Slope Intercept Scenarios

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Objective

SWBAT write an equation for a line in slope-intercept form modeling a real world situation. SWBAT determine appropriate restrictions for the model.

Big Idea

Real world situations like cell phone plan situations, savings accounts, or car rental scenarios can be modeled with linear equations in order to make predictions.

Accessing Prior Knowledge

15 minutes

Accessing Prior Knowledge:

Prior to the start of class, write the following questions on the board:

1. Suppose a line contains the point (10, 23), find another point on this line if the slope of the line is:    (a) -4      and    (b) ¼  or 0.25

2. What does it mean to have a slope of ¼ ?

After letting the students work on the problems for a few minutes, call on a few students to verbally share their answers and explain their thinking. 

 

Common Misconceptions:

The most common response to the second question is that it means the line goes up 1 for every 4 it goes over. Not that this is wrong, but when students have this view of slope, they may not understand the meaning of a line with a slope of 2.32 for example. Tell the students that slope is a single number, not a pair of numbers and that it always measures the change in height. This will reduce the common error they make when calculating slope, getting the horizontal and vertical changes mixed up. This also makes it easier to make sense of positive, negative, and zero slopes. In the slope-intercept equation for a line, an increase of 1 in x means an increase of m in y. So, thinking of increasing x by 1 makes students interpret the slope intercept form better.

                                       

New Info/Application

45 minutes

New Info/ Application

Write the following statement on the board for all to see:

Terri pays a monthly cell phone fee of 10 dollars. She also pays 5 cents per minute of use when she uses her phone for telephone calls.”

Ask the class, “What two quantities are being related here?” Another way of asking this question would be, “What determines what, in this scenario? Tell them to discuss the question with another student if they wish. Students should be able to answer that minutes spoken determine phone fee.

Once students answer, write on the board “minutes spoken determines monthly phone fee.

Pair up

At this point, students will work in pairs so they can discuss the task. Each pair should be provided with graph paper and the resources, Terri's Phone Bill and WordProblems_newinfoStudent

Tell them that they will be creating equations in slope intercept form, y = mx + b to model Terri's phone bill. Allow students time to discuss and complete the handout. Walk around listening and helping only enough to guide students, rather than evaluating or checkign answers. After all the students have completed the handout, call on different students to answer each of the handout questions. Allow the students to correct each other if someone gives a incorrect answer.

 “Milk” each question of the handout with other questions. Ask students how they obtained their answers. Ask for the different ways they found the slope. Ask for equivalent ways of writing the slope intercept form of the equation.                                                      

Practice

After answering and discussing the handout. Tell students that you will be projecting real world situations (Teacher Resource: wordProblems_NewInfo) on the board and they will use the resource, slopeintercept_Res2B, to complete with their partners. Each problem should take at most, 15 minutes to complete and graph.

Project one problem at a time and allow the pairs of students to read the problem to themselves, discuss it with their partners and then complete the corresponding section in resource 2B

After they’re done, ask a group to come to the board , state their answers and sketch the corresponding graph on Graph Chart paper and stick it on the board for all to see. Allow a couple of minutes of discussion with the class if needed. Do the same for each of the remaining word problems.

 For students that may be having difficulties, you may ask them to watch this video titled "Linear Equation Word Problems" 

Resources for NewInfo/Application section:

  • slopeintercept_NewInfo
  • wordProblems_NewInfo Word Problems for teacher to project)
  • Word Problems_newinfoStudent
  • Graph Chart Paper (4) (teacher)

 

 


Generalization

15 minutes

Generalization

In order to revisit the goal and help students retain what was learned in class today; ask each group to take a few minutes to summarize the goals of this lesson. They can write it down first before stating it out loud. In their summary they should:

  • Mention how they determine the slope and the y intercept of the equation from the context of the problem. Allow the use of examples.
  • Mention how they know when there are restrictions or not.
  • Mention how their equation is used to make extrapolations.

 Call on various students to read their summaries out loud.

HOMEWORK:  See Resource: HOMEWORK_SlopeInterceptform.docx

Extension:

Analyze the graph below, or see Resource: extension_graph.

1. Create a real world situation that can be modeled by this graph.

2. Write the equation of the line in slope intercept form.

3. State what the slope and y intercept mean in your problem.

4. Describe the restrictions, if any.