Lesson Title: Function Notation
Date: _____________ Teacher(s): ____________________
Course: Common Core Algebra I, Unit 1
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
F.IF.A.1 Students will be able to understand functions and use function notation.
MP1: Make sense of problems and persevere in solving them.
MP2: Reason abstractly and quantitatively.
MP7: Look for and make use of structure.
Common Core Algebra I, Unit 1
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Distribute the resource sheet “Functions vs. NonFunctions,” and ask students to inspect the graphs and
determine a definition for “function.” (Look for
evidence of MP2 and MP7.)
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.


There are many different real-world applications of
functions. Identify a few.
Given the function f (x)  3x  5 , compute the
values for f(0), f(3), f(a) and f(x+4). What does f(x+4)
mean? (Look for evidence of MP1.)
 specific activities, investigations,
Lesson Tasks, Problems, and Activities (attach resource sheets): What
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. After students write their definitions, have them put the resource sheet aside to be revisited later. As a class,
discuss and determine a definition for “function,” or list possible definitions on the board.
2. Ask a few students to tell you their favorite vending machine snacks. Draw a “vending machine” on the board,
and assign a “slot” to each snack: A1 to chips, B1 to candy, C1 to gum, etc.
3. Ask, “How does a vending machine work?” Ask the students to choose a snack that they would like to buy.
4. Ask, “What is supposed to happen after you input your money and push the button for your snack? What is the
output supposed to be if I input A and then 1?” Go through a few different examples and encourage students to
see that each input is assigned one specific output. In other words, each element of the domain is mapped to a
specific element of the range. Ask, “Is it possible for different inputs to be assigned to different outputs?” Using
the vending machine analogy, encourage them to see that this would be like having chips in the slots for A1 and
for A2.”
Additional Examples: A person’s birthday is an example of a relation that is a function. Two different people
can have the same birthday but one person can only have one birthday. Speed is an example of a function where
your distance traveled is a function of the time you have been driving.
5. Revisit “Functions and Non-Functions.” Have students look at the tables to identify the difference between
functions and non-functions. Notice that with the functions, for every x there is a unique y. Re-examine this
concept given the graphs. Show that certain x-values in the right hand column of graphs will give you two
different y-values. With the left-hand functions, every x-value will only give you one y-value. Have the students
compare their definitions of function to the one they have now. Ask, “Does anyone have a close definition?”
6. Discovery Streaming video on calories-Write the function for calories burned as a function of time run in
function notation. It is important to note that f (t) is “f of t” and not “f times t.” In this specific scenario
“calories burned is a function of time.” Have students compute several values of inputs given proper notation
f(10), f(3), etc. Another way to show functions is with the “function box.” The input or domain value goes into
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.

Lesson Title: Function Notation
Course: Common Core Algebra I, Unit 1
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
the function box; the function then applies its property and then gives you an output or range value. (Look for
evidence of MP1.)
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
Do students understand the definition of a function? Are the students able to understand what f(x) means? Can
students calculate outputs given an input value?
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
When working with the vending machine problem, use vocabulary like “input” as the set of the domain, “output” as
the set of the range and function, etc.
Vocabulary of f(x). f of x as opposed to f times x is a common mistake and misconception.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
“Function vs. Non-function” Resource Sheet
Discovery Streaming video on calories
Sketch three examples of graphs that are functions and
three non-examples.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
How can you identify the difference between a function and a non-function?
What are several real-world examples of functions?
What purpose does function notation serve in a given problem?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.