Jason Colombino COLLINS MIDDLE, SALEM, MA
Algebra I : Unit #1 - Thinking Like a Mathematician: Modeling with Functions : Lesson #5

# The World's Language: Function Notation

Objective: SWBAT employ function notation in real life contexts. SWBAT correctly identify the domain and range of a function.
Standards: HSF-IF.A.1 HSF-IF.A.2 MP1 MP2 MP3 MP7
Subject(s): Math
60 minutes
1 Entry Ticket - Stock Traders and Function Notation - 15 minutes

To open the lesson, students complete the Entry Ticket: Stock Traders - Function Notation comparing the profit earned by four different stock traders. Problems 1 and 3 and problems 2 and 4 describe the same relationship, but for each pair one Trader is represented as an equation with x and y while the second of the pair is represented in function notation.

Students evaluate the profit for each of the four traders and answer a series of questions. I have students examine the four relationships as a way to identify what is the same and what is different among the four.

To conclude students complete a Turn and Talk,  where the task is to categorize the four traders based on a shared characteristics. During this peer conversation, I will listen in and encourage students to justify their thinking in order to expose students to Math Practice 3 (MP3). Since we are still early in the year, I will help students to develop their arguments. I will also look to support the critiquing of peer arguments, since we are still establishing norms for safe and respectful discussion.

2 Function Notation - Video and Note-Taking - 20 minutes

To open this section, I share a Khan Academy video presentation with the class that reviews function notation. I will follow this video with a second clip that compares and contrasts equations and functions.

I like using external resources, like Khan Academy, during note-taking source because I want students to develop the skill of identifying resources that are valid and useful. By using Khan Academy, as I do in this lesson, and other online resources, I am exposing students to different venues for accessing knowledge. As I facilitate the video presentation, I intervene in ways that encourage students to become better consumers of information. If I can contribute to helping my students learn how to learn, then I feel like I am doing my job well.

What is a Function?

Source URLhttps://www.youtube.com/watch?v=kvGsIo1TmsM (Accessed May 15, 2014)

During this time students are actively engaging in the four domains of language (listening, reading, speaking and writing). I have students take Two-Column Notes as a form of active note-taking, including an elevator statement at the end (a summarizing statement to help students work on processing and pulling out the most salient points of the lecture).

The Difference between Equations and Functions

Source URL: https://www.youtube.com/embed/l3iXON1xEC4 (Accessed May 15, 2014)

I show two videos today because I want students to have a thorough review of the conventional meaning of the term, function, in mathematics. I think that it helps my students to receive both an explanation of a function, and, a detailed comparison of equations and functions.

3 Function Example Problems and Note-Taking - 20 minutes

As a class, we then turn to a Khan Academy video (Accessed Aug 7 2013) that goes through a number of different examples of using and applying function notation. Students continue to take Two-Column Notes with the problem on the left side of the page and the work on the right side of the page. Rather than a large summary statement, I ask that students jot down ideas or thoughts about what was difficult and what they feel they understood for each problem so they can reflect and use the information to study and learn the material more efficiently and effectively.

Function Example Problems (Accessed Aug 7 2013)

I pause the video throughout and provide verbal cues to students (this sounds important, everyone should write this down). I also ask students to predict the answers to the problem before the answer is presented in the video.

Zooming in Video by Video
4 Exit Ticket and Homework: Bagels and Function Notation - 15 minutes

Students then work on the Exit Ticket: Bagels and Function Notation. This Exit Ticket is a problem based on a function (as represented in a table) of bagels sold on different days of the week at a popular local bagel shop. The context to the problem is something students can relate to and the work drives at the conceptual understanding and content taught about function notation in the day's lesson. If there is additional time at the end of class, students can complete a Think, Pair, Share  to discuss how they thought about the exit ticket.

For homework (Homework: Bagels and Function Notation - Idea Organizer), students are asked to analyze a function, expressed in f(x) terms for the profit of a bagel shop based on the number of coffees they sell. The homework requires students to be able to demonstrate their ability to apply the math knowledge and concepts about function notation and to organize their ideas (through the Idea Organizer) and then into a complete and polished 1-2 paragraph written response.

Writing as a Tool to Develop Conceptual Understanding
Developing a Conceptual Understanding

In the Student Sample Function Notation and Writing  in this reflection, I wanted to point out how writing can be utilized as an integral tool to develop conceptual understanding.

In this particular work sample, the student does a nice job of rephrasing the prompt and understanding what the assignment is asking for. In addition, the Idea Organizer provides space and a framework for the student to make different points and back up claims with evidence.

This sample suggests to me that the student has a good grasp of the day's lesson. In addition, this work sample helps me identify areas for continued improvement, both in mathematics and in writing. For example, writing strong concluding sentences and recapping mathematical ideas is one area for improvement based on this work sample.