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Tuesday, April 23, 2024, 11:16 PM

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Class: BPSS (MAT) Mathematics Standards (S-MAT)

Glossary: MAT-HS: Function

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

Function Notation WS:
- Word Version
- PDF Version
Function Notation WS 2:
- Word Version
- PDF Version

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

Interpreting Distance - Time Graphs

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

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

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

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

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

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

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

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