F.1.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

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Formative Assessments
Formative Assessments
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CPALMS: Students are asked to determine if each of three equations represents a function.

Identifying Algebraic Functions

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CPALMS: Students are asked to define the term function including important properties.

What Is a Function?

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CPALMS: Students are asked to determine whether or not each of two graphs represent functions.

Recognizing Functions

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CPALMS: Students are asked to determine whether or not tables of ordered pairs represent functions.

Tabulating Functions

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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This animation helps students to understand the function concept through the machine metaphor. The domain elements are dragged into the machine, which then goes through some process and outputs the range element corresponding to the input.

Function Machine by National Library of Virtual Manipulatives (Java Required)

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This activity allows the user to explore simple linear functions; the function is determined by looking for patterns in the outputs. It can be used to can be used to practice students' pattern finding skills, introduce basic notions from algebra, and motivate the idea of a function of one variable.

Introduction to Functions – “Function Machine” by Shodor Interactivate

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CPALMS: This lesson is designed to introduce students to the vertical line test for functions as well as practice plotting points and drawing simple functions.

Functions and Vertical Line Test by Shodor Interactivate

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Students enter inputs into a function machine. Then, by examining the outputs, they must determine what function the machine is performing. It allows students to explore functions and what inputs are most useful for determining the function rule.

Number Cruncher by Shodor Interactivate

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This activity allows the user to explore simple linear functions; the function is determined by looking for patterns in the outputs. The function is always a simple line of the following form: y = m * x + b where m, the slope, and b, the y-intercept, can be any integer between -10 and 10.

Linear Function Machine by Shodor Interactivate

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This manipulative is great for students to practice recognizing the function rule. Student or computer can choose the input. Different activity levels for play and self-checking.

Function Machine by Math Playground (Java Required)

Assessment Questions
Assessment Questions
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Multiple Choice
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Table Item 4
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Open Response
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Table Item 3
Video of Expert Instruction
Video of Expert Instruction
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A table is given with information regarding height. Sal models and explains how to plot the ordered pairs and discusses what to consider in order to decide if there is a functional relationship between each person and his or her height. Video is approx. 4:35 min.
“Recognizing Functions from a Table” by Khan Academy
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In this video, vocabulary (independent and dependent variables, input and output values, function, domain, range) are important. What does/doesn’t make a function is modeled as well as explained. Demonstrations of linear and nonlinear functions are shown. The vertical line test is demonstrated.
“Vertical Line Test” by WhyU
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This video is approx. 4:00 min and explains examples and non-examples of a function, given points on the coordinate plane.
Identifying a Function from a Graph by Khan Academy
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This video (approx. 7:30 min) explains how a “binary relation” is a way of associating or relating elements of one set to elements of another set and how this information can be conveyed using ordered pairs. Domain and Range are initially explained with visuals that are not numbers.
“Binary Relations” by WhyU
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This short video (approx. 1:15 min.) uses a table of ordered pairs in order to explain how to decide if each represents a function or not.
“Checking if a Table Represents a Function” by Khan Academy
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This video (approx. 6:25 min) connects to prior WhyU Algebra series videos and extends understanding of binary relations to a function and its characteristics. The concepts of domain and codomain are initially explained with examples that are more “friendly” than numbers.
“Functions” by WhyU
Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics: This task could introduce functions. It illustrates examples as well as non examples of functions. Since the data is a collection of input-output pairs, no verbal description is given, so students can process what the ``rule form`` of the proposed functions would look like.

Foxes and Rabbits

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Illustrative Mathematics: The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task.

Pennies to Heaven

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Illustrative Mathematics: The purpose of this task is to connect the function described by a verbal rule with corresponding values in a table. It also encourages students to think more broadly about functions as relating objects other than numbers.

Function Rules

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Illustrative Mathematics:The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation.

The Customers

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Illustrative Mathematics: The goal of this task is to give motivation to understanding the definition of a function by carefully analyzing different relationships. In some, one quantity can be determined in terms of the other, while in others this isn't possible. At least 2 valid approaches are open.

Introducing Functions

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Illustrative Mathematics: This task presents an opportunity to explore a more general and non-algebraic view of functions. This will help with students with conceptual understanding of the rule of a function when the context offers a real-world ``input`` and exactly one ``output``.

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