Mathematics Curriculum Levels
Comparison of mathematics education levels across different countries
Elementary School Mathematics
United States
Elementary School
Kindergarten (Grade K)
Ages 5-6
Counting, basic shapes, patterns, number recognition
- Counting to 100
- Basic addition and subtraction
- Shape recognition
- Measurement concepts
Grades 1-2
Ages 6-8
Basic arithmetic, place value, simple word problems
- Addition and subtraction up to 20
- Place value (ones, tens)
- Time and money concepts
- Basic geometry
Grades 3-5
Ages 8-11
Multiplication, division, fractions, decimals
- Multiplication and division
- Fractions and decimals
- Measurement and data
- Basic geometry concepts
Canada
Elementary School
Primary (Grades 1-3)
Ages 6-9
Number sense, basic operations, measurement
- Number recognition and counting
- Addition and subtraction
- Measurement concepts
- Basic geometry
Junior (Grades 4-6)
Ages 9-12
Multiplication, division, fractions, decimals
- Multiplication and division
- Fractions and decimals
- Measurement conversion
- Geometry and spatial sense
United Kingdom
Key Stages 1-2
Key Stage 1 (Years 1-2)
Ages 5-7
Number bonds, counting, basic shapes
- Number bonds to 20
- Addition and subtraction
- Simple fractions
- Properties of shapes
Key Stage 2 (Years 3-6)
Ages 7-11
Times tables, fractions, decimals, percentages
- Times tables up to 12×12
- Fractions, decimals, percentages
- Measurement and geometry
- Statistics
Australia
Foundation - Year 6
Foundation - Year 2
Ages 5-8
Number patterns, basic operations, shapes
- Number sequences
- Addition and subtraction
- Basic measurement
- 2D and 3D shapes
Years 3-6
Ages 8-12
Multiplication, division, fractions, decimals
- Multiplication and division
- Fractions and decimals
- Angles and geometry
- Data representation
Middle School Mathematics
United States
Middle School
Grade 6
Ages 11-12
Ratios, rates, percentages, expressions
- Ratios and proportional relationships
- Arithmetic operations
- Rational numbers
- Expressions and equations
Grade 7
Ages 12-13
Proportional relationships, operations with rational numbers
- Proportional relationships
- Operations with rational numbers
- Expressions and equations
- Statistics and probability
Grade 8
Ages 13-14
Linear equations, functions, geometric transformations
- Linear equations and functions
- Systems of equations
- Geometric transformations
- Pythagorean theorem
Canada
Middle School
Grades 7-8
Ages 12-14
Algebra fundamentals, number operations, geometry
- Number operations
- Patterns and relationships
- Shape and space
- Statistics and probability
United Kingdom
Key Stage 3
Years 7-9
Ages 11-14
Algebra, geometry, probability, ratio and proportion
- Algebra
- Geometry and measures
- Probability
- Ratio and proportion
Australia
Years 7-10
Years 7-8
Ages 12-14
Real numbers, patterns, algebra, linear relationships
- Real numbers
- Patterns and algebra
- Linear and non-linear relationships
- Geometry
Years 9-10
Ages 14-16
Algebra, geometry, statistics, financial mathematics
- Algebraic techniques
- Geometric reasoning
- Statistical analysis
- Financial mathematics
High School Mathematics
United States
High School
Algebra I
Typically Grade 9
Linear equations, inequalities, functions, systems
- Linear equations and inequalities
- Functions
- Systems of equations
- Exponents and polynomials
Geometry
Typically Grade 10
Geometric proofs, transformations, trigonometry
- Geometric proofs
- Transformations
- Trigonometry
- Circles and volume
Algebra II
Typically Grade 11
Advanced algebra, complex numbers, logarithmic functions
- Complex numbers
- Logarithmic functions
- Polynomial functions
- Rational expressions
Pre-Calculus & Calculus
Typically Grade 12
Trigonometry, limits, derivatives, integrals
- Trigonometric functions
- Limits and continuity
- Derivatives
- Integrals
Canada
High School
Grade 9-10 Mathematics
Ages 14-16
Algebra, linear relations, analytic geometry
- Algebraic expressions
- Linear relations
- Analytic geometry
- Measurement and geometry
Grade 11-12 Mathematics
Ages 16-18
Functions, advanced functions, calculus, data management
- Functions
- Advanced functions
- Calculus and vectors
- Data management
United Kingdom
Key Stages 4-5
GCSE Mathematics
Ages 14-16
Algebra, geometry, statistics, ratio and proportion
- Algebra
- Geometry and measures
- Statistics
- Ratio and proportion
A-Level Mathematics
Ages 16-18
Pure mathematics, mechanics, statistics
- Pure mathematics
- Mechanics
- Statistics
- Decision mathematics
Australia
Senior Secondary
Years 11-12 Mathematics
Ages 16-18
Mathematical methods, specialist mathematics, general mathematics
- Mathematical methods
- Specialist mathematics
- General mathematics
- Essential mathematics