The Tablet Wars: Comparing Linear Functions in Different Representations

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SWBAT compare and contrast linear functions represented in different ways (graph, table, equation). SWBAT use evidence from their work to strengthen logical arguments

Big Idea

Students make the connections between different representations of linear functions to analyze profit trends for different companies selling tablets!

Entry Ticket

15 minutes

For the Entry Ticket: Tablet Wars - Comparing Linear Functions in Different Representations student first work independently on problems involving finding the slope and y-intercepts for linear functions. The twist to this entry ticket is the functions are not always represented in the same way - some are represented as equations, others graphically and others in tables. The intent is to start having students to become experts at identifying what it means to be a linear function, no matter what the representation.

I typically give the class about 7-10 minutes to complete the problems, and then have them complete a Turn and Talk with a partner. For the turn and talk student pick one problem and dive deep in terms of their thinking about the problem and what strategies they needed to solve the problem. This also give an opportunity for students to talk about problems that they had difficulty with and perhaps figure out why they had difficulty with the problem. 

After students have a chance to complete the turn and talk, I reconvene the class and begin the next section of the lesson.


Direct Instruction and Active Note-Taking

20 minutes

In this section students are active note-takers using Two-Column Note Form. In this 20-minute section of Direct Instruction, I review a number of problems similar to that found on the entry ticket. The Problems are found as a resource in this section.

As an alternative, teachers can print copies of the problems and have students take notes on the problems that are already setup for them. For each problem, I ask students to translate the linear function into other representations (table, equation, graph and a set of points).

During this time I am sure to provide Explicit Instruction, clearly stating the how and the why of solving the different problems.  I write each of the problems below one at a time and work through the problems with the class. I encourage students to engage in active note-taking strategies during this process so the problems serve as a reference that they can use for help with homework and studying for tests.

Student engagement is a big part of the note-taking process. While I have a set of problems and solutions to review with the class, I try to include a number of prompts along the way to keep students engaged and thinking about the process. What I want to avoid is students passively copying down notes from the board. 

Some example prompts I use are...

-How does x change compared to y based on the table of values?

-What is the value of y when x =0? What does this tell us about the function?

-What other observations about the table of values do you notice?

Collaborative Class Activity: Tablet Wars, Part 1

20 minutes

Students continue working on the Class Activity: Tablet Wars - Comparing multiple representations of linear functions in this section. This activity fits in well with the Math Practice MP.4 of modeling as well as MP.3 as students are working in partners and have to navigate and reconcile their own arguments with that of their peers. 

The activity consists of a packet, with one company on each page. Students have to translate between different forms of the linear functions (for example, for the first example, students are given the information on profit for Samsung as a graph and are asked to calculate and interpret key features of the graph). 


Collaborative Class Activity: Tablet Wars, Part 2

20 minutes

After students complete the information about Dell, Samsung and Apple then they turn to composing a written response to a number of questions about the data. The prompts for the written response are on the last page of the Class Activity on Tablet Wars.  

I like to use the Idea Organizer, a template that I use to help students organize their writing (in the resource section of this section). I would suggest that students type their responses they they can edit and polish them at home, but writing out on lined paper is a perfectly fine alternative. Teachers can also use a laptop cart, computer lab or any other access to technology and have students type up their responses that way. 

In this section the focus is on giving students an opportunity to apply the mathematics about linear functions to a real-world situation and engage in meaningful critical thinking skills. I like to focus on question d that asks students to make a decision about which company they would choose to invest in. This is once example of pushing students to provide examples of mathematics to back up their arguments.

As students work on the written response, I am circulating the room checking in on students, first focusing on students who are not moving their pen/not typing - with writing I think it is crucial for students to start the process in the first few minutes to avoid writer's block, or the anticipatory anxiety that can snowball with the writing process. 

Exit Ticket and Homework

15 minutes

To conclude class, students work on the Exit Ticket and begin the Homework: Comparing Linear Functions in Different Representations as time permits.

For the Exit Ticket, students complete a Think, Pair, Share as a way to reflect on the day's lesson. 

I write the following reflection prompt on the board for students to ponder:  

Reflection – write at least one sentence describing how you felt about this assignment – which representation (graph, table or equation) is easiest for you to work with and why. Write down one task or problem from this assignment that you think you need more review/work on. 

Students are given 2-3 minutes to write down their ideas and reactions to the prompt. For the next 3-5 minutes, students turn and talk to a partner about the reflection. For the remaining 7-10 minutes, I have a class discussion with different students sharing their thoughts about what students understood and what areas students need more help with. 

The Homework for tonight is twofold: 1. complete the written response and edit the class activity on tablets (for any students who did not complete the assignment) and 2. practice problems on calculating the rate of change and intercept for linear functions in different forms (similar type problems to the entry ticket - this way I have pre and post data that I can anlyze to see trends in student learning on the topic).