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Goddard: High School Common Core State Standards (CCSS) Mathematics - Functions

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.1Cluster: Understand the concept of a function and use function notation.Standard: 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).

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐

Know (nouns) DefinitionList the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.

Domain: input values or x-values Range: output values or y-values Element: a member of the set Function: a relationship that assigns one element of the domain exactly one element of the range

Be Able to Do (Verbs) Level I Level II Level III Level IV Level V

List the verbs that are key learning targets, then determine the cognitive demand level (Bloom’s/SEC) with verbs in context by placing a checkmark in the appropriate square:

Knowledge/ Remembering

Memorize facts, definitions, &

formulas

Comprehension/ Understanding

Perform Procedures

ApplicationDemonstrate

understanding of math

AnalysisConjecture,

Generalize, Prove

Synthesis/Evaluate/ Create; Solve non-routine problems; make connections

Understand ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Recognize if a relationship is a function or not. Essential Questions:

Given a set of data, determine if it represents a function. What learning progressions are needed to master this standard? Give specific, measurable skill statements.

1

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand(Depth of Knowledge

Concept of ordered pairs I ☐ II ☒ III ☐ IV ☐ V ☐ Familiarity with graphs I ☐ II ☒ III ☐ IV ☐ V ☐ Familiarity with tables I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)

Instructional Resources/Tools:

Assessment Item Type: Selected Response ☒ Extended Constructed Response ☒ Technology Enhanced ☒ Performance Task ☒ Oral Response ☐ Eligible as summative item ☒Example: Provide possible instructional learning example/formative assessment item(s) for this standard:

Example 1: Example 2: Example 3:

2

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.2Cluster: Understand the concept of a function and use function notation.Standard: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒

Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐Know (nouns) Definition

List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Function Notation: a method of naming functions that also indicates the input value Input: the x-value; independent variable





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


evaluate ☐ ☒ ☐ ☐ ☐ use ☐ ☒ ☐ ☐ ☐ interpret ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Rewrite an equation in function notation and substitute in given domain values.Essential Questions:

What does the output of the function represent in a given situation? Can you find the range of a function given its domain? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


2 Knowledge of domain and range I ☐ II ☐ III ☐ IV ☐ V ☐

3

1 Order of operations I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




4

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.3Cluster: Understand the concept of a function and use function notation.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Sequences: a recurring or repeated pattern of numbers Subset: portion of a set Integers: numbers that can be written without decimals or fractions





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Recognize ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Know that a pattern can be modeled as a functionEssential Questions:

Can you recognize that a set of a numbers creates a pattern? Given a set of numbers, can you tell if it can be modeled by a function? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

Learning Sequence Prior skill(s) needed Check Level of Rigor/Cognitive Demand

5

(Depth of Knowledge Pattern recognition I ☐ II ☒ III ☐ IV ☐ V ☐ Number systems I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




6

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.4Cluster: Interpret functions that arise in applications in terms of the context.Standard: 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.★

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒Level 3: Strategic Thinking ☐ Level 4: Extended Thinking ☐


Intercepts: Where the graph of the function crosses the x-axis and y-axis Intervals (increasing/decreasing): Section of the graph where the y-values are increasing/ decreasing Relative Maximum/ Minimum: Where a graph changes from increasing to decreasing (maximum), or decreasing to increasing (minimum) End Behavior: Appearance of the graph as it goes to negative and positive infinity Symmetries: repetitive patterns Periodicity: Tendency to recur at regular intervals





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Interpret ☐ ☒ ☐ ☐ ☐ Sketch ☐ ☐ ☐ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Identify features of a graph from a visual representation and create a graph given specific characteristics of a graph.Essential Questions:

Given relative maximums, minimums, and intercepts, can you graph a function? Can you identify key features of a function given its graph? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

7


Graphing- including key features I ☐ II ☐ III ☐ IV ☐ V ☐ Interpreting graphs I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




8

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.5Cluster: Interpret functions that arise in applications in terms of the context.Standard: 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.★



Quantitative Relationship: A quantity that can be represented by number values.





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Relate ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Determine the appropriate domain from a graph or a situation.Essential Questions:

Can you explain how the domain of a function is represented in its graph? Can you state the appropriate domain of a function that represents a problem situation, defend your choice, and explain why other numbers might be

excluded from the domain? What learning progressions are needed to master this standard? Give specific, measurable skill statements.

