MATH-08 · Secondary · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Geometry: Shapes, Proof and Space
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Sign in to save this learning pathPractical outcome: Create a justified construction for a tiled sign.
Explain points lines and planes using a visual and one worked real-world example. Context: Create a justified construction for a tiled sign. End with a prediction or check-for-understanding.
Explain angle types using a visual and one worked real-world example. Context: Create a justified construction for a tiled sign. End with a prediction or check-for-understanding.
Explain parallel-line angles using a visual and one worked real-world example. Context: Create a justified construction for a tiled sign. End with a prediction or check-for-understanding.
Explain triangle angle sum using a visual and one worked real-world example. Context: Create a justified construction for a tiled sign. End with a prediction or check-for-understanding.
Use the first concepts from this section. Create a justified construction for a tiled sign. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain congruence criteria using a visual and one worked real-world example. Context: Create a justified construction for a tiled sign. End with a prediction or check-for-understanding.
Explain similarity criteria using a visual and one worked real-world example. Context: Create a justified construction for a tiled sign. End with a prediction or check-for-understanding.
Explain writing a geometric proof using a visual and one worked real-world example. Context: Create a justified construction for a tiled sign. End with a prediction or check-for-understanding.
Explain counterexamples to geometric claims using a visual and one worked real-world example. Context: Create a justified construction for a tiled sign. End with a prediction or check-for-understanding.
Create a justified construction for a tiled sign. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Points lines and planes, Angle types, Parallel-line angles and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Determine a ramp length and compare circle designs.
Explain pythagorean theorem using a visual and one worked real-world example. Context: Determine a ramp length and compare circle designs. End with a prediction or check-for-understanding.
Explain converse of pythagoras using a visual and one worked real-world example. Context: Determine a ramp length and compare circle designs. End with a prediction or check-for-understanding.
Explain triangle inequalities using a visual and one worked real-world example. Context: Determine a ramp length and compare circle designs. End with a prediction or check-for-understanding.
Explain circle circumference using a visual and one worked real-world example. Context: Determine a ramp length and compare circle designs. End with a prediction or check-for-understanding.
Use the first concepts from this section. Determine a ramp length and compare circle designs. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain circle area using a visual and one worked real-world example. Context: Determine a ramp length and compare circle designs. End with a prediction or check-for-understanding.
Explain arcs and sectors using a visual and one worked real-world example. Context: Determine a ramp length and compare circle designs. End with a prediction or check-for-understanding.
Explain inscribed angles using a visual and one worked real-world example. Context: Determine a ramp length and compare circle designs. End with a prediction or check-for-understanding.
Explain tangents to circles using a visual and one worked real-world example. Context: Determine a ramp length and compare circle designs. End with a prediction or check-for-understanding.
Determine a ramp length and compare circle designs. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Pythagorean theorem, Converse of Pythagoras, Triangle inequalities and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Design packaging with a measured net and material budget.
Explain prism surface area using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Explain cylinder volume using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Explain cone volume using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Explain sphere volume using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Explain nets using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Use the first concepts from this section. Design packaging with a measured net and material budget. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain translations using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Explain reflections using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Explain rotations using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Explain dilations using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Explain coordinate proofs using a visual and one worked real-world example. Context: Design packaging with a measured net and material budget. End with a prediction or check-for-understanding.
Design packaging with a measured net and material budget. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Prism surface area, Cylinder volume, Cone volume and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Design packaging with a measured net and material budget. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Geometry: Shapes, Proof and Space, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
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