US Common Core · Common Core · US Math
US Common Core Common Core US Math Syllabus
The complete US Common Core Common Core US Math specification mapped to 213 topics. Click any topic for free revision notes and practice questions.
213 topics70 practice questions5 revision guides
Algebra – Creating Equations
creating equations and inequalities in one or more variables, representing constraints, rearranging formulas
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Algebra – Reasoning with Equations and Inequalities
solving linear and quadratic equations, solving systems of equations and inequalities, graphical interpretation of solutions
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Algebra – Seeing Structure in Expressions
interpreting parts of expressions, factoring and completing the square, geometric sequences and series
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Algebra — Creating Equations
Creating equations that describe numbers or relationships (linear, quadratic, exponential, rational)
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Algebra — Reasoning with Equations and Inequalities
Representing and solving equations and inequalities graphically
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Solving equations and inequalities in one variable (linear, quadratic)
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Solving systems of equations (substitution, elimination, graphical methods)
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Understanding solving equations as a process of reasoning
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Algebra — Seeing Structure in Expressions
Interpreting the structure of algebraic expressions
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Writing expressions in equivalent forms to solve problems (factoring, completing the square)
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Counting and Cardinality
Comparing numbers 1–10
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counting sequences, one-to-one correspondence, comparing numbers
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Counting to 100 by ones and tens
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Expressions and Equations
Analyzing and solving linear equations and pairs of simultaneous linear equations
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Applying and extending understanding to algebraic expressions (writing, reading, evaluating)
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equivalent expressions, linear equations in one variable, inequalities, solving real-world problems
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integer exponents, scientific notation, square and cube roots, proportional relationships and linear equations, systems of linear equations
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Reasoning about and solving one-variable equations and inequalities
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Representing and analyzing quantitative relationships between dependent and independent variables
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Solving real-life and mathematical problems using numerical and algebraic expressions and equations
20 Qs⚡ Practice
Understanding the connections between proportional relationships, lines, and linear equations
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Using properties of operations to generate equivalent expressions
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Working with radicals and integer exponents (properties of integer exponents, scientific notation)
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writing and evaluating expressions, equivalent expressions, solving one-step equations and inequalities
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Functions
defining and interpreting functions, comparing functions, linear vs. nonlinear functions
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Defining, evaluating, and comparing functions (function concept, linear vs. non-linear)
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Using functions to model relationships between quantities
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Functions – Building Functions
building new functions from existing functions, transformations, inverses, composition of functions
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Functions – Interpreting Functions
understanding function notation, interpreting features of graphs and tables, sketching and analyzing functions
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Functions – Linear, Quadratic, and Exponential Models
constructing and comparing linear, quadratic and exponential models, interpreting parameters
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Functions – Trigonometric Functions
extending trigonometry to the unit circle, modeling periodic phenomena, proving and applying trigonometric identities
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Functions — Building Functions
Building a function that models a relationship between two quantities
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Building new functions from existing functions (transformations, inverses, compositions)
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Functions — Interpreting Functions
Analyzing functions using different representations (graphs, tables, algebraic expressions)
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Interpreting functions that arise in applications in terms of context (domain, range, rate of change, max/min)
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Understanding the concept of a function and using function notation
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Functions — Linear, Quadratic, and Exponential Models
Constructing and comparing linear, quadratic, and exponential models to solve problems
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Interpreting expressions for functions in terms of the situation they model
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Functions — Trigonometric Functions
Extending the domain of trigonometric functions using the unit circle
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Modeling periodic phenomena with trigonometric functions (amplitude, frequency, phase shift)
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Proving and applying trigonometric identities (Pythagorean identity, sum and difference formulas)
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Geometry
area of triangles, quadrilaterals, and polygons; surface area and volume of prisms and pyramids
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Classifying two-dimensional figures into categories based on their properties
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coordinate plane, classifying 2-D figures in a hierarchy
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Drawing and identifying lines and angles, and classifying shapes by properties
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drawing and identifying lines, angles, parallel and perpendicular lines, symmetry, classifying 2-D figures
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Drawing, constructing, and describing geometrical figures and relationships between them (scale drawings, geometric constructions)
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Graphing points on a coordinate plane to solve real-world and mathematical problems
