraically

    • graphically

    • numerically in tables

    • verbal descriptions


The student exhibits no major errors or omissions.


 

The ordered pairs below represent one function, and the verbal description represents a different function. How are the functions similar? How are they different?

 

(0, 2), (1, 4), (2, 6), (3, 8)

 

This function has a slope of - ½ and a y-intercept of -3

 

 

 
  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 terminology such as:

    • equation, maximum, minimum, x and y intercept, rate of change, slope

  • can identify properties of a function, but can not compare with another function

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, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes. -
  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).

Alg II Comparing 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.

Which of the functions have a larger increasing interval on the domain from [-2, 3]?

f(x)=ex-3+2   g(x)=x3-4x
  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:
  • compare the key features of two functions that are represented in different ways.

The student exhibits no major errors or omissions.		  

Determine which of the functions presented has the largest maximum value.

f(x)=2x2-28x+90

g(x)=(x+3)(x-2)


Compare the two functions below.  Determine the x-intercept they both share.

x y
-14 -2
-7 0
0 2
7 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:

  • classify a function given a table, graph, or equation.

  • find the key features of a graph, a table, or an equation.
  • recognize and recall basic terminology, such as:
    • linear
    • quadratic
    • vertex
    • exponential
    • intercept
    • maximum/minimum
    • line of symmetry
    • increasing/decreasing intervals
    • opens up/opens down

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

 

 
Match the correct equation to the correct graph.Given the two equations, decide which function has the greater slope.     f(x)=2x+9          
x y
-2 -3
0 -2
2 -1
4 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

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