9


Sequences I ☐ II ☐ III ☐ IV ☐ V ☐ Word problem analysis I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




10

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.6Cluster: Interpret functions that arise in applications in terms of the context.Standard: 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.★



Rate of Change: slope of the function in the context of the problem





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Calculate ☒ ☐ ☐ ☐ ☐ Interpret ☐ ☒ ☐ ☐ ☐ Estimate ☐ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Find the slope of the function over a given intervalEssential Questions:

Can you find the average rate of change of a function over a given interval? Can you find the average rate of change over different intervals in a function? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


11

(Depth of Knowledge Finding slope I ☐ II ☐ III ☐ IV ☐ V ☐ Interpreting graphs I ☐ II ☐ III ☐ IV ☐ V ☐ Estimation I ☐ II ☐ III ☐ IV ☐ V ☐ Recognizing that slope represents dependent over independent labels. I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




12

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.7Cluster: Analyze functions using different representations.Standard: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated

cases.★



Function: a relationship that assigns one element of the domain exactly one element of the range Graph:





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


graph ☐ ☒ ☐ ☐ ☐ show ☐ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Graph & interpret functionsEssential Questions:

Can you graph a function? Can you identify key concepts after graphing a function? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


13

(Depth of Knowledge Familiarity with graphs I ☐ II ☒ III ☐ IV ☐ V ☐ Graphing –including key features I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




14

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.7aCluster: Analyze functions using different representations.Standard: Graph linear and quadratic functions and show intercepts, maxima, and minima.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Linear Function: equation of a line Quadratic Function: degree two function Maximum: The ordered pair with the largest y-value Minimum: The ordered pair with the smallest y-value





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Graph ☐ ☐ ☒ ☐ ☐ Show ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Graph a linear or quadratic functionEssential Questions:

Can you graph a linear function? Can you graph a quadratic function? Can you identify the vertex, maximum and minimum of a parabola? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


15

Graphing I ☐ II ☐ III ☐ IV ☐ V ☐

Find the x-value of the vertex of a parabola with x=−b2a

I ☐ II ☐ III ☐ IV ☐ V ☐

Table of values I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




16

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.7bCluster: Analyze functions using different representations.Standard: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Square root function: function with a variable under the square root Cube root function: function with a variable under the cube root Piece-wise function: a function that is defined over different intervals Step functions: a function whose range is constant over consistent intervals Absolute value function: a function with the variable inside the absolute value symbols





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


graph ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Graph square root, cube root and piece-wise functions.Essential Questions:

Can you identify the type of function to be graphed? Can you identify the key characteristics of each specific function? Can you graph a square root, cube root, piece-wise, step and absolute value equation? What learning progressions are needed to master this standard? Give specific, measurable skill statements.


17

Order of operations I ☐ II ☐ III ☐ IV ☐ V ☐ Square root, cube root, absolute value I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




18

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.7cCluster: Analyze functions using different representations.Standard: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Polynomial function: a function with any whole number degree Zeros: x-intercepts, when the function is equal to zero Factorizations: factors of the polynomial





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Graph ☐ ☒ ☐ ☐ ☐ Identify ☐ ☐ ☒ ☐ ☐ Show ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Graph polynomial functionsEssential Questions:

What learning progressions are needed to master this standard? Give specific, measurable skill statements.


19

Factoring I ☒ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐

I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




20

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.7dCluster: Analyze functions using different representations.Standard: (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Rational Function: a function expressed as a quotient of two polynomial function Asymptote: a line approached by a graph but never touched by the graph





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Graph ☐ ☒ ☐ ☐ ☐ Identify ☐ ☐ ☒ ☐ ☐ Show ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

FORMTEXT Essential Questions:



21

I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




22

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.7eCluster: Analyze functions using different representations.Standard: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and

amplitude.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Exponential functions: Function where the exponent is in the variable Logarithmic functions: inverse of the exponential function Trigonometric functions: sine, cosine, tangent, secant, cosecant and cotangent Period: the interval for one cycle of the graph Midline: the constant (horizontal) line that cuts the graph in half Amplitude: the distance from the midline to the maximum or minimum





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Graph ☐ ☒ ☐ ☐ ☐ Show ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)



23


factoring I ☒ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




24

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.8Cluster: Analyze functions using different representations.Standard: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. See 8a -8b Function: a relationship that assigns one element of the domain exactly one element of the range properties expression





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




25





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Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.8aCluster: Analyze functions using different representations.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Factoring: to separate a product into its factors Completing the square: the method used to solve a quadratic equation Extreme values: Maximum or minimum values





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Use ☐ ☐ ☒ ☐ ☐ Show ☐ ☐ ☒ ☐ ☐ Interpret ☐ ☐ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




27

(Depth of Knowledge factoring I ☒ II ☐ III ☐ IV ☐ V ☐ Completing the square I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




28

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.8bCluster: Analyze functions using different representations.Standard: 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.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Properties of exponents: properties that apply the manipulation of exponents Exponential growth: all increasing, always positive exponential functions Exponential decay: all decreasing, always positive exponential functions





