Use accurate diagrams, definitions, measurements, and reasoning to frame, build, test, document, and defend a geometric investigation or design using evidence, proof, and responsible limitations.
Success evidence
Label the figure and units before calculating.
Select and justify the governing definition, theorem, relationship, or construction.
Show enough work that another learner can audit the conclusion.
Check the result against the diagram, scale, and stated constraints.
Visual model
Frame, build, test, document, and defend a geometric investigation or design using evidence, proof, and responsible limitations.
Process: Define the question and constraints, select appropriate geometry, build and test the model, document limitations, and revise after critique.
Read the figure and rewrite all given information with correct notation.
Identify the exact relationship that connects the known and unknown quantities.
Substitute, construct, or prove one justified step at a time.
State the result with units and a sentence explaining what it means.
Misconception check: A polished final product does not replace mathematical evidence; the model must show how measurements, constructions, and conclusions were validated.
Khaemenes Academy · Open-Age Geometry
Present, Defend and Revise the Design
Find, construct, prove, or explain each result. Show reasoning and label units.
U13 · L05
Name
Date
1
Write one geometric question that is measurable, constrained, and answerable.
Answer: A clearly defined design or investigation question Reasoning: It must identify the object, measurements, and decision to be made.
2
Distinguish an assumption from a verified measurement.
Answer: An assumption is accepted for modelling; a verified measurement is observed or checked Reasoning: Both must be labeled.
3
Name two ways to validate a geometric model.
Answer: Independent calculation and a second construction/measurement Reasoning: Agreement across methods strengthens confidence.
4
What is sensitivity analysis?
Answer: Testing how conclusions change when inputs or assumptions change Reasoning: It reveals fragile decisions.
5
What belongs in a technical portfolio?
Answer: Brief, diagrams, calculations, proof, outputs, validation, limitations, and reflection Reasoning: The portfolio should make the reasoning traceable.
6
What should happen after critique reveals a weakness?
Answer: Revise the model and document the change Reasoning: Revision is part of mathematical practice.