SECTION

CONTENTS

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The Story of Algebra 1 (A1)

Unit 2 (U1):

Graphing Functions

The overarching goals of this unit are to introduce functions and the course in general. The big ideas of function concepts & notation and interpreting functions help meet both goals. Reasoning quantitatively and using units to solve problems are connecting standards ,standards that repeat throughout multiple units, and can be explored explicitly to provide depth or interleaved when interpreting functions to support those who struggled in the previous unit. By selecting linear functions, exponential functions, quadratic functions, and other functions presented in symbolic form, as tables, or especially as graphs - all in context - an overview of the entire course is created and a foundation is laid for understanding each in greater detail in future units.

Rigor in Claim 1 (bolded I cans from SBAC Evidence statements)

Learning

Goals

Develop

Conceptual

Understanding

Solidify

Procedural

Proficiency

Formalize

Application

& Transfer

A1.U2.G1 Relations: Function or Not? Students understand that a function from one set (the domain) to another set (the range) assigns to each element of the domain exactly one element of the range, distinguish between functions and non-functions (level 1), understand the concept of a function in order to distinguish a relation as a function or not a function (level 2), and recognizes that sequences are functions whose domain is a subset of the integers (level 3).

Target K

• I understand that a function from one set (the domain) to another set (the range) assigns to each element of the domain exactly one element of the range, distinguishing between functions and non-functions. (level 1)

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• I can recognize that sequences are functions whose domain is a subset of the integers. (level 3)

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• I understand the concept of a function in order to distinguish a relation as a function or not a function. (level 2)

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A1.U2.G2 Domain & Range Students should be able to state the domain and range given a graph (level 1) of a quadratic, linear, cubic, or absolute function (level 2), and identify the domain and range for any given function presented in any form, e.g., as a graph, a verbal description, or a sequence. (level 3)

Target K

• I can state the domain and range given a graph. (level 1)

• I can state the domain and range given a graph of a linear function. (level 2)
• I can state the domain and range given a graph of an absolute function. (level 2)
• I can state the domain and range given a graph of a quadratic function. (level 2)
• I can state the domain and range given a graph of a cubic function. (level 2)

• I can identify the domain and range for any given function presented in any form, e.g., as a graph, a verbal description, or a sequence. (level 3)

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A1.U2.G3 Evaluation, Graphs & Equations of Functions Students should understand that the graph of a function f(x) is the graph of the equation y = f(x) (level 2), use function notation to evaluate a function given in function notation for a particular input (level 3), and be able to find the input for a given output when given in function notation (level 4).

Target K

• I understand that the graph of a function f is the graph of the equation y= f(x). (level 2)

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• I can use function notation to evaluate a function given in function notation for a particular input. (level 3)

• I can find the input for a given output when given in function notation. (level 4)

Rigor in Claim 1 (bolded I cans from SBAC Evidence statements)

Learning Goals

Instructional Notes

A1.U1.G2

Develop

Conceptual

Understanding

Solidify

Procedural

Proficiency

Formalize

Application

& Transfer

A1.U2.G4 Key Features of Graphs Students should be able to interpret linear functions in context, and given the key features of a linear graph, they should be able to identify the appropriate graph (level 1); interpret quadratic and other polynomial functions in two variables in context of the situation, and given the key features of a graph of a polynomial function, they should be able to identify the appropriate graph (level 2); graph various types of functions and interpret and relate key features, including range and domain, in familiar or scaffolded contexts (level 3); and interpret complex key features such as holes, symmetries, and end behavior of graphs and functions in unfamiliar problems or contexts (level 4). Target L

• I can interpret linear functions in context. (level 1)
• I can interpret quadratic functions in two variables in context of the situation. (level 2)
• I can interpret the key features of a graph representing a function modeling the relationship between two quantities (level 2)

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• I can interpret the key features of a table representing a function modeling the relationship between two quantities (level 2)

• I can sketch graphs showing key features given a verbal description of the relationship between two quantities that can be modeled with a function (level 3)

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• I can relate the domain of a function to its graph (level 3).
• Given the key features of a linear graph, I can identify the appropriate graph. (level 1)

• When applicable, I can relate the domain of a function to the quantitative relationship it describes (level 3).

