Unit 6 · Core unit
Choosing a function family from data and defending the choice. This unit is where the rest of the course becomes usable.
What a strong answer looks like
A strong answer names the family, justifies it from the pattern of change, and interprets each parameter in context.
Know
Constant differences indicate linear, constant second differences quadratic, and constant ratios exponential.
Apply
Compute differences and ratios from the data before selecting a family.
Watch out
Choosing a model because the data grows quickly, without checking which pattern of change it follows.
Study move
Given three tables, identify the family for each with evidence.
Know
Every parameter means something in the situation: a rate, a starting value, a growth factor, or a shift.
Apply
State each parameter in a sentence with units.
Watch out
Reporting a fitted model without saying what its numbers mean.
Study move
Interpret every parameter of a model in one sentence each.
Know
Some equations have exact algebraic solutions; others must be solved graphically or numerically. Knowing which is part of the skill.
Apply
Attempt algebra first, then switch to a graphical intersection when no exact route exists.
Watch out
Reporting a rounded graphical answer as exact.
Study move
Solve one equation exactly and one graphically, labelling which is which.
Modeling drill
Given a table of values, choose a family with evidence, fit a model, interpret its parameters, and predict one value.
