{"schema_version":"task-form-representation.payload.v1","representation":{"schema_version":"task-form-representation.v2","task_form_ref":"task-form.geometry.grid-region-partition-count.v1","public_slug":"connected-grid-exact-cover-partition-and-count","owning_skill_refs":["geom.spatial.compose-shapes","logic.proof-counterexample.artifacts"],"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.connected-grid-exact-cover-count.v1","public_title":"Connected grid exact-cover partition and count","teacher_summary":"Connected grid exact-cover partition and count asks the player to partition every active grid cell into equal-size connected regions, then enter the derived region count.","teacher_purpose_md":"Partition every active grid cell into equal-size connected regions, then enter the derived region count.","player_action_public":"Partition every active grid cell into equal-size connected regions, then enter the derived region count.","answer_affordance_public":"Move or assign each object to the matching zone.","visual_primitive_public_refs":["cell_assignment_state","connectivity_evidence","integer_response","parameterized_grid_mask"],"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":["Connected grid exact-cover partition and count","task-form.geometry.grid-region-partition-count.v1","connected_grid_partition_state_plus_region_count","cell_assignment_state","connectivity_evidence","integer_response","parameterized_grid_mask"],"teacher_questions":["What does Connected grid exact-cover partition and count mean?","How does Connected grid exact-cover partition and count adapt?","Can I see an example of Connected grid exact-cover partition and count?"],"keywords":["connected grid exact-cover partition and count","connected_grid_partition_state_plus_region_count","geom.spatial.compose-shapes","logic.proof-counterexample.artifacts"],"short_answer_public":"Connected grid exact-cover partition and count asks the player to partition every active grid cell into equal-size connected regions, then enter the derived region count.","canonical_links":[{"label":"Connected grid exact-cover partition and count","url":"#taskform-connected-grid-exact-cover-partition-and-count"}],"safe_to_quote_snippets":["Connected grid exact-cover partition and count asks the player to partition every active grid cell into equal-size connected regions, then enter the derived region count."],"example_refs":[]}},"canonical_target":{"href":"/math/skills/geom/spatial-compose-shapes#taskform-connected-grid-exact-cover-partition-and-count","skill":{"schema_version":"teacher-skill-representation.v2","skill_ref":"geom.spatial.compose-shapes","domain_slug":"geom","skill_slug":"spatial-compose-shapes","canonical_url":"/math/skills/geom/spatial-compose-shapes","public_title":"Spatial Compose Shapes","family_ref":"module-family.geom.spatial-transformations-coordinates.v1","family_name":"Spatial Composition, Transformations, Symmetry, and Coordinates","pattern_cluster_refs":["pattern-cluster.geom.transformations-composition-visualization.v1"],"task_pattern_refs":["task-pattern.geometry.connected-grid-exact-cover-count.v1","task-pattern.geometry.contour-fit-candidate-choice.v1","task-pattern.geometry.planar-composition-fit-inventory-choice.v1","task-pattern.geometry.voxel-piece-cover-color-partition-choice.v1","task-pattern.geometry.segment-relocation-shape-transform.v1"],"task_form_refs":["task-form.geometry.grid-region-partition-count.v1","task-form.geometry.contour-fit-candidate-choice.v1","task-form.geometry.planar-composition-fit-inventory-choice.v1","task-form.geometry.voxel-piece-cover-color-partition-choice.v1","task-form.geometry.segment-relocation-shape-transform.v1"],"teacher_summary":"Spatial Compose Shapes builds spatial composition, transformations, symmetry, and coordinates through visual tasks, examples, and next-step routes.","teacher_explanation_md":"Spatial Compose Shapes practice with teacher guidance, common slips, and next-step routes.","player_surface_summary_md":"This skill appears in Connected grid exact-cover partition and count, Contour-fit candidate choice, Planar composition fit and inventory choice, Voxel piece-cover and color-partition choice, Segment relocation shape transform.","common_mistake_tags":["Gap overlap ignored.","Rotation disallowed.","Size match by appearance only."],"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 with visible movement, fitting, nets, layers, grids, routes, or solid viewpoints"],"prerequisite_skill_refs":[],"next_skill_refs":["geom.spatial.decompose-shapes","geom.symmetry.complete-figure","geom.symmetry.identify-line"],"next_family_refs":["module-family.geom.shape-attributes-classification.v1","module-family.logic.constraint-deduction-combinatorics.v1","module-family.prealg.ratio-rate-scaling.v1"],"public_example_refs":[],"retrieval":{"aliases":["Spatial Compose Shapes","geom.spatial.compose-shapes","Spatial Composition, Transformations, Symmetry, and Coordinates","Connected grid exact-cover partition and count","Contour-fit candidate choice","Planar composition fit and inventory choice","Voxel piece-cover and color-partition choice","Segment relocation shape transform"],"teacher_questions":["What does Spatial Compose Shapes mean?","How does Spatial Compose Shapes adapt?","Can I see an example of Spatial Compose Shapes?"],"keywords":["spatial compose shapes","geom","spatial-compose-shapes","spatial composition, transformations, symmetry, and coordinates","task-form.geometry.grid-region-partition-count.v1","task-form.geometry.contour-fit-candidate-choice.v1","task-form.geometry.planar-composition-fit-inventory-choice.v1","task-form.geometry.voxel-piece-cover-color-partition-choice.v1","task-form.geometry.segment-relocation-shape-transform.v1"],"short_answer_public":"Spatial Compose Shapes builds spatial composition, transformations, symmetry, and coordinates through visual tasks, examples, and next-step routes.","canonical_links":[{"label":"Spatial Compose Shapes","url":"/math/skills/geom/spatial-compose-shapes"}],"safe_to_quote_snippets":["Spatial Compose Shapes builds spatial composition, transformations, symmetry, and coordinates through visual tasks, examples, and next-step routes."],"example_refs":[]}}},"examples":[],"preview_artifacts":[]}