Our goal was to simply look at function equations and identify what the numbers meant and stood for.
The background of our text...cell phone plans.
We had already analyzed f(x) = 18 + 0.04x and f(x) = 0.10x.
Finding when the two plans would cost the same.
I put up the function f(x) = 10 + 0.05x.
Someone asked when it would cost the same as the first one.
Within seconds, a student answered 800 minutes.
I was amazed at how fast he got the answer.
I wanted to get in his head.
So I asked him how he solved that.
He explained,
No one followed.
Not even me.
He explained it again.
Aha!
We then looked at f(x) = 8+0.06x.
We found intersecting points.
I all of a sudden realized my students were solving systems of equations without even knowing it!
A beautiful math moment.
We extended it then by graphing them on a calculator.
Everything on the graph confirmed what we had just solved.
The students quickly realized that graphs help to support their answers.
A student wanted to know when the "red line" would cross at (200, 20).
This required changing one part of the original function.
Students quickly jumped at the challenge and found the answer.
f(x) = 12 + 0.04x
f(x) = 18 + 0.01x
The wonderment and awe.
The perseverance.
A math teacher's dream.
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