# Adaptive math map

A modeled path showing how age band, skill profile, practice focus, and evidence change task selection.

Schema: example-story-path.v1
Graph version: math-map-fbd343cc3f23eec1
Stops: 40
ModuleFamilies: 17

## Controls

- Age 6-7: Concrete objects, shorter prompts, larger touch targets.
- Age 8-9: Representations, tables, and multi-step choices.
- Age 10-11: Symbols, proof language, rates, and challenge presentation.
- Emerging: Starts with support and repair checks until fresh independent evidence appears.
- On-track: Starts on the core route and advances when recent independent work holds.
- Advanced: Starts with transfer and opens challenge only where a challenge anchor exists.
- Balanced: Keeps story fit and evidence as the main drivers.
- Facts: Softly favors facts, arrays, equal groups, and calm fluency when compatible.
- Fractions: Softly favors shares, parts, equivalence, benchmarks, and fraction repair.
- Word problems: Softly favors model choice, bar models, operation choice, and reasonableness.
- Geometry: Softly favors shape, measure, tools, paths, and spatial work.
- Mixed review: Softly favors skill checks and fresh review without child-facing test labels.
- Weak spots: Softly favors diagnostic and repair choices once evidence points to a need.

## Hierarchy

- Episode opportunity: Story action and objects create a math opening.
- Math family: Curriculum neighborhood and prerequisite owner.
- Story lane: Episode-fit mechanic cluster inside the family.
- Reasoning ladder: The reasoning step selected before numbers, route, or row.
- Practice pattern: Reusable visual question grammar.
- Evidence: Fresh independent evidence drives the next choice.