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


interpret ☐ ☐ ☒ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




29

(Depth of Knowledge Percent of change I ☒ II ☐ III ☐ IV ☐ V ☐ Properties of change I ☒ II ☐ III ☐ IV ☐ V ☐

I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




30

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Interpreting Functions Code: F.IF.9Cluster: Analyze functions using different representations.Standard: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Properties of functions: maximum, minimum, zeros, increasing, decreasing, intercepts





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Compare ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Comparisons of 2 functions represented in multiple waysEssential Questions:



31

(Depth of Knowledge Calculate & find vertex I ☒ II ☐ III ☐ IV ☐ V ☐ Find roots I ☒ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




32

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.1Cluster: Build a function that models a relationship between two quantities.Standard: Write a function that describes a relationship between two quantities.★



See 1a & 1b





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






33





34

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.1aCluster: Build a function that models a relationship between two quantities.Standard: Determine an explicit expression, a recursive process, or steps for calculation from a context.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Explicit expression: polynomial in one variable Recursive process: repeatedly applying the same rule





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Determine ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Solve an application problemEssential Questions:



35





36

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.1bCluster: Build a function that models a relationship between two quantities.Standard: Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding

a constant function to a decaying exponential, and relate these functions to the model.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Standard function types: polynomial, exponential Arithmetic operations: add, subtract, multiply or divide





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Combine ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




37

(Depth of Knowledge I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




38

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.1cCluster: Build a function that models a relationship between two quantities.Standard: (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a

function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context.





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Compose ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




39





40

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.2Cluster: Build a function that models a relationship between two quantities.Standard: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the

two forms.★



Arithmetic sequences: A sequence that contains a common difference Geometric sequences: a sequence that contains a common ratio





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Write ☐ ☐ ☐ ☐ ☒ Use ☐ ☒ ☒ ☐ ☐ Model ☐ ☐ ☒ ☐ ☐ Translate ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




41





42

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.3Cluster: Build new functions from existing functions.Standard: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value

of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.



Even function: a function with symmetry around the y-axis, f(x) = f(-x) Odd function: a function with symmetry over the origin, f(x) = -f(-x)





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Identify ☐ ☒ ☐ ☐ ☐ Define ☒ ☐ ☐ ☐ ☐ Experiment ☐ ☐ ☐ ☒ ☐ Illustrate ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)



43






44

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.4Cluster: Build new functions from existing functions.Standard: Find inverse functions.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. See 4a,4d





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






45





46

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.4aCluster: Build new functions from existing functions.Standard: Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the in-verse. For example, f(x) =2 x3 or f(x)

= (x+1)/(x-1) for x ≠ 1.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Inverse: function where the independent and dependent variables are reversed





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Solve ☐ ☒ ☐ ☐ ☐ Write ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




47





48

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.4bCluster: Build new functions from existing functions.Standard: (+) Verify by composition that one function is the inverse of another.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Composition: substitution of one function into another





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Verify ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




49





50

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.4cCluster: Build new functions from existing functions.Standard: (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Read ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




51





52

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.4dCluster: Build new functions from existing functions.Standard: (+) Produce an invertible function from a non-invertible function by restricting the domain.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Invertible function: A function that has an inverse Non-invertible function: a function that does not have an inverse





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Produce ☐ ☐ ☐ ☐ ☒ Restricting ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




53





54

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Building Functions Code: F.BF.5Cluster: Build new functions from existing functions.Standard: (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and

exponents.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






55



Assessment Item Type: Selected Response ☒ Extended Constructed Response ☒ Technology Enhanced ☒ Performance Task ☒ Oral Response ☐ Eligible as summative item ☐Example: Provide possible instructional learning example/formative assessment item(s) for this standard:


56

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Linear, Quadratic, and Exponential Models★ Code: F.LQE.1Cluster: Construct and compare linear, quadratic, and exponential models and solve problems.Standard: Distinguish between situations that can be modeled with linear functions and with exponential functions.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒

Level 3: Strategic Thinking ☒ Level 4: Extended Thinking ☐Know (nouns) Definition

List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Linear functions: equation of a nonvertical line Exponential functions: a function where the exponent is a variable





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Distinguish ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Differentiate the rate of change for the situationEssential Questions:



57

Linear & exponential growth & decay I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




58

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Linear, Quadratic, and Exponential Models★ Code: F.LQE.1aCluster: Construct and compare linear, quadratic, and exponential models and solve problems.Standard: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. intervals factors





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Prove ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Demonstrate that an exponential function has a constant common ratio over equal intervalsEssential Questions:



59

Exponential functions I ☐ II ☒ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐ I ☐ II ☐ III ☐ IV ☐ V ☐Assessments: (What will be acceptable evidence the student has achieved the desired results?)




