Everything is Relative: An Introduction to Linear Functions

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Objective

SWBAT interpret an equation in y = mx+b form as a linear function whose graph is a straight line.

Big Idea

Students think like Mathematicians as we preview our unit on linear functions!

Entry Ticket and Turn and Talk

15 minutes

During the Entry Ticket: Everything is Relative - Reintroducing Linear Functions, students are asked to complete a series of questions assessing previously taught concepts about the slope-intercept form of a linear function. The reason for this entry ticket is to assess where students are at in their understanding (many students may have mastered the concepts last year in 8th grade, but did not generalize the material for a variety of reasons).

I also like to use this particular entry ticket because it acts as a catalyst to activate students' prior knowledge. Just like an enzyme makes a chemical reaction more efficient, this entry ticket is designed to make the upcoming work on linear functions more productive and economical. 

To conclude the entry ticket, I have students work in pairs to complete a Turn and Talk. For this exercise, students choose one of the four problems from the entry ticket and try to describe the relationship modeled by the equation. I use this cue to get students thinking about the similarities and differences between equations and functions, and to begin thinking about y=mx+b as one definition of a linear function.

Pre-Algebra Review: y=mx+b

20 minutes

To begin the class, I hand out copies of the Reference Sheet on linear equations and functions. I provide students with this information because I want to balance the tight rope of providing all students more basic information they need to fully access upcoming lessons in the unit with students already being exposed to the material. 

During this section, I first give students a few minutes to silently review the Reference Sheet: Reintroducing Linear Functions.

Students then work on the Create your own Linear Function Review Quiz assignment. Students interact with the reference sheet to create their own example problems AND explanations/answers to questions. I have students explain their answers because I want to get a better sense of how they are thinking about the material and what prior knowledge they have generalized about linear functions. 

After creating their quiz, students switch quizzes with a partner and take each other's quizzes for practice. If there is a problem that is incorrect, I encourage the partner to make a note about the error along with a suggestion on how to improve it. I review all of the quizzes after class and provide feedback to students to identify any misconceptions they have in addition to checking in with students during the activity.

Paired Practice: Linear Functions

20 minutes

During this part of the lesson, students work in pairs on the Paired Practice: Everything is Relative - Reintroducing Linear Functions related to linear functions. I want students to have a chance to converse more and practice the skills and concepts reviewed in the reference sheet from the previous section.

Students are working together to complete the Practice Problems. During this time, I am checking in with the various student groups and giving support based on the level students are at. 

For pairs that complete the practice early, they can work on writing out an explanation to one of the problems and ask them to prepare to "teach" the problem to their peers when we review the problems. 

For the last 5 minutes or so of the section I reconvene the whole class and ask students to identify problems that they had difficulty with. I first turn to peers to provide support and ways to solve the problem. If the class as a whole gets stuck (which does not happen often, unless I have an unusually short wait time that day!) then I will help with the solution to the problem for the class. 

Vocabulary: Linear Functions

20 minutes

Next, I have students work independently on completing the Vocabulary: Linear Functions Unit for the unit. I explicitly teach students the difference between Brick and Mortar Words as I firmly believe students need to be taught what types of conversation and language are valued in school AND how to engage in those skills.

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 to allow students to focus more on generating multiple representations of meaning for each word to develop a deeper understanding of the vocabulary terms. I have included two versions of the vocabulary for teachers - one with definitions - Vocabulary: Linear Functions - With Definitions and one without - Vocabulary: Linear Functions Unit

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

To conclude the lesson, I have students complete the Exit Ticket: Everything is Relative - Reintroducing Linear Functions that asks them to connect Einstein's famous quote "Everything is Relative" with linear functions.

For Homework, students are asked to complete a number of practice problems identifying and interpreting the slope and y-intercept for linear equations and graphs. 

For more information, check out the video narrative in this section: