Math Monday -- Parent Graph Transformations Lessons

 

The start of this year is tough. My schedule is tough. I teach straight through on Mondays, Wednesdays and Fridays with only lunch as a break. I have two prep periods on Tuesdays and Thursdays, but they are usually spent giving extra help to students. Our school requires teachers to be there from 7:30 to 4. School goes from 8:15 to 3:15. I have to say the extra time until 4 is a waste for me because my brain just needs a break before I can really think or function on work. I often have to wait until after dinner to get any more work done. As a teacher I feel it is a little ridiculous for any school to have set hours for teachers besides the required ones when the school is open. Teachers by nature will do the work they need to on their own time. We are not teaching because we want to be rich or famous. We teach because we want to teach and be with the kids. After three weeks in, I'm still getting use to the schedule and figuring things out.

Besides our new schedule I have new books for three of my four preps. (My fourth prep doesn't have a book.) The new books are different from other books I have used in the past. They don't begin with review and assume students have prior knowledge. The geometry book I am fine with as a geometry book is a geometry book. Geometry for the most part is its own entity. The algebra books however jump into some hard concepts. I struggled with the Algebra 1 book until I realized the second module (instead of chapters) was more what I would expect, and I skipped the first module. The Algebra 2 book however assumes kids know set and interval notation. This is a topic not usually taught in Algebra 1 and sometimes isn't seen before precalculus. So I spent a few days teaching it and did not show the kids where one of the authors calls it bookkeeping and not math. I got them through topics like domain, range and end behavior. Then we began transformations. I tried to teach it like the book but found the kids were just getting more confused for the most part. Now we picked these books because we felt kids could use them on their own if they missed a class or were not completely understanding a topic. But my kids were really struggling and coming to me for extra help constantly. I am lucky enough to teach in a school where there is no rush and we can teach at the pace required to get the kids to understand. I was spending days on these. Then I went home after several days and really thought about how to help the kids understand this topic. I made up a graphing worksheet to do together with two quadratic equations and two absolute value equations and the next section was doing transformations to these parent functions. We got through the two quadratic equations the next day. As I did them on the board for the kids, I added in more tools for them like the mapping equations and a table. Basically, I came up with something like this sheet for my kids. I made this sheet today for you to use in your classroom. Please share a link to this post if you want to share it with another teacher. Do not sell my sheet as I offer it free to anyone. 

Once the kids get better at this they won't need the transformation section or the printed mapping rules. For some graphs they will want to graph on a piece of graph paper, but I wanted to provide a grid on the same page to begin. In the Google Doc I also provided the following examples (without the graph since I did them by hand). 

For each of the parent graphs I have given the kids the points to use with x-values -2, -1, 0, 1, and 2. If they are doing other graphs you may want to change the points and if they are doing a transformation to a piece of graph they can read the points from the graph. Many of the kids now understand the transformations much better with this new method. Some have asked to use the old method or the book method and that is fine as well. 

Have you found a good way to explain graph transformations? Today I plan to show them a desmos graph of the sine function and show the vertical and horizontal stretches, etc. so they can truly see the differences between them. 

I will turn off some of the graphs as we discuss the various transformations. Since we have mostly been working with even functions the vertical and horizontal stretches and compressions look very similar so the sine function will be good to show them the difference. I would love to hear any suggestions for explaining transformations or if you try my method how it works for you.