Grade 3 – Grade 12 + SAT Prep

US Math Curriculum at a Glance

Full Common Core–aligned mathematics syllabus from Grade 3 through Grade 12, including PSAT 8/9, PSAT/NMSQT, and Digital SAT Math prep. Used by 41+ US states.

✓ Common Core Aligned ✓ Grade 3–12 Coverage ✓ PSAT & SAT Math Prep ✓ All US States ✓ Live 1-to-1 Tutoring
About This Syllabus

Structured Math Learning from Elementary to High School

This syllabus presents the complete progression of US school mathematics from Grade 3 through Grade 12, followed by a guide to PSAT and SAT Mathematics. It is aligned to the Common Core State Standards (CCSS) — the foundation for 41+ US states — and serves as a reference for parents and students planning a structured learning journey with MathsWonder.

States that use their own standards (Texas TEKS, Virginia SOL, Florida B.E.S.T.) follow a closely comparable progression — this syllabus is a strong general reference nationwide. Deepti tailors every student's programme to their specific school's requirements.

Grade-by-Grade Curriculum

Part 1 — Mathematics Curriculum: Grade 3 to Grade 12

Click any grade to expand its full syllabus. Each grade shows major domains, topics, and learning objectives.

Year focus: Multiplication & division within 100, fractions as numbers, area, and properties of shapes.

Operations & Algebraic Thinking
Topics
  • Interpret products and quotients of whole numbers
  • Multiplication and division within 100 — strategies and relationships
  • Two-step word problems using four operations; estimate reasonableness
  • Arithmetic patterns (even/odd, multiplication table patterns)
Learning Objectives
  • Fluently multiply and divide within 100 — know all products from memory
  • Apply commutative, associative, distributive properties as strategies
  • Solve problems with equal groups, arrays, and measurement quantities
Number & Operations in Base Ten
Topics
  • Round whole numbers to nearest 10 or 100
  • Fluently add and subtract within 1,000
  • Multiply one-digit numbers by multiples of 10
Learning Objectives
  • Use place-value understanding to perform multi-digit arithmetic accurately
Number & Operations — Fractions
Topics
  • Fraction 1/b as one part when whole is partitioned into b equal parts
  • Represent fractions on a number line
  • Equivalence of simple fractions; compare fractions with same numerator or denominator
Learning Objectives
  • Develop understanding of fractions as numbers, not just shaded regions
Measurement & Data
Topics
  • Time to nearest minute; elapsed-time problems
  • Liquid volumes and masses; one-step problems
  • Scaled picture and bar graphs; line plots
  • Area as an attribute; relate area to multiplication and addition
  • Perimeters of polygons
Learning Objectives
  • Connect area measurement to multiplication and the distributive property
Geometry
Topics
  • Shared attributes of shapes; quadrilaterals — examples and non-examples
  • Partition shapes into equal parts; express as unit fractions
Learning Objectives
  • Reason about shapes and attributes to build foundation for fractions and area

Year focus: Multi-digit multiplication, division with remainders, fraction equivalence and operations, geometric measurement.

Operations & Algebraic Thinking
Topics
  • Multiplicative comparison — interpret multiplication equations
  • Multi-step word problems with four operations; interpret remainders
  • Factor