Monday, October 29, 2012

Transformations Unit

Last year, I shared the transformations matching cards I used with my Advanced Algebra 2 students. With teaching transformations for the first time to all Algebra 2 students, I have revamped my lesson and cards. Thanks are due to @druinok for her help in hashing out what I was doing with this unit.

I'm working with F.BF.3:
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

After discussions with both @druinok and our pre-calculus teacher, I decided to hold off on the f(kx) portion. @druinok shared that in her state, they don't do the horizontal stretches and compression in Algebra 2 and our pre-calculus teacher said that until you are working with a periodic function, the horizontal and vertical appear to be the same. So I will wait to bring in the f(kx) part until we get to graphing sine and cosine later this year.

I began very similarly to what Rebecka Peterson did by introducing parent functions to my students on day one. Here is what I gave my students:

(I don't know WHY the graphs keep showing up wrong, but they do. It looks right in Word but I can't get it to show correctly.)

It went way quicker than I anticipated - it only took about 20-25 minutes from start to finish. I haven't decided if in future years I will start into the notes following this or what to do to not leave so much open time on day one.

The second and third day, we worked through this packet:

 (Like the last one, still having issues with the graphs. Not sure why.)

The second day, we got through the first two pages of the packet. I had students work through the three graphs and descriptions and we did the summary piece together.

The fourth day, I had a meeting. I left an activity that their Algebra 1 teacher called "Around the World." I've done this as a scavenger hunt before. Here are the pages I used:

I had a brainstorm for my fifth day activity. I didn't feel real comfortable coming in after being out the day before and having them start into the assessment activity. So, after going over questions from the practice problems and the Around the World activity, I had students make "appointments" like in the Appointment Test Review activity that Mrs. H blogged about. Then I had students make up 1 or 2 equations for functions that they transformed (depending on how much time was left in class). The only guideline I gave them was that each equation had to have at least 2 transformations. Then, when they met with each appointment, they exchanged equations and had to find the transformations. This went pretty well for many students, although some still had some difficulty coming up with the transformations after they made up their equations. Most students went with two transformations. I collected their cards at the end of the period.

On the sixth day, I had students do the Transformations Matching Cards as their assessment for the activity. I had them work in pairs and allowed them to use the note pages. Rather than have them complete 5 sets like I had last year, I had them work through 3 sets. Students are matching pictures of the graph with the description of the transformations and the equation of the graph. I had students work with the five parent functions they graphed on the first day. Many of the equations came from what they generated on the 5th day. Here is the what I gave them:

They did very well with the assessment - I am sure part of that is that I allowed them to use their notes and their cards with the parent functions. Possibly next year I would allow them to work in partners but without notes, but still with the parent function cards. Overall, i am pleased how this unit went.

All of the files I used are shown through - they are in docx format and you are welcome to download and adjust them as needed. If you are having trouble, feel free to email me at lmhenry9 at gmail dot com and I'll be happy to email you a copy directly. I hope this helps someone out.

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