Change in Tandem
Every function is a record of two quantities changing in tandem: input moves, output responds. This topic sets the vocabulary the whole course leans on, increasing and decreasing for the output’s direction, concave up and concave down for whether the rate of change is growing or shrinking. The two layers are independent: a function can fall while its rate of change rises, and a graph can bend down while the thing it describes gets wider.
The mistakes here are not computational. They come from collapsing the rate into the value ("concave up means increasing") and from reading a graph as a picture of the scene instead of a relationship between quantities. Both are named, drilled, and un-learned in the lesson.
The work
3 ways in · any order
Lesson
Change in Tandem
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Increasing and decreasing describe the output; concavity describes the rate of change. The lesson keeps the two layers separate, walks the vase-filling classic, then closes with ten scenarios: read graphs and tables for direction and bend without turning them into pictures.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 1.1 misconceptions: collapsing concavity into increase/decrease, and reading a covariation graph as a literal picture of the scene. The bank ships with the Unit 1 data drop.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.