12th Grade Math : Unit #1 - Basic Functions and Equations : Lesson #6

Shifting Functions: How can we describe them?

Objective: SWBAT use horizontal and vertical shifts and stretching to sketch the graphs of functions and identify key features of the graphs and how transformations change these key features.
Standards: HSF-IF.B.4 HSF-IF.C.7a HSF-IF.C.7b HSF-BF.B.3 MP1 MP2 MP3 MP6
Subject(s): Math
60 minutes
1 Warm-up: Clicker Questions - 15 minutes
Shifty Functions - describing, video narrative, warm-up.MP4
2 Application: Shifting and Key Features of Basic Graphs - 30 minutes

Before starting today’s activity, I am going to take a few minutes to talk about the mathematical practice standard of the day. Today I want students to focus on MP6 by attending to precision as they complete this worksheet. I want student to understand that this is definitely a practice that we all should always be cognizant of in a mathematics classroom. To help students better understand this standard I will give them a few examples: This practice could mean making precise graphs by labeling the axis and scaling and accurately plotting the points. Or it could mean working precisely with numbers by rounding correctly and as appropriate (maybe an estimate is only required) and using the correct units. It could mean communicating (listening, reading, writing, and speaking) precisely by using correct vocabulary and symbols. And THIS is specifically what I would like them to workon today. Work on using correct notations to communicate to others the key features of the graphs.

Students should complete the five problems on the Shifting and Key Features of Basic Functions worksheet today in class. One goal of this lesson is for students to have time to work on this in class so that they can get help on any concepts they don’t understand. I am not going to limit the questions students ask today. Instead, I plan to just make myself available in the classroom and have students come sit down with me when they need some extra tutoring. This will allow me to do some small group tutoring to catch up struggling students. When I do a ‘tutoring station’ like this, I am sure to not sit at my desk. Typically, I pull up together a few student desks on the side or back of the room (somewhere I can still keep an eye on the class and that my students feel I am accessible). Then I like to have some whiteboards and markers available to assist with tutoring. Due to not working the classroom as much as I normally do and the fact that I am not sure how motivated my students are going to be, I am planning on ‘collecting’ (or really just walking around and checking it off on a roster) and grading this worksheet on completion.

Tip for newbies: New teachers: stop collecting so many papers! That was the best advice I ever received from a veteran teacher. Eventually we hope to get our students so intrinsically motivated to learn mathematics that we won’t need to score their work other than for the sake of providing feedback, however, my students aren’t there yet. So if I do feel the need to check in on their work, I like to just carry around a clipboard and check off whether or not a student has completed the work. They then get a stamp for completion and are asked to go file their paper in their folder (I have 5 crates labeled by period with a manila folder with students’ names). I tell students that I will go back and look at it in more detail later. Does that happen? Not typically. :)

To move on or not to move on?

On the third day of shifting graphs, I still feel like I don’t have all of my students on board. My classes at this point are really struggling with me not telling them how to do things. They are really yearning for some formalized notes. Some don’t seem to be retaining the information from that first day of exploring shifting packet. Their misunderstandings became apparent to me for some in their postcard to absent student closure (see examples in the reflection below). I do believe this is an important concept, but I am going to move on at this point. I know that transformations of graphs is a common theme throughout the school year, so I if it hasn’t quite settled in for students at this point I know they will be getting the information again.

3 Closure: Postcard to Absent Student - 5 minutes

Narrative: In the last few minutes of class today, have students stop and summarize today’s learning by writing a Postcard to Absent Student.  If you choose to do so, now would be a good time to check students work while they decompress the learning for today.

Preparation: You may want to have index cards available for students to complete today’s closure on. I think it helps to have this limited space to write so that students are required to summarize the learning instead of writing about everything.

Postcard Examples

I found that my students’ responses on their postcard fell into one of three categories. Either students demonstrated some level of (A) mastery of the learning target, (B) misunderstandings of the learning target or (C) a summary of the activity. A and B postcards were helpful, C postcards were not. So I need to find a way to better prompt students in the closure. Next time I am going to be clear that I don’t want students to just summarize the directions they had on their worksheet.  If anything, I would rather they pick one thing they learned and really explain how to do it. The key here, I think, is to ask students to ‘teach’ the absent kid how to do it. Not just tell them what we did in class today.

To start class tomorrow, I am going to pick out my ‘favorite yes’ and my ‘favorite no’ and discuss these with the class. Also, I did note how many of these postcards focused on shifting of function, but not many talked about describing functions. Interesting! I guess we need to talk more about describing functions. We will be doing that more as the unit continues.