{"schema_version":"teacher-skill-representation.payload.v1","representation":{"schema_version":"teacher-skill-representation.v2","skill_ref":"geom.geometric-constructions-properties","domain_slug":"geom","skill_slug":"geometric-constructions-properties","canonical_url":"/math/skills/geom/geometric-constructions-properties","public_title":"Geometric constructions and property reasoning","family_ref":"module-family.geom.shape-attributes-classification.v1","family_name":"Geometry Shape Attributes and Classification","pattern_cluster_refs":["pattern-cluster.measure.area-perimeter-angle.v1","pattern-cluster.geom.transformations-composition-visualization.v1"],"task_pattern_refs":["task-pattern.geometry.exact-incidence-angle-solve.v1","task-pattern.geometry.coordinate-grid-construction-state.v1"],"task_form_refs":["task-form.geometry.exact-diagram-angle-entry.v1","task-form.geometry.coordinate-grid-construction-state.v1"],"teacher_summary":"Geometric constructions and property reasoning builds geometry shape attributes and classification through visual tasks, examples, and next-step routes.","teacher_explanation_md":"Geometric constructions and property reasoning practice with teacher guidance, common slips, and next-step routes.","player_surface_summary_md":"This skill appears in Exact constructed-diagram angle entry, Coordinate-grid construction state.","common_mistake_tags":["Treating grade, year, source family, or contest label as level.","Treating a representation or answer primitive as public focus.","Applying a procedure without explaining the relationship that makes it valid."],"hint_reveal_summary_md":"Hints keep attention on the visible structure; reveals show the path without counting as independent evidence.","adaptation_summary_md":"Fresh independent work can move toward Core, Transfer, or Challenge routes; help use or confusion keeps support visible.","route_variant_refs":["support_repair","core","stretch_transfer"],"presentation_profile_refs":["presentation_compact","presentation_standard","presentation_extended"],"practice_focus_refs":["practice-focus.balanced.v1","practice-focus.geometry-measurement.v1"],"standards_refs":[],"school_program_refs":[],"challenge_refs":[],"story_fit_tags":["episodes where geometric measure is derived from a visible exact construction or decomposition","episodes with visible movement, fitting, nets, layers, grids, routes, or solid viewpoints"],"prerequisite_skill_refs":[],"next_skill_refs":["geom.lines.segments-rays","geom.parallel-perpendicular","geom.polygons.classify"],"next_family_refs":["module-family.data.classification-tables-graphs.v1","module-family.geom.spatial-transformations-coordinates.v1","module-family.measure.geometric-measurement.v1"],"public_example_refs":[],"retrieval":{"aliases":["Geometric constructions and property reasoning","geom.geometric-constructions-properties","Geometry Shape Attributes and Classification","Exact constructed-diagram angle entry","Coordinate-grid construction state"],"teacher_questions":["What does Geometric constructions and property reasoning mean?","How does Geometric constructions and property reasoning adapt?","Can I see an example of Geometric constructions and property reasoning?"],"keywords":["geometric constructions and property reasoning","geom","geometric-constructions-properties","geometry shape attributes and classification","task-form.geometry.exact-diagram-angle-entry.v1","task-form.geometry.coordinate-grid-construction-state.v1"],"short_answer_public":"Geometric constructions and property reasoning builds geometry shape attributes and classification through visual tasks, examples, and next-step routes.","canonical_links":[{"label":"Geometric constructions and property reasoning","url":"/math/skills/geom/geometric-constructions-properties"}],"safe_to_quote_snippets":["Geometric constructions and property reasoning builds geometry shape attributes and classification through visual tasks, examples, and next-step routes."],"example_refs":[]}},"task_forms":[{"schema_version":"task-form-representation.v2","task_form_ref":"task-form.geometry.coordinate-grid-construction-state.v1","public_slug":"coordinate-grid-construction-state","owning_skill_refs":["geom.coordinate.plot-points","geom.geometric-constructions-properties"],"primary_family_ref":"module-family.geom.spatial-transformations-coordinates.v1","pattern_cluster_ref":"pattern-cluster.geom.transformations-composition-visualization.v1","task_pattern_ref":"task-pattern.geometry.coordinate-grid-construction-state.v1","public_title":"Coordinate-grid construction state","teacher_summary":"Coordinate-grid construction state asks the player to place the required snapped points and straight segments on an exact coordinate grid, edit them until the submitted terminal construction satisfies every declared incidence, topology, coordinate, and exact geometric constraint, then submit that construction state.","teacher_purpose_md":"Place the required snapped points and straight segments on an exact coordinate grid, edit them until the submitted terminal construction satisfies every declared incidence, topology, coordinate, and exact geometric constraint, then submit that construction state.","player_action_public":"Place the required snapped points and straight segments on an exact coordinate grid, edit them until the submitted terminal construction satisfies every declared incidence, topology, coordinate, and exact geometric constraint, then submit that construction state.","answer_affordance_public":"Complete the coordinate-grid construction state action.","visual_primitive_public_refs":["integer_coordinate_grid","snapped_point_state","straight_segment_state","closed_cycle_topology","strict_convexity_certificate","exact_angle_relation_overlay","coordinate_label","local_invalid_mark","proof_reveal_overlay"],"player_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without changing the next route by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version after steady fresh solves."