Change Us and See What Happens!

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SWBAT analyze differences and similarities in graphs as the slope and the y-intercept of are changed.

Big Idea

In this lesson students discuss difference in steepness, translations, and parallelism using graphs and equations.

Warm up

15 minutes

For this Warm up, I allow students to use an online interactive tool to view changes made to a line when changing the y-intercept or the slope. By adjusting the sliders for the slope and the y-intercept, students can dynamically interact with the equation for a line. I want the students to visually see the change on the graph as they adjust the parameters. This activity could easily be done using a number of different technologies (Geogebra, Desmos, Graphing Calculator).  

I expect that my students will recognize the translation movement of the line vertically (up and down the y-axis) when the y-intercept slider is adjusted. At this point, my students should be able to recognize if the slope is increasing or decreasing. Today, I will be observing and listening to the comparison statements that they make as they change the parameters using the sliders. I want my students to accurately and precisely describe the differences between graphs.

I will check for understanding of the transformations when either parameter changes by questioning students when reviewing the Warm Up.

Slope Stations

30 minutes

For our next activity students will complete five different tasks, working in groups at their tables (see my Pedagogy of Slope reflection). I already have my students grouped in homogeneous pairs at their tables. For this station work I combine two pairs of students together. I have decided not to rotate groups to new stations, because it will take up necessary time today.

As we begin I hand each student a packet of the Slope Stations Instructions. The groups may work through stations in any order they choose. I have each group set a timer on one of their cell phones and place it on the table. Each station should take approximately six minutes. However, I encourage groups not to rush, and some stations may  take longer or shorter than 6 minutes. The timer is to guide the group on how much time is left in the 30 minutes.

In order to discourage distractions I let students know that the uncompleted stations will be completed for homework. As I announce this, I encourage groups to select problems that seem more difficult to complete first. I say, "Work together on the hardest problems, then you'll have the easy ones for homework if you can't get through them all."

I expect Station 4 will be the most difficult station for my students. I demonstrate this problem in the video below.


Independent Practice

20 minutes

We may or may not get to this activity, depending on the pace and flow of the Slope Stations activity. If my students all complete the Slope Stations, I will assign the Independent Practice as homework.

The Independent Practice worksheet takes about 20 minutes to complete. The problems challenge students to use their of slope to understand real world problems and graphs.  They assess my students' ability to think of slope as a ratio comparing the independent and dependent variable of a function. Students create their own graph. They review the idea that two lines that have the same slope are parallel.  

Although I will be flexible in how I implement this activity, I will try to use it in a way that allows me to collect it during tomorrow's lesson to see how my students are progressing with their understanding of slope.