Here is a poster of the functions in the order we plan to teach them.
The idea is to start the course with asking what they notice and wonder about the equations. Then as we study that equation, we have a giant You Are Here arrow.
Hopefully the students will see more connections and realize that only the pictures are changing.
Here is the powerpoint if you want to reorder or change the colors. Obviously my room is green and blue.
Love this. It REALLY highlights the relationships between the different types of functions. I think you (or someone that worked with you) may briefly told me about this at TMC. Its a shame that I never saw/taught it this way in the past! Using the h and k throughout is genius. Thanks for sharing.
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It's totally Glenn's (@gwaddellnvhs) idea, I just made a poster. He presented it in the morning Algebra 2 session. See my post here for a recap.
DeleteI've got a Desmos graph I used in Algebra 1 to start the exploration of the transformations. I tweaked it to align with your poster: https://www.desmos.com/calculator/bo0yytywqx
ReplyDeleteWhat if this was the final product from the students? A collection of functions defined and shifted in Desmos, with a description of how each parameter effects the graph?
There's a neat connection between the multiplying constant and the average rate of change in the interval [h, h+1] that is nicely highlighted in the polynomial and absolute-value graphs. It turned out to be a great challenge question to adjust the typical a*f(x-h)+k so that it would be highlighted for the exponential function, too!
I'm sorry, I don't really understand what you mean? Like the students would figure out what each letter means or write their own equations with numbers and explain each number?
DeleteAnd I don't really understand the last paragraph. Could you break it down?
Thanks for the Desmos!
Thank you for having posted this! I came looking for it this morning and found your post within a few minutes!
ReplyDeleteHappy to be of help!
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