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"presentation_profiles":[{"id":"presentation_compact","public_label":"Compact","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"presentation_standard","public_label":"Standard","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"presentation_extended","public_label":"Extended","teacher_note_md":"Allow denser explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.geometry-measurement.v1","public_label":"Geometry, shapes, and measurement","teacher_note_md":"Schedule visual shape or measure review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["episodes with visible movement, fitting, nets, layers, grids, routes, or solid viewpoints","Story object role: reference shape.","Story object role: moving shape.","Story object role: grid point.","Story object role: solid piece.","Story object role: viewpoint marker."],"retrieval":{"aliases":["Coordinate-grid construction state","task-form.geometry.coordinate-grid-construction-state.v1","coordinate_grid_construction_state","integer_coordinate_grid","snapped_point_state","straight_segment_state","closed_cycle_topology","strict_convexity_certificate","exact_angle_relation_overlay","coordinate_label","local_invalid_mark","proof_reveal_overlay"],"teacher_questions":["What does Coordinate-grid construction state mean?","How does Coordinate-grid construction state adapt?","Can I see an example of Coordinate-grid construction state?"],"keywords":["coordinate-grid construction state","coordinate_grid_construction_state","geom.coordinate.plot-points","geom.geometric-constructions-properties"],"short_answer_public":"Coordinate-grid construction state asks the player to place the required snapped points and straight segments on an exact coordinate grid, edit them until the submitted terminal construction satisfies every declared incidence, topology, coordinate, and exact geometric constraint, then submit that construction state.","canonical_links":[{"label":"Coordinate-grid construction state","url":"#taskform-coordinate-grid-construction-state"}],"safe_to_quote_snippets":["Coordinate-grid construction state asks the player to place the required snapped points and straight segments on an exact coordinate grid, edit them until the submitted terminal construction satisfies every declared incidence, topology, coordinate, and exact geometric constraint, then submit that construction state."],"example_refs":[]}},{"schema_version":"task-form-representation.v2","task_form_ref":"task-form.geometry.exact-diagram-angle-entry.v1","public_slug":"exact-constructed-diagram-angle-entry","owning_skill_refs":["measure.angles.additive-unknown","geom.geometric-constructions-properties"],"primary_family_ref":"module-family.measure.geometric-measurement.v1","pattern_cluster_ref":"pattern-cluster.measure.area-perimeter-angle.v1","task_pattern_ref":"task-pattern.geometry.exact-incidence-angle-solve.v1","public_title":"Exact constructed-diagram angle entry","teacher_summary":"Exact constructed-diagram angle entry asks the player to inspect a deterministic geometry construction, add only permitted auxiliary relations, and enter the exact target angle in the declared angular unit.","teacher_purpose_md":"Inspect a deterministic geometry construction, add only permitted auxiliary relations, and enter the exact target angle in the declared angular unit.","player_action_public":"Inspect a deterministic geometry construction, add only permitted auxiliary relations, and enter the exact target angle in the declared angular unit.","answer_affordance_public":"Complete the exact constructed-diagram angle entry action.","visual_primitive_public_refs":["angle_marker","angular_unit_response","exact_incidence_graph","metric_constraints","permitted_auxiliary_relations"],"player_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without changing the next route by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version after steady fresh solves."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"presentation_profiles":[{"id":"presentation_compact","public_label":"Compact","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"presentation_standard","public_label":"Standard","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"presentation_extended","public_label":"Extended","teacher_note_md":"Allow denser explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.geometry-measurement.v1","public_label":"Geometry, shapes, and measurement","teacher_note_md":"Schedule visual shape or measure review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["episodes where geometric measure is derived from a visible exact construction or decomposition","Story object role: measured side.","Story object role: angle arc.","Story object role: auxiliary relation.","Story object role: decomposition region.","Story object role: measure field."],"retrieval":{"aliases":["Exact constructed-diagram angle entry","task-form.geometry.exact-diagram-angle-entry.v1","exact_angle_numeric_entry","angle_marker","angular_unit_response","exact_incidence_graph","metric_constraints","permitted_auxiliary_relations"],"teacher_questions":["What does Exact constructed-diagram angle entry mean?","How does Exact constructed-diagram angle entry adapt?","Can I see an example of Exact constructed-diagram angle entry?"],"keywords":["exact constructed-diagram angle entry","exact_angle_numeric_entry","measure.angles.additive-unknown","geom.geometric-constructions-properties"],"short_answer_public":"Exact constructed-diagram angle entry asks the player to inspect a deterministic geometry construction, add only permitted auxiliary relations, and enter the exact target angle in the declared angular unit.","canonical_links":[{"label":"Exact constructed-diagram angle entry","url":"#taskform-exact-constructed-diagram-angle-entry"}],"safe_to_quote_snippets":["Exact constructed-diagram angle entry asks the player to inspect a deterministic geometry construction, add only permitted auxiliary relations, and enter the exact target angle in the declared angular unit."],"example_refs":[]}}],"examples":[],"preview_artifacts":[]}