Writing Linear Equations (Day 1 of 2)

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Objective

SWBAT write equations in slope intercept form in scenarios depicting linear growth.

Big Idea

Students will analyze the different components of slope intercept form, and the purpose of each component in the entire equation.

Do-Now

10 minutes

Students will complete today's Do Now. While students are working, I will circulate around the room passing back the graded exit cards from our last class.

After about 4 minutes, I will ask volunteers to come to the front of the room to walk the class through their responses to the Do-Now.  Then, we will quickly discuss the responses to the old exit cards. 

Next a student volunteer will read today's lesson objective,  "SWBAT write equations in slope intercept form in scenarios depict linear growth".

Before we begin, I will ask students what word is hidden in the word "linear" and to make a prediction about the meaning of this word.

Group Challenge

20 minutes

** Multiple bags of 8 ounce styrofoam cups are needed to complete this activity **

The primary activity in today's lesson is a group challenge. As they pursue the challenge, students will record data using the top section of their Guided Notes. They will follow along using this Presentation.

I begin by telling my students that their challenge is to figure out how many stacked styrofoam cups it would take to reach to the top of my head. But, they will only be given 4 cups to figure out an answer to this question.

I will give students a quiet moment to think about the task. Then, I will ask students to think about what information is needed to be able to answer this question. I will again pause, and after a moment allow students to share their plan of attack to the group.

I expect that right away, at least one student will say "We need to know how tall you are..." or "We need to know how tall the cup is..." I will ask 2 volunteers to come up to the front of the room to measure my height and the height of the cup in centimeters.

Next, I will ask students to predict the height of two stacked cups. Many of my students will immediately double the height of one cup. I expect at least one will announce that it would only take 18 stacked cups to reach the top of my head. If (when) this occurs, I will stack 18 cups to show students that that cup tower barely reaches my shin. 

At this point students will immediately see that this situation will require more thought than initially anticipated. I will let the class continue to brainstorm aloud for a few more minutes. If the suggestion is not made by a student after a few more minutes, I will prompt students create a table to measure the height of 1, 2, 3, and 4 cups.  I will use the questions below to guide the discussion:

  • Why is the height of one cup 9 cm but the height of two cups 10 cm?
  • Does anyone see a pattern?
  • What is the height increasing by each time?
  • What would the height be if I stacked 20 cups?
  • How should we measure the cup?
  • What are the two important sections of the cup? 
  • How tall is the base? how tall is the lip? (See image)
  • Look at your notes from the last class. We created three equations from the carnival example. Can anyone create an equation for this situation?
  • What would f(6) referred to in this situation?
  • How many cups would it take to step to the top of my head? Use your equation to figure this out.

To close our investigation, we will stack the predicted number of cups to visually test if the function that my students found is correct. 

Guided Notes + Partner Practice

40 minutes

Students will copy slope intercept form inside of the box on the middle section of their Guided Notes. I will ask students to help me create a list underneath each component of the equation. Eventually the section should look like this.

We will complete Problems 1 and 2 as a whole group so that I can model the exact type of thinking and reasoning needed to interpret a linear situation. Students will work in pairs on the rest of the problems until the end of class. We will check back in every 10 minutes or so to review the responses to a few problems at a time.  Many of my students did not finish this entire activity in one day, so we will continue working on the problems during our next class.

The most common issue that I see when my students work on these problems is that they answer questions with the words "input" and "output", and not in terms of what is happening in the context of the problem. I have found that the best way of combating this misconception is through continued practice. To help students who are still struggling, I will prompt them to make a table of values for each, and to use the headings of the table to interpret the meaning of the situation.

 

Closing

10 minutes

To conclude today's lesson I will ask students to compare the functions f(x) = 1x + 5 and g(x) = 5x + 1. I will ask students to decide if these functions are the same, and if the order of the numbers is important. I will ask a students to use a table of values to justify their response.

Students will then complete an Exit Card so that I can review each students' work before tomorrow's lesson.