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Foundations and Quantity
Counting and Cardinality FoundationsQuantity Comparison and Order ReasoningBase-Ten Place Value and Whole-Number Notation
Operations and Models
Whole-Number Operations and Fact FluencyOperations Models, Bar Models, and Word ProblemsEquations, Variables, Expressions, and InequalitiesRatio, Rate, Scaling, and Proportional Foundation
Parts, Measure, and Proportion
Fractions as Parts, Wholes, and Fair SharesFraction Equivalence, Comparison, and OperationsDecimal and Percent ReasoningMeasurement Units, Tools, Time, and MoneyGeometric Measurement
Geometry, Space, and Data
Data Classification, Tables, and Graph ReasoningGeometry Shape Attributes and ClassificationSpatial Composition, Transformations, Symmetry, and Coordinates
Patterns, Logic, and Enrichment
Patterns, Functions, and GeneralizationLogic, Constraint, Deduction, and Combinatorics
Math›Patterns, Logic, and Enrichment

Patterns, Logic, and Enrichment

Patterns, Functions, and GeneralizationIdentify, extend, generate, compare, and explain visual, numeric, growing, and input-output rules.Logic, Constraint, Deduction, and CombinatoricsUse visible and hidden clues, eliminations, impossibility, truth, parity, invariants, systematic lists, tree diagrams, product-rule readiness, guarantees, counterexamples, contradiction, and nonblocking olympiad-method adapters while routing arithmetic, data, geometry, spatial, symbolic, fraction, measurement, ratio, and pattern-primary work to owning families.
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