In this unit, students will grasp the concept of a function as a rule that assigns to each input exactly one output. Students will also understand that functions describe situations where one quantity determines another. These ideas build on previous knowledge of how independent and dependent variables relate to each other. Another key understanding for students is the ability to translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and describe how aspects of the function are reflected in the different representations. At times, students may struggle to recognize that nonlinear relationships can still be functions. They may also struggle with identifying important features or components of functions based on varied representations of a function.
Key Concepts:
 A function is a rule that assigns to each input exactly one output, and the inputoutput pairs can be related or displayed in different ways, such as showing values in tables, graphically, or verbally. (Lesson 1)
 Graphing the inputs and outputs as coordinate pairs allows us to describe the behavior of the function qualitatively (examples: as the inputs increase the outputs also increase, as the inputs increase, the outputs decrease; only whole number inputs make sense in this context, but the outputs may not be whole numbers, as the inputs increase, the outputs increase up to a certain input value and then decrease). (Lesson 4)
 Graphing the inputs and outputs as coordinate pairs, or looking at graphs of functional relationships, allows us to describe the behavior of the function qualitatively. (compare multiple functions with the same input/output descriptions, such as two kids racing). (Lesson 8)
Prior Knowledge Needed:
 There is a specific relationship between independent and dependent variables; (Grade 6, Unit 5; 6.EE.C.9)
 Proportional relationships exist between quantities and can be represented in a variety of ways; (Grade 7, Unit 2; 7.RP.A.2)
 Writing equivalent ratios maintains the specific relationship between quantities; (Grade 6, Unit 1; 6.RP.A.3)
 The constant of proportionality can be described as the unit rate for the proportional relationship; (Grade 7, Unit 2; 7.RP.A.2b)
Units on the Horizon:
 Linearity (Grade 8, Unit 7)
 Relationships with Bivariate Data (Grade 8, Unit 8)
 Introduction to Nonlinear Functions (Grade 8, Unit 9)
Lessons

Lesson objective: Understand that a function pairs each input with exactly one output. Students bring prior knowledge of relationships between variables from 6.EE.C.9. This prior knowledge is extended to functions as students recognize how inputs and ou...

Lesson objective: Fluently identify functions from various representations. This lesson helps to build fluency with identifying functions. Tables of values, mappings, verbal descriptions and graphs are used here because it supports the idea that a funct...

Lesson objective: Apply the definition of a function to a realworld situation. This lesson provides an opportunity for students to apply their knowledge and understanding of the definition of a function to a reallife situation. Students are asked to c...

Lesson objective: Understand the behavior of a function. Students bring prior knowledge of interpreting unit rates from 6.EE.C.9, as well as understanding of proportional relationships and points on a graph of proportional relationships from 7.RP.A.2d. ...

Lesson objective: Describe the behavior of a function given a graph or table of values. This lesson helps to build fluency with describing function behavior. Graphs and tables of values are used here because they support the understanding that represent...

Lesson objective: Graph a function given a description of the behavior of the function. This lesson helps to build procedural skill with representing the behavior of a function graphically. Verbal descriptions and graphs are used here because they highl...

Lesson objective: Relate behaviors of a function to a realworld situation. This lesson provides an opportunity for students to apply their knowledge and understanding of behaviors of a function to a reallife situation. Students are asked to describe t...

Lesson objective: Extend understanding of behaviors of functions in order to compare functions. Students bring prior knowledge of functions' behaviors from 8.F.B.5. This prior knowledge is extended to multiple functions as students describe and identify...

Lesson objective: Compare the behaviors of multiple functions. This lesson helps to build skill with comparing behaviors of functions. Graphs, tables of values, and verbal descriptions are used here because they represent the various ways functions can ...

Lesson objective: Solve a reallife problem by comparing behaviors of functions. This lesson provides an opportunity for students to apply their knowledge and understanding of function behaviors to a reallife situation. Students are asked to decide whi...