Synthesize and demonstrate mastery across the full year: proportional relationships, rational-number operations, expressions and equations, circles and geometry, and probability.
This final week celebrates the whole seventh-grade toolkit: testing and using proportional relationships, adding, subtracting, multiplying, and dividing signed numbers, simplifying and solving equations and inequalities, circles and cylinders, and probability of simple and compound events.
Real problems often combine more than one of these tools at once, the same way this week's example blends circle area with probability -- noticing which tools a problem needs, and in what order, is the true test of a year of learning.
Mastery looks like: They correctly solve multi-step problems that combine at least two tools from across the year, with accurate, checked computation.
Common stumbles: Applying only one tool to a problem that actually needs two chained together; rushing the synthesis instead of identifying each needed step first.