1. Question and context
Frame a specific, ethical, measurable question that genuinely uses this unit’s mathematics. Identify stakeholders, desired outcome, and what would count as useful evidence.
Unit 05 applied investigation
Radical Measurement & Inverse-Relationship Lab
How do radicals, rational exponents, inverse relationships, and domain restrictions describe quantities that grow by roots and powers?
2. Variables and assumptions
Define all quantities, units, domain, data source, constraints, and assumptions. Explain why the selected mathematical structure fits.
3. Build and compute
Create at least two representations, show exact and approximate work, use technology strategically, and preserve enough detail for reproduction.
4. Validate and revise
Check with substitution, residuals, alternate methods, or cases. Analyze sensitivity, uncertainty, fairness, and model limitations.
5. Communicate
Present claim, evidence, reasoning, visualizations, limitations, and a conclusion that distinguishes mathematical result from recommendation.
6. Defense and reflection
Answer critique, revise transparently, and explain what the model can and cannot support.
100-point analytic rubric
| Criterion | Points | Evidence |
|---|---|---|
| Question, context, ethics | 15 | Specific and answerable; stakeholders and constraints identified. |
| Mathematical structure | 25 | Correct Algebra II methods, representations, and domain. |
| Computation and technology | 15 | Transparent, reproducible, verified work. |
| Validation and uncertainty | 20 | Checks, residuals or cases, sensitivity, limitations. |
| Communication and defense | 15 | Clear claim-evidence-reasoning and response to critique. |
| Revision and reflection | 10 | Meaningful improvement and honest reflection. |