Function Model Construction and Application
Construction is where a model stops being a family and becomes a formula: quantities named with their units, each number from the story placed in its proper slot, and easy cases fed back through to confirm the roles. When the new situation is an old one rescaled or re-zeroed, the transformation rules do the building, with the same inside-versus-outside discipline they demanded on bare graphs.
Application is the honest use of what was built: parameters read in context (the 40 in 500 - 40t is gallons per minute, not a capacity), units carried through every rate, error sized rather than denied, and predictions kept inside the window of data that earned them. The lesson drills each of these, because every one has a signature mistake attached.
The work
3 ways in · any order
Lesson
Function Model Construction and Application
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Naming quantities before writing formulas, building new models by transforming parents, and reading every parameter back out with its units. The lesson closes with ten scenarios: construct the model from the story, interpret its numbers, size its error, and know where its authority ends.
Diagnostic
10-item topic check
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Ten items spanning the Topic 1.14 misconceptions: story numbers placed in the wrong slots, transformations attached to the wrong side of the function, parameters misread in context, and predictions trusted far outside the data window. 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.