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A1.U2.G5 Average Rate of Change They should be able to specify the average rate of change from an equation of a linear function and approximate it from a graph of a linear function (level 2); specify the average rate of change of a function on a given domain from its equation or approximate the average rate of change of a function from its graph, and calculates and interprets the average rate of change of a function presented symbolically or as a table (level 3). Target L

• I can interpret the average rate of change of a function presented symbolically (level 3).
• I can interpret the average rate of change of a function presented in a table (level 3).

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• I can specify the average rate of change from an equation of a linear function. (level 2)
• I can calculate the average rate of change of a function presented symbolically (level 3).

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• I can calculate the average rate of change of a function presented in a table (level 3).

• I can approximate the average rate of change from a graph of a linear function (level 2)
• I can estimate a rate of change of a function from a graph (level 3).

The Story of Algebra 1 (A1)

Unit 2 (U1):

Graphing Functions

The overarching goals of this unit are to introduce functions and the course in general. The big ideas of function concepts & notation and interpreting functions help meet both goals. Reasoning quantitatively and using units to solve problems are connecting standards ,standards that repeat throughout multiple units, and can be explored explicitly to provide depth or interleaved when interpreting functions to support those who struggled in the previous unit. By selecting linear functions, exponential functions, quadratic functions, and other functions presented in symbolic form, as tables, or especially as graphs - all in context - an overview of the entire course is created and a foundation is laid for understanding each in greater detail in future units.

The Story of Algebra 1 (A1)

Unit 2 (U1):

Graphing Functions

The overarching goals of this unit are to introduce functions and the course in general. The big ideas of function concepts & notation and interpreting functions help meet both goals. Reasoning quantitatively and using units to solve problems are connecting standards, standards that repeat throughout multiple units, and can be explored explicitly to provide depth or interleaved when interpreting functions to support those who struggled in the previous unit. By selecting linear functions, exponential functions, quadratic functions, and other functions presented in symbolic form, as tables, or especially as graphs - all in context - an overview of the entire course is created and a foundation is laid for understanding each in greater detail in future units.

Rigor in Claim 1 (bolded I cans from SBAC Evidence statements)

Learning

Goals

Develop

Conceptual

Understanding

Solidify

Procedural

Proficiency

Formalize

Application

& Transfer

A1.U1.G3 Scaling Graphs & Data Displays Students should be able to correctly scale a graph with unit increments, and identify a quantity from a graph with a scale in unit increments of a specified measurement (level 1), identifying a quantity from a graph with the scale in increments of various sizes (level 2). They should be able to identify appropriate levels of measurement precision in context and to choose and interpret the scale and origin of a graph or data display (level 3) Target C

• I can choose the scale for data displays. (level 1)

• I can identify a quantity from a graph with a scale in unit increments of a specified measurement. (level 1)
• I can identify a quantity from a graph with the scale in increments of various sizes. (level 2)

• I can identify appropriate levels of measurement precision in context, and choose and interpret the scale and origin of a graph. (level 3)
• I can identify appropriate levels of measurement precision in context, and choose and interpret the scale and origin of a data display. (level 3)

A1.U1.G4 Units in Problem Solving Students should be able to choose the units in a formula (level 1), reason quantitatively to interpret the units in a formula given in a familiar context (level 2) and unfamiliar context (level 3), including making measurement conversions between simple units (level 2) and compound units (level 3) They should be able to use units to guide the solution of a familiar multi-step problem with scaffolding (level 2) and an unfamiliar multi-step problem without scaffolding (level 3). Target C

• I can choose the units consistently in formulas. (level 1)

• I can reason quantitatively to interpret the units in a formula given in a familiar context. (level 2)
• I can make measurement conversions between simple units. (level 2)
• I can make measurement conversions between compound units. (level 3)
• I can use units to guide the solution of a familiar multi-step problem with scaffolding. (level 2)

• I can reason quantitatively to interpret the units in a formula given in an unfamiliar context. (level 3)
• I can use units to guide the solution of an unfamiliar multi-step problem without scaffolding. (level 3)

A1.U1.G5 Models:Defining Quantities & Measures Students should be able to define appropriate quantities or measurements in familiar contexts with some scaffolding to construct a model (level 3) and define appropriate quantities or measurements in unfamiliar contexts with little to no scaffolding to construct a model. (level 4) Target C

• I can choose appropriate quantities for answering a question in a real world context. (level 1)

• I can define appropriate quantities or measurements in familiar contexts with some scaffolding to construct a model. (level 3)

• I can define appropriate quantities or measurements in unfamiliar contexts with little to no scaffolding to construct a model. (level 4)