Writing the Equation of A Linear Function (Day 2 of 2)
Lesson 17 of 19
Objective: SWBAT build a linear function given two coordinates that lie on the graph of that function.
Students should work individually for the first 3 minutes on write_linear_equation2_warmup. They can choose whatever means they would like to solve each of the questions including graphing the points. Students should be able to explain the answer to each question using the concept of slope. Students should also look for the pattern in the structure of the change in the x and y coordinates in each point (MP7). After the first three minutes have the students do a turn and talk to compare and justify their answers with their partner (MP3).
Students should start to realize that a minimum of two points define a line and that the slope of the line will determine which other points are on the line.
This clip from the Big Bang Theory shows Sheldon talking about the number of chirps a cricket makes based on the temperature in the room. This funny clip will hook students interest and get them thinking about the problem before they attempt to solve it themselves.
Without any instruction share write_linear_equation2_launch and let students work with their partner to determine a way to solve the problem (MP1). Explain to students that they may be sharing their results with the class using the document camera. Because of this, once they have a plan they should try to make their work as easy to follow as possible. Make sure there is graph paper, rulers, etc. available so that students can access it if they choose to do so (MP5).
While students are working, make note of the solution methods that each pair of students is attempting to use. Some students may be able to determine that there is a 4 chirp increase for each increase in degree (MP2) (the slope of the line or common difference). They may, however, get stuck in trying to find an explicit formula for the number of chirps based on the temperature.
After students have been given time to work and think bring the class back together to share ideas about how to find the explicit formula. Start with groups that were having difficulty finding the slope of 4 and build off of their ideas first. Then work backwards to find an equation either in point-slope form (y-124=4(x-68)) or slope-intercept form (y=4x-148). Help students understand how both of these equations can be used to find either the number of chirps or the temperature.
Traditionally, this lesson will include some instruction on the slope formula (y2-y1)/(x2-x1). I have chosen to focus on the concept of slope as change in one variable compared to change in another. This helps students understand the concept of one variable changing proportionally in relation to another rather than simply memorizing a formula. Teaching this formula is certainly an option and is not being discouraged.
Let students work on write_linear_equation2_independent with a partner and observe which students are starting to grasp the concepts and which students are struggling. This could be a good time to regroup students, if necessary, so that they can work in a more guided way with you on this question. Let one or two pairs of students share out their thinking with the class and allow others to discuss the solution method in comparison to their own (MP3).
This Ticket out the Door is an intentional step down in rigor from the day's work. The idea is to use the first question to give you a baseline understanding of the underlying concept of slope. Students can solve this problem in any way they choose. The solution method will give you some good insight into the way students are thinking about the problem.
The last two questions are designed to revisit the concept of writing the equation of horizontal and vertical lines. However, the question also ties in finding the equation between two points. You may see a lot of hands go up when students see that there is no slope or a zero slope between the points. Many students may be confused. You can tell students that they should write down what they are thinking in the best way they can. Tell them not to be concerned about the right answer, you just want to see what they are thinking.