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MathNumbers & CountingCounting ObjectsNumber NamesComparing NumbersNumber OperationsCounting SequenceNumbers 0-10Place Value Understanding and SystemAdd and Subtract Within 20Addition and Subtraction ConceptsAddition and Subtraction EquationsAddition and Subtraction ProblemsFoundations for MultiplicationMultiplication and Division PropertiesMultiply and Divide Within 100Multiplication and Division ProblemsFactors and MultiplesProperties of OperationsPatterns and RelationshipsGenerate and Analyze PatternsMulti-Digit ArithmeticPlace Value OperationsMulti-Digit and Decimal OperationsNumerical ExpressionsFour Operations and PatternsFour Operations Problem SolvingMeasurement & DataMeasurable AttributesMeasuring LengthsMeasure and Estimate Lengths in Standard UnitsRelate Addition and Subtraction to LengthClassifying and Counting ObjectsTime and MoneyArea Concepts and MeasurementPerimeter and Area MeasuresAngle Concepts and MeasurementTime, Volume, and MassMeasurement Unit ConversionsGeometryIdentifying ShapesShapes and AttributesShape Attributes and ReasoningShapes and CompositionClassifying 2D FiguresGeometric Figures and RelationshipsLines, Angles, and ShapesAngle, Area, and VolumeGeometric MeasurementVolume of 3D ShapesCoordinate Plane ApplicationsTransformations in the PlaneCongruence and SimilarityUnderstand congruence in terms of rigid motionsSimilarity and TransformationsProve Theorems Involving SimilarityPythagorean TheoremTrigonometry for General TrianglesMake Geometric ConstructionsProve Geometric TheoremsTheorems About CirclesFind Arc Lengths And Areas of Sectors of CirclesVolume FormulasRelationships Between Two-Dimensional and Three-Dimensional ObjectsProve Simple Geometric Theorems AlgebraicallyTranslate Between Geometric Description and Equation for Conic SectionApply Geometric Concepts in Modeling SituationsFractions & DecimalsFractions as NumbersBuilding FractionsFraction Equivalence and OrderingAdding and Subtracting FractionsMultiplying and Dividing FractionsDividing FractionsDecimal FractionsMulti-Digit Computation and FactorsAdd, Subtract, Multiply, and Divide Rational NumbersRational Number SystemIrrational Numbers and ApproximationsRatiosRatios and ProportionsProportional RelationshipsUnit RateAlgebraAlgebraic ExpressionsGenerate Equivalent ExpressionsQuantitative RelationshipsProportional Relationships and Linear EquationsEquations and InequalitiesEquation Solving and ReasoningLinear Equations and SystemsGraph Equations and InequalitiesSystems of EquationsReal-World Algebraic ProblemsQuantitative Reasoning with UnitsExpression StructureEquivalent Expression FormsRadicals and Integer ExponentsRational ExponentsRational and Irrational NumbersPolynomial OperationsPolynomial IdentitiesPolynomial Zeros and FactorsRational ExpressionsComplex Number OperationsComplex Numbers in PolynomialsComplex Numbers on PlaneStatistics & ProbabilityRepresent and Interpret DataData DistributionsStatistical VariabilityProbability ModelsCompound Event ProbabilitiesStatistical SamplingInterpret Categorical and Quantitative DataBivariate Data PatternsInterpret Linear ModelsComparing Two PopulationsRandom Processes in StatisticsIndependence and Conditional ProbabilityExpected ValuesProbability-Based Decision MakingStatistical Inference and ConclusionsFunctionsFunction Concepts and NotationDefine and Compare FunctionsInterpret Functions in ContextAnalyze Function RepresentationsModel Relationships with FunctionsIdentify Linear vs Exponential GrowthDistinguish Between Function TypesCompare Growth RatesInterpret Function ExpressionsBuild Functions from RelationshipsConstruct and Model FunctionsTransform and Combine FunctionsModel Comparison and SelectionSolve Exponential EquationsTrigonometryTrigonometric Ratios Involving Right TrianglesTrigonometric Functions and Unit CircleModel with Trigonometric FunctionsTrigonometric IdentitiesVectors & MatricesIntroduction to Vectors and MatricesVector QuantitiesVector OperationsMatrix OperationsCalculusLimits and ContinuityDerivative Concepts and NotationDerivative Rules and TechniquesApplications of DerivativesOptimization ProblemsRelated RatesCurve Sketching and AnalysisIntegration Concepts and NotationAntiderivatives and Indefinite IntegralsDefinite Integrals and AreaFundamental Theorem of CalculusIntegration TechniquesApplications of IntegrationDifferential EquationsSequences and SeriesParametric and Polar FunctionsVector-Valued Functions

