BFFs: Domain and Range of Functions

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Objective

SWBAT understand domain and range and how they are related to each other. SWBAT choose and interpret scales and units to guide problem solving.

Big Idea

Situations that are relevant to students' lives are modeled as students engage in learning about the domain and range of a function.

Entry Ticket

15 minutes

For this Entry Ticket: Domain and Range students examine a table that relates months and the number of iphones sold. The purpose of this exercise is to get students to start thinking about what variable we are measuring and what the relationship is between the variables. During this time students are quietly working on the entry ticket during the first few minutes of class. This allows for a smooth transition into class and engages students to work right at the bell in a structured routine so that they know what to expect at the beginning of each class.

The challenge section is an example of Differentiated Instruction as it provides a greater opportunity to learn and explore for students who are ready. This entry ticket also sets up the lesson as I will use this example to introduce and clarify some of the key concepts for the lesson in the next section. 

Video Presentation and Active Note-Taking: Domain, Range and Functions

30 minutes

For this section I review a Khan Academy video presentation with the class that reviews a number of problems.

 

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).

I pause the video throughout and provide external cues to students (this sounds important, everyone should write this down) and also ask students to hypothesize what the answers will be before having the answer given to them.

 

 

Vocabulary on Functions

30 minutes

Next, I have students work independently on completing the Vocabulary: Functions Unit for the unit. I explicitly teach students the difference between Brick and Mortar Words. I believe students need to be taught what types of conversation and language are valued in school AND how to engage in those skills. As this is the first time students are exposed to this particular setup for vocabulary I take the time to explain the concepts of Brick and Mortar words to the class. 

During this section, students work on ipad minis (part of a technology grant for Modeling with Mathematics and Universal Design for Learning in the Math Classroom) using a math dictionary to look up the definitions for the terms. As an alternative, students could use an online math dictionary. I recommend Wolfram Alpha as it provides excellent knowledge, is accurate and also provides good visual examples for many terms. Teachers can also choose to provide students with the definitions of the words (Vocabulary: Functions Unit (with definitions))to allow students to focus more on generating multiple representations of meaning for each word to develop a deeper understanding of the vocabulary terms.  

As they wrap up, I have students file the work in a vocabulary section of their notebook and remind them vocabulary is part of the Notebook Check. We will be using the vocabulary later in the unit for a writing exercise on creating their own functions. 

 

Exit Ticket and Homework

15 minutes

For the Exit Ticket Domain and Range, I ask the same questions as on the Entry Ticket for this lesson, but add in some terminology for domain and range. I keep the context similar (a different cell phone company) because I want to provide students with a grounded example in which to work with the novel math concepts being taught. I want students to focus on the math and not have to worry about shifting contexts or coming to an understanding of a brand new problem for this lesson. While being able to make cognitive shifts is an important skill, it is one that not many ninth graders are readily able to make when learning novel material. 

During this time students are working on the exit ticket that I hand out to them. They are expected to work until the end of the period. I am rotating among students and checking in to assess progress and providing support and cues to students depending on where they are in their understanding.

For Homework: BFFs Domain and Range, students are asked to determine the domain and range of different representations of functions and describe the relationship of the variables being measured.