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identifying and describing 2-D and 3-D shapes, relative positions
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Identifying and describing shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, spheres)
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partitioning shapes into equal shares, recognizing shape attributes
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reasoning about shapes, attributes of shapes, composing shapes
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Reasoning with shapes and their attributes (classifying shapes by properties)
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Reasoning with shapes and their attributes (partitioning circles and rectangles into halves and fourths)
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Reasoning with shapes and their attributes (partitioning shapes into equal shares)
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scale drawings, constructing geometric figures, area and circumference of circles, surface area and volume of 2-D and 3-D figures, angle relationships
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Solving real-world problems involving angle measure, area, surface area, and volume
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Solving real-world problems involving area, surface area, and volume of 2D and 3D figures
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Solving real-world problems involving volume of cylinders, cones, and spheres
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transformations (translations, reflections, rotations, dilations), congruence and similarity, Pythagorean theorem, volume of cylinders, cones, and spheres
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Understanding and applying the Pythagorean Theorem
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Understanding congruence and similarity using physical models, transparencies, or geometry software (transformations, congruence, similarity)
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understanding shapes and their attributes, quadrilaterals, partitioning shapes
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Geometry – Circles
circle theorems (inscribed angles, chords, arcs), arc length and area of sectors, equations of circles
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Geometry – Congruence
transformations in the plane, congruence through rigid motions, geometric proofs, congruent triangles, geometric constructions
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Geometry – Expressing Geometric Properties with Equations
slope criteria for parallel and perpendicular lines, distances, coordinate proofs, equations of parabolas and conic sections
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Geometry – Geometric Measurement and Dimension
area and volume formulas, Cavalieri's principle, surface area and volume of cylinders, cones, spheres
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Geometry – Modeling with Geometry
applying geometric methods to model real-world and design problems
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Geometry – Similarity, Right Triangles, and Trigonometry
similarity transformations, triangle similarity, Pythagorean theorem proofs, trigonometric ratios, applied trigonometry
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Geometry — Circles
Finding arc lengths and areas of sectors of circles
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Understanding and applying theorems about circles (inscribed angles, chords, secants, tangents)
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Geometry — Congruence
Experimenting with transformations in the plane (translations, reflections, rotations, dilations)
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Making geometric constructions (compass and straightedge, dynamic geometry software)
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Understanding congruence in terms of rigid motions and proving geometric theorems
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Geometry — Expressing Geometric Properties with Equations
Translating between geometric description and the equation for a conic section (circles, parabolas)
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Using coordinates to prove simple geometric theorems algebraically
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Geometry — Geometric Measurement and Dimension
Explaining volume formulas and using them to solve problems (prisms, cylinders, pyramids, cones, spheres)
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Visualizing relationships between two-dimensional and three-dimensional objects (cross-sections, rotations)
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Geometry — Modeling with Geometry
Applying geometric methods to solve design and real-world problems
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Geometry — Similarity, Right Triangles, and Trigonometry
Applying trigonometry to general triangles (Law of Sines, Law of Cosines)
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Defining trigonometric ratios and solving problems involving right triangles (sine, cosine, tangent)
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Proving theorems involving similarity
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Understanding similarity in terms of similarity transformations
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Measurement and Data
Converting like measurement units within a given measurement system
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converting measurement units, volume of rectangular prisms, representing and interpreting data
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converting units, area and perimeter problems, line plots with fractions, angles and angle measurement
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Describing and comparing measurable attributes
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describing and comparing measurable attributes, classifying objects
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Measuring and estimating lengths in standard units
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Measuring lengths indirectly and by iterating length units
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ordering and comparing lengths, telling time, organizing and interpreting data
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Relating addition and subtraction to length
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Representing and interpreting data (line plots with fractions, operations on data)
20 Qs⚡ Practice
Representing and interpreting data (line plots with fractions)
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Representing and interpreting data (picture graphs, bar graphs, line plots)
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Representing and interpreting data (scaled picture and bar graphs, line plots)
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Representing and interpreting data using graphs and charts
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Solving problems involving measurement and conversion of measurements (customary and metric)
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Solving problems involving measurement and estimation of intervals of time, liquid volumes, and masses
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Solving problems involving perimeters of polygons