Math

Math

Quantitative reasoning and logical structures across arithmetic, geometry, and advanced analysis. Builds problem-solving skills through pattern recognition and modeling.

Numbers & CountingOne-to-one correspondence, numeral identification, and comparison of quantities using terms like greater than or less than. Establishes the foundation for numerical literacy and early arithmetic operations.

Counting Objects

One-to-one correspondence and cardinality skills through counting discrete objects in various arrangements. Strengthens number recognition and the understanding of quantity.

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Number Names

Identification and spelling of number words from zero through millions. Connects numerical symbols to their written linguistic representations to strengthen mathematical literacy.

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Comparing Numbers

Mathematical symbols including greater than (>), less than (<), and equal to (=) to evaluate numerical relationships. Builds fluency in ordering sets and comparing quantities from single digits to multi-digit integers.

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Measurement & DataDevelops proficiency in estimating and measuring length, area, volume, and mass using standard units and unit conversions. Integrates time, money, angle measurement, and data classification through counting and arithmetic applications.

Measurable Attributes

Identification and comparison of length, weight, and capacity through direct observation. Builds foundational vocabulary for describing and ordering objects based on their physical properties.

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Classifying and Counting Objects

Sorting by physical attributes such as color, size, and shape to organize data sets. Develops counting skills within specific categories and establishes foundations for early data analysis.

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GeometryGeometric classification, measurement of area and volume, and the study of transformations and rigid motions. Builds toward complex proofs, trigonometry for general triangles, and the algebraic representation of conic sections.

Identifying Shapes

Visual recognition and naming of two-dimensional and three-dimensional geometric figures. Builds classification skills based on properties such as sides, vertices, and curves.

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Shapes and Attributes

Properties of two-dimensional and three-dimensional geometric figures, focusing on sides, angles, and vertices. Strengthens spatial awareness through classification and construction activities.

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Shape Attributes and Reasoning

Identification of properties including sides, vertices, and angles in two-dimensional and three-dimensional shapes. Classifies and sorts objects based on shared attributes to build foundational geometric reasoning.

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Shapes and Composition

Identification of 2D and 3D shapes alongside their defining attributes like sides, angles, and vertices. Builds spatial reasoning by composing simple shapes into complex figures and decomposing larger objects into constituent parts.

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Number OperationsCounting sequences, place value systems, and the four mathematical operations across whole numbers and decimals. Builds proficiency in solving equations, identifying numerical patterns, and applying properties of operations to multi-digit arithmetic.

Counting Sequence

Sequential number naming and cardinal counting principles for early learners. Develops fluency in forward and backward sequences while introducing skip-counting patterns.

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Numbers 0-10

Numeral recognition, counting, and cardinality for integers zero through ten. Strengthens one-to-one correspondence and basic number sense through visual sets and tracing.

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Addition and Subtraction Concepts

Mental math strategies, regrouping techniques, and the inverse relationship between operations. Builds computational fluency through visual models, number lines, and real-world word problems.

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Patterns and Relationships

Identification, extension, and creation of repeating and growing patterns using shapes, colors, and numbers. Develops algebraic thinking by analyzing sequences and defining functional relationships between variables.

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