I teach out of the Discovering Algebra Book. Last year I tried out the order in the book, and it was disastrous. The book introduces a new parent graph with each transformation. That did not go well with my students. It was confusion city. This year, I went back to what I know. I taught parent graphs first, then transformations. Finally, they learned how to write equations given the graph with dilations. Whew.
Glenn’s convinced me to use the “transformation form” (AKA h,k form) last year in Geometry. That was a great start with my students in Algebra 2, as we were able to use it right away starting with linears. I can’t tell you how many problems using the transformation form solves, and how relieved kids eventually are, not to be married to the y-interecept. Many times, they aren’t given the y-intercept, so y=mx+b is used much more sparingly this year. It takes my newbies a while, but they get it. Why kill yourself trying to find where this stinking graph crosses the y-axis when you could put pick ANY point out on the line.
Thanks to Glenn, I knew to use transformation form from the start. Thanks to Meg, I had a ton of material to draw from. And thanks to Desmos, the kids could actually discover transformations ON THEIR OWN. Disclaimer. Even with all of this wonderful discovery and conceptual learning, students NEED you to summarize what they have learned with them, and then keep them practicing their new discoveries to cement those discoveries into their brains. With conceptual learning, many times they are pretty sure they understand what is going on, but they really love when you affirm that. Also, some kids have a tough time getting there, so a thorough summary at the end helps everyone.
When I taught transformations years ago, I would teach parent graphs, then give them a list of transformation rules to learn and apply. It was pretty dry and procedural. Now, I have moved to Desmos, where the students play with graphs to learn what the transformations do without ever seeing any “rules”. It is awesome, and it sticks.
I still teach parent graphs first and function notation first, along with domain, range and interval notation. I actually teach them with the material in the previous chapter so they can know the parent graphs cold before we even start looking at transformations. After they learn the parent graphs, they study transformations and reflections and then move to dilations. Oh, those dilations. My students work with computers and each other for the entire unit. I also give them handouts so they can take notes and graph as they go along. I didn’t give them the “transformation rules” until one of the last days.
All of my transformation files are in this box folder. And the Desmos Teacher Activities are linked below. You can’t use my activities, but you can’t copy Desmos activities YET for editing. I am sure that is coming soon. You will see a vocabulary sheet referred to in the Desmo’s activities. To start every chapter, I give my students a vocabulary sheet. They takes notes on it and then most of their important terms are together in the same place. The vocab sheet is also in the box.
Desmos Teacher Activities – Transformations
- Transformations – Shifts and Reflections
- Transformations – Dilations
- Dilations again (as a short review in-class lesson)
- Transformation – Extra practice