## Modeled Path

| # | Stop | Family | Lane | TaskAtom | Default route | Default age form | Focus behavior |
|---:|---|---|---|---|---|---|---|
| 1 | Counting foundation | Counting and Cardinality Foundations | Count sequence and set meaning | Visible set count | Core | Count-on and skip-count bridge | Balanced |
| 2 | Object sort | Data Classification, Tables, and Graph Reasoning | Object classification | Classification rule | Core | Table and graph transfer | Balanced |
| 3 | Quantity compare | Quantity Comparison and Order Reasoning | Visible set comparison | Visible compare | Core | Difference and comparison reasoning | Balanced |
| 4 | Count sequence repair | Counting and Cardinality Foundations | Count sequence and set meaning | Visible set count | Core | Count-on and skip-count bridge | Balanced |
| 5 | Object sort transfer | Data Classification, Tables, and Graph Reasoning | Object classification | Classification rule | Core | Table and graph transfer | Balanced |
| 6 | Constraint choice | Logic, Constraint, Deduction, and Combinatorics | Visible clue elimination | Clue elimination | Core | Near-miss deduction | Balanced |
| 7 | Constraint challenge | Logic, Constraint, Deduction, and Combinatorics | Visible clue elimination | Clue elimination | Core | Near-miss deduction | Balanced |
| 8 | Place-value grouping | Base-Ten Place Value and Whole-Number Notation | Place-value notation | Place-value cards | Core | Place-value notation transfer | Balanced |
| 9 | Fact fluency loop | Whole-Number Operations and Fact Fluency | Fact strategy and fluency | Fact strategy loop | Core | Fact strategy fluency | Balanced |
| 10 | Operation model choice | Operations Models, Bar Models, and Word Problems | Story model selection | Model choice | Core | Bar-model choice | Balanced |
| 11 | Tools, time, and money | Measurement Units, Tools, Time, and Money | Tools, units, and conversion | Tool and unit choice | Core | Unit conversion choice | Balanced |
| 12 | Perimeter and area | Geometric Measurement | Area and perimeter measure | Area/perimeter board | Core | Area and perimeter transfer | Balanced |
| 13 | Shape attributes | Geometry Shape Attributes and Classification | Shape attribute classification | Shape attribute choice | Core | Classify by attributes | Balanced |
| 14 | Symmetry and turns | Spatial Composition, Transformations, Symmetry, and Coordinates | Spatial paths and transformations | Path transform | Core | Coordinate path | Balanced |
| 15 | Pattern rule | Patterns, Functions, and Generalization | Pattern rule tables | Rule table | Core | Rule table and missing term | Balanced |
| 16 | Classification rule | Data Classification, Tables, and Graph Reasoning | Object classification | Classification rule | Core | Table and graph transfer | Balanced |
| 17 | Deduction depth | Logic, Constraint, Deduction, and Combinatorics | Visible clue elimination | Clue elimination | Core | Near-miss deduction | Balanced |
| 18 | Fair-share parts | Fractions as Parts, Wholes, and Fair Shares | Parts and whole partition | Partition whole | Core | Unit fraction partition | Balanced |
| 19 | Equivalent fractions | Fraction Equivalence, Comparison, and Operations | Fraction equivalence and compare | Fraction compare | Core | Equivalent fraction model | Balanced |
| 20 | Decimals and percent | Decimal and Percent Reasoning | Decimal and percent benchmark | Benchmark meter | Core | Decimal-percent benchmark | Balanced |
| 21 | Ratio scaling | Ratio, Rate, Scaling, and Proportional Foundation | Ratio table and scale | Scale table | Core | Rate and scale factor | Balanced |
| 22 | Unknown-number equation | Equations, Variables, Expressions, and Inequalities | Expression and inequality choices | Expression choice | Core | Equation choice | Balanced |
| 23 | Base-ten notation transfer | Base-Ten Place Value and Whole-Number Notation | Place-value notation | Place-value cards | Core | Place-value notation transfer | Balanced |
| 24 | Operations fluency loop | Whole-Number Operations and Fact Fluency | Fact strategy and fluency | Fact strategy loop | Core | Fact strategy fluency | Balanced |
| 25 | Word-problem model transfer | Operations Models, Bar Models, and Word Problems | Story model selection | Model choice | Core | Bar-model choice | Balanced |
| 26 | Measurement conversion | Measurement Units, Tools, Time, and Money | Tools, units, and conversion | Tool and unit choice | Core | Unit conversion choice | Balanced |
| 27 | Shape class proof | Geometry Shape Attributes and Classification | Shape attribute classification | Shape attribute choice | Core | Classify by attributes | Balanced |
| 28 | Coordinate path | Spatial Composition, Transformations, Symmetry, and Coordinates | Spatial paths and transformations | Path transform | Core | Coordinate path | Balanced |
| 29 | Table-to-graph data | Data Classification, Tables, and Graph Reasoning | Object classification | Classification rule | Core | Table and graph transfer | Balanced |
| 30 | Function table | Patterns, Functions, and Generalization | Pattern rule tables | Rule table | Core | Rule table and missing term | Balanced |
| 31 | Combinatorics logic | Logic, Constraint, Deduction, and Combinatorics | Visible clue elimination | Clue elimination | Core | Near-miss deduction | Balanced |
| 32 | Geometric measurement transfer | Geometric Measurement | Area and perimeter measure | Area/perimeter board | Core | Area and perimeter transfer | Balanced |
| 33 | Fraction partition | Fractions as Parts, Wholes, and Fair Shares | Parts and whole partition | Partition whole | Core | Unit fraction partition | Balanced |
| 34 | Fraction comparison operations | Fraction Equivalence, Comparison, and Operations | Fraction equivalence and compare | Fraction compare | Core | Equivalent fraction model | Balanced |
| 35 | Percent benchmark | Decimal and Percent Reasoning | Decimal and percent benchmark | Benchmark meter | Core | Decimal-percent benchmark | Balanced |
| 36 | Scale factor | Ratio, Rate, Scaling, and Proportional Foundation | Ratio table and scale | Scale table | Core | Rate and scale factor | Balanced |
| 37 | Expression inequality | Equations, Variables, Expressions, and Inequalities | Expression and inequality choices | Expression choice | Core | Equation choice | Balanced |
| 38 | Logic capstone challenge | Logic, Constraint, Deduction, and Combinatorics | Visible clue elimination | Clue elimination | Core | Near-miss deduction | Balanced |
| 39 | Operations model capstone | Operations Models, Bar Models, and Word Problems | Story model selection | Model choice | Core | Bar-model choice | Balanced |
| 40 | Proportional reasoning bridge | Ratio, Rate, Scaling, and Proportional Foundation | Ratio table and scale | Scale table | Core | Rate and scale factor | Balanced |

## Family Coverage

- Counting and Cardinality Foundations: 2 stop(s).
- Quantity Comparison and Order Reasoning: 1 stop(s).
- Base-Ten Place Value and Whole-Number Notation: 2 stop(s).
- Whole-Number Operations and Fact Fluency: 2 stop(s).
- Operations Models, Bar Models, and Word Problems: 3 stop(s).
- Fractions as Parts, Wholes, and Fair Shares: 2 stop(s).
- Fraction Equivalence, Comparison, and Operations: 2 stop(s).
- Decimal and Percent Reasoning: 2 stop(s).
- Measurement Units, Tools, Time, and Money: 2 stop(s).
- Geometric Measurement: 2 stop(s).
- Data Classification, Tables, and Graph Reasoning: 4 stop(s).
- Geometry Shape Attributes and Classification: 2 stop(s).
- Spatial Composition, Transformations, Symmetry, and Coordinates: 2 stop(s).
- Patterns, Functions, and Generalization: 2 stop(s).
- Equations, Variables, Expressions, and Inequalities: 2 stop(s).
- Logic, Constraint, Deduction, and Combinatorics: 5 stop(s).
- Ratio, Rate, Scaling, and Proportional Foundation: 3 stop(s).