My renewed enthusiasm for old childhood joys has come at an opportune time. In Tuesday's lesson, we will be working on transforming functions. I have a few transformers that have (incredibly) survived until now, which are currently gathering dust on my mantle. Hmm... do I bring in the opportunistic, irritating Starscream, the powerful, pea-brained Grimlock, or, everyone's favorite transforming boombox, Soundwave (though his head is broken off and I don't have any of his tape-minions).
In any case, my idea for this lesson is to have the students work on a scaffolded exploration for most of the class. They will work on learning transformations, as well as absolute value (of linear) functions. They can work individually, in pairs, or in groups, but each person must turn in their own paper by the end, and it will be graded like a quiz. The exploration/quiz is broken into 4 parts:
1) Creating absolute value functions.
In this part, students will graph a linear function. They will then graph the absolute value of the same line by looking at the y-coordinates of several points, and plotting their absolute values. They will have to then answer questions that help them see that y = |mx + b| will always make a V shape.
2) Translating absolute value functions.
In this part, students will review horizontal and vertical shifts from the previous lesson, but applied to absolute value functions.
3) Transforming absolute value functions.
In this part, students will plot out y = |x| and various transformations in the form y = a|x| to see what happens. By the end of this part, they should have a good sense for how the coefficient a affects the shape of the graph.
4) Synthesis
In the final part, students will put together what they know about translations and transformations to create the graph of f(x) = 2|x + 4| - 3. Then, they will generate a table and see if their ordered pairs fall on the graph that was created via the translation/transformation process.
After this, we will end the class with 15 - 20 minutes of direct instruction where I help formalize their understanding of transformations. I'm worried about running out of time for this. If I do, I can push it to the next class, and that will be ok, though it would be better in the same period. I hope that making the exploration into a quiz will help students focus and be more efficient with their time.
The lesson will be posted on ILoveMath.
Update:
Whoops.. I forgot that the entire sophomore class is out on a field trip to the Monterey Bay Aquarium for biology. My classes today have had about 4 people each. I got some good one-on-one time with my handful of juniors, and I'll just have to push things back to Thursday.
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2 comments:
Grimlock pea-brained??
from Wikipedia:
"One of his most distinguishing features is his famous speech impediment, which leads him to shorten sentences and refer to himself constantly as "Me," never "I" - the reason for this varies from depiction to depiction, with some making it the result of true mental limitations, and others a ruse Grimlock perpetrates to allow others to think of him as less intelligent than he actually is."
In step with silly 80's cartoon life lessons, perhaps Grimlock was the smartest of them all!
And here I was questioning the value of Wikipedia. I never knew a Dinobot could be so Machiavellian.
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