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standard units of length, time intervals, money, line plots, picture graphs, bar graphs
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Telling and writing time to the hour and half-hour
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Telling and writing time to the nearest five minutes
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time, liquid volume, mass, area, perimeter, representing and interpreting data
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Understanding concepts of angle and measuring angles
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Understanding concepts of area and relating area to multiplication and addition
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Understanding concepts of volume and relating volume to multiplication and addition
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Working with money (dollars, quarters, dimes, nickels, pennies)
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Number and Operations – Fractions
adding and subtracting fractions with unlike denominators, multiplying and dividing fractions, fraction word problems
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equivalent fractions, comparing fractions, adding and subtracting fractions with like denominators, multiplying fractions by whole numbers, decimal notation for fractions
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understanding fractions as parts of a whole, fractions on a number line, equivalent fractions, comparing fractions
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Number and Operations — Fractions
Applying understanding of multiplication and division to multiply and divide fractions
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Building fractions from unit fractions (adding, subtracting, multiplying fractions)
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Comparing fractions with the same numerator or denominator
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Extending understanding of fraction equivalence and ordering
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Understanding decimal notation for fractions and comparing decimal fractions
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Understanding fractions as numbers on the number line
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Using equivalent fractions to add and subtract fractions with unlike denominators
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Number and Operations in Base Ten
Fluently adding and subtracting within 1000
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Generalizing place value understanding for multi-digit whole numbers
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generalizing place value, multi-digit multiplication and division algorithms
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Performing operations with multi-digit whole numbers and decimals
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place value foundations, composing/decomposing numbers 11–19
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place value to 100, comparing two-digit numbers, adding and subtracting within 100
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place value to 1000, reading and writing numbers, adding and subtracting within 1000
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place value to decimals, powers of 10, multi-digit whole number and decimal operations
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rounding to nearest 10 or 100, multi-digit addition and subtraction, multiplying multiples of 10
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Understanding place value for three-digit numbers
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Understanding place value for two-digit numbers
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Understanding the place value system (powers of 10, decimals to thousandths)
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Using place value understanding and properties of operations to perform multi-digit arithmetic
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Using place value understanding and properties to perform multi-digit arithmetic (multiplication and division)
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Using place value understanding to add and subtract within 100
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Working with numbers 11–19 to gain foundations for place value
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Number and Quantity – Quantities
reasoning with units, defining appropriate quantities, choosing a level of accuracy
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Number and Quantity – The Complex Number System
operations with complex numbers, complex solutions to quadratic equations, polar form and complex plane
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Number and Quantity – The Real Number System
properties of rational and irrational numbers, using properties of exponents
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Number and Quantity – Vector and Matrix Quantities
representing and operating on vectors, matrices as transformations, solving systems using matrices
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Number and Quantity — Quantities
Reasoning quantitatively and using units to solve problems (dimensional analysis, appropriate levels of accuracy)
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Number and Quantity — The Complex Number System
Performing arithmetic operations with complex numbers
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Representing complex numbers and their operations on the complex plane
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Number and Quantity — The Real Number System
Extending properties of exponents to rational exponents
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Using properties of rational and irrational numbers
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Number and Quantity — Vector and Matrix Quantities
Performing operations on matrices and using matrices in applications
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Representing and modeling with vector quantities
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Operations and Algebraic Thinking
addition and subtraction concepts within 10
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addition and subtraction within 100, arrays, even and odd numbers, foundations of multiplication
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addition and subtraction within 20, word problems, properties of operations
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Analyzing patterns and relationships (numerical patterns, graphing ordered pairs)
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Gaining familiarity with factors and multiples
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Generating and analyzing patterns
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Identifying and explaining arithmetic patterns
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multi-step word problems, factors and multiples, patterns and rules
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multiplication and division within 100, properties of multiplication, arithmetic patterns
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Representing and solving addition and subtraction problems within 20