60

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Linear, Quadratic, and Exponential Models★ Code: F.LQE.1bCluster: Construct and compare linear, quadratic, and exponential models and solve problems.Standard: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Unit interval: the change in the y-value per one unit of the x-value





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






61





62

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Linear, Quadratic, and Exponential Models★ Code: F.LQE.1cCluster: Construct and compare linear, quadratic, and exponential models and solve problems.Standard: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Growth Decay





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






63





64

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Linear, Quadratic, and Exponential Models★ Code: F.LQE.2Cluster: Construct and compare linear, quadratic, and exponential models and solve problems.Standard: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-

output pairs (include reading these from a table).Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Input-output pairs: an ordered pair that relate to a function





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Construct ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




65



Assessment Item Type: Selected Response ☐ Extended Constructed Response ☒ Technology Enhanced ☒ Performance Task ☒ Oral Response ☐ Eligible as summative item ☒Example: Provide possible instructional learning example/formative assessment item(s) for this standard:


66

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Linear, Quadratic, and Exponential Models★ Code: F.LQE.3Cluster: Construct and compare linear, quadratic, and exponential models and solve problems.Standard: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more

generally) as a polynomial function.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. graphs tables function





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Observe ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)

Recognize in graphs & tables that an exponential function grows faster than a polynomial functionEssential Questions:



67





68

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Linear, Quadratic, and Exponential Models★ Code: F.LQE.4Cluster: Construct and compare linear, quadratic, and exponential models and solve problems.Standard: For exponential models, express as a logarithm the solution to a bct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the

logarithm using technology.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. e; an irrational number, the inverse of the natural logarithm.





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Express ☐ ☐ ☒ ☐ ☐ Evaluate ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




69





70

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Linear, Quadratic, and Exponential Models★ Code: F.LQE.5Cluster: Interpret expressions for functions in terms of the situation they model.Standard: Interpret the parameters in a linear, quadratic, or exponential function in terms of a context.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Parameters: Possible domain and range values





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Interpret ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




71





72

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Trigonometric Functions Code: F.TF.1Cluster: Extend the domain of trigonometric functions using the unit circle.Standard: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☐



Radian measure: π180times the degree of the angle measure

Unit Circle: a circle with radius 1





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Understand ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




73





74

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Trigonometric Functions Code: F.TF.2Cluster: Extend the domain of trigonometric functions using the unit circle.Standard: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian

measures of angles traversed counter-clockwise around the unit circle.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Unit Circle Trigonometric functions





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Explain ☐ ☒ ☐ ☐ ☐ Interpreted ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




75





76

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Trigonometric Functions Code: F.TF.3Cluster: Extend the domain of trigonometric functions using the unit circle.Standard: (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π /3, π/4 and π/6, and use the unit circle to express the

values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






77





78

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Trigonometric Functions Code: F.TF.4Cluster: Extend the domain of trigonometric functions using the unit circle.Standard: (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.Depth of Knowledge: Level 1: Recall ☐ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






79





80

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Trigonometric Functions Code: F.TF.5Cluster: Model periodic phenomena with trigonometric functions.Standard: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.★



Frequency: one divided by the period





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Choose ☐ ☒ ☐ ☐ ☐ Model ☐ ☐ ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




81





82

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Trigonometric Functions Code: F.TF.6Cluster: Model periodic phenomena with trigonometric functions.Standard: (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be

constructed.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






83





84

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Trigonometric Functions Code: F.TF.7Cluster: Model periodic phenomena with trigonometric functions.Standard: (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them

in terms of the context.★

Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒Level 3: Strategic Thinking ☒ Level 4: Extended Thinking ☐






formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






85





86

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Trigonometric Functions Code: F.TF.8Cluster: Prove and apply trigonometric identities.Standard: Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒


List the key concepts (nouns/noun phrases) and provide a common definition of the nouns/noun phrases as used in this context. Sine Cosine Tangent Quadrant: one of the four sections in the coordinate plane





formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove


Prove ☐ ☐ ☐ ☒ ☐ Use ☐ ☐ ☒ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐ ☐This standard means a student will know and be able to do…(use your own words)




87





88

Quarter Taught: Quarter 1 ☐ Quarter 2 ☐ Quarter 3 ☐ Quarter 4 ☐Domain: Trigonometric Functions Code: F.TF.9Cluster: Prove and apply trigonometric identities.Standard: (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.Depth of Knowledge: Level 1: Recall ☒ Level 2: Basic Application-skill/concept ☒







formulas


Perform Procedures



AnalysisConjecture,

Generalize, Prove






89





90

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