## Unit 1

Modeling Linear Functions

**Unit Description**

This unit contains learning plans containing tasks and activities organized in comprehensive learning plans to support teachers and help students master the concepts of arithmetic sequences and modeling linear functions. The learning plans included in this unit should be strategically used to teach the standards using a conceptual, student-centered approach to teaching and learning. The information presented in this unit is a support for teachers through the implementation of the Effective Mathematics Teaching Practices by providing suggestions and examples for teachers that will allow students to be engaged in the Mathematical Practices. The learning plans provide further guidance and support and are designed with several key components adding clarity for implementation. Teachers should provide students with a broad range of contextual problems that offer opportunities for understanding and modeling mathematics through contextual situations.

This unit builds upon the understanding of linear functions in Grade 8:

• Determining if relations are functions

• Interpreting parts of a linear function

• Graphing linear inequalities (support for interval notation)

This unit builds upon the understanding of linear functions in Grade 8:

• Determining if relations are functions

• Interpreting parts of a linear function

• Graphing linear inequalities (support for interval notation)

**Learning Targets**

- I can recognize f(x) notation, as well as “sub” n, such as Sn
- I can identify and define arithmetic sequences
- Using the formula for an arithmetic or recursive sequence, I can determine the next “n” terms of a sequence
- I can recognize connections between linear functions and arithmetic sequences
- I can define the input value of a sequence as its sequential term number of the sequence (domain of a sequence is 1, 2, 3, 4…)
- I can use function notation to evaluate f(x) at a given value of x.
- I can connect equations of lines to arithmetic sequences with appropriate domains
- I can convert arithmetic from recursive, explicit, and function notation
- I can represent and interpret key characteristics of a linear graph to model real world phenomena (domain and range, intercepts, intervals of increase and decrease, positive or negative, maximum or minimum over a specified interval, end behavior).
- I can use interval and set notation to describe domain and range of a function.
- I can construct (by hand or with technology) the graphs of linear functions from function or table or verbal descriptions by hand and using technology.
- I can compare linear functions with nonlinear functions, identifying key features of both.
- I can name the types of parent functions by graph and equation.

**Textbook Connection**

**Module 3**Lesson 2 Functions: Students determine whether a relation is a function and find function values.

Lesson 3 Linearity and Continuity of Graphs: Students identify linear and nonlinear functions and continuous and discrete functions

Lesson 4 Intercepts of Graphs: Students identify intercepts and solve equations by graphing.

Lesson 5 Shapes of Graphs: Students identify symmetry, extrema, and end behavior of functions

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**Module 4**Lesson 1 Graphing Linear Functions: Students graph linear functions by using tables and intercepts

Lesson 3 Slope Intercept Form: Students graph equations in slope-intercept form.

Lesson 4 Transformation of Linear Functions: Students identify the effects of transformations of the graphs of linear functions.

Lesson 5 Arithmetic Sequences: Students write and graph arithmetic sequences.

Lesson 7 Absolute Value Functions: Students identify the effects of transformations of the graphs of absolute value functions.

__Module 9__Lesson 1 Exponential Functions: Students graph exponential functions

Lesson 6 Recursive Formulas: Students write arithmetic and geometric sequences recursively.

**Module 11**

Lesson 1 Graphing Quadratic Functions: Students analyze and graph quadratic functions.

**ixl skills**

__Arithmetic Sequences:__

- P.2, P.7
- Identifying: P.1 (includes Geometric)
- Converting Formulas: P.10, P.11
- Recursive: P.6 (includes Geometric), P.9 (includes Geometric),

__Comparing:__

- LEQ: DD.2
- Graph, Table, Equation: T.15,16

__Characteristics of Linear Functions:__

- Evaluating: Q.7
- Characteristics, slope, y-intercept: T.1-27 and 29