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Representing and solving multiplication and division problems within 100
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Representing and solving one- and two-step addition and subtraction problems within 100
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Solving two-step word problems using four operations
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Understanding addition as putting together and adding to
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Understanding and applying properties of operations
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Understanding properties of multiplication and the relationship between multiplication and division
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Understanding subtraction as taking apart and taking from
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Using the four operations with whole numbers to solve problems
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Working with addition and subtraction equations
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Working with equal groups to gain foundations for multiplication
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writing and interpreting expressions, patterns and relationships
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Writing and interpreting numerical expressions
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Ratios and Proportional Relationships
Analyzing proportional relationships and using them to solve real-world problems
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Computing unit rates with ratios of fractions; representing proportional relationships
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proportional relationships, unit rates with fractions, percent problems
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Understanding ratio concepts and using ratio reasoning to solve problems
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understanding ratios, unit rates, ratio reasoning to solve problems
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Understanding unit rate and applying ratio and rate reasoning
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Statistics and Probability
Developing understanding of statistical variability (statistical questions, distribution, center, spread)
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Drawing informal comparative inferences about two populations
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Investigating chance processes and developing, using, and evaluating probability models
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Investigating patterns of association in bivariate data (scatter plots, line of best fit, two-way tables)
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random sampling, comparing populations, probability models and simulations, compound events
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scatter plots, patterns of association, two-way tables, linear models
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statistical questions, distributions, measures of center and variability, displays of numerical data
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Summarizing and describing distributions (dot plots, histograms, box plots, mean, median, mode, range, MAD)
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Using random sampling to draw inferences about a population
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The Number System
Applying and extending previous understanding of multiplication and division to divide fractions by fractions
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Applying and extending previous understanding of numbers to the system of rational numbers (negative numbers, absolute value, coordinate plane)
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Applying and extending previous understanding of operations with fractions to add, subtract, multiply, and divide rational numbers
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Computing fluently with multi-digit numbers and finding common factors and multiples
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dividing fractions by fractions, multi-digit arithmetic, rational numbers on a number line, absolute value
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Knowing that there are numbers that are not rational and approximating them by rational numbers (irrational numbers, square roots, cube roots)
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operations with rational numbers, converting between fractions and decimals
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rational vs. irrational numbers, approximating irrational numbers
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All topics
Algebra
polynomial operations, remainder theorem, polynomial identities, rational expressions
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Performing arithmetic operations on polynomials
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Rewriting rational expressions
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Understanding the relationship between zeros and factors of polynomials (Remainder Theorem, Factor Theorem)
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Using polynomial identities to solve problems
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Functions
Geometry
Number and Quantity
Statistics and Probability
sample spaces, addition and multiplication rules, conditional probability, independence
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summarizing distributions, comparing datasets, interpreting linear models, two-way frequency tables
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probability and statistical inference, simulation, evaluating reports
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expected value, probability distributions, evaluating outcomes of decisions using probability
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Understanding independence and conditional probability and using them to interpret data
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Using the rules of probability to compute probabilities of compound events (Addition Rule, Multiplication Rule, Bayes' Theorem basics)
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Interpreting linear models (slope, intercept, correlation coefficient, causation vs. correlation)
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Summarizing, representing, and interpreting data on a single count or measurement variable (dot plots, histograms, box plots, mean, standard deviation)
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Summarizing, representing, and interpreting data on two categorical and quantitative variables (scatter plots, correlation, linear regression)
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Making inferences and justifying conclusions from sample surveys, experiments, and observational studies
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Understanding and evaluating random processes underlying statistical experiments
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Calculating expected values and using them to solve problems
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Using probability to evaluate outcomes of decisions (probability distributions, fair decisions)
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Practise the whole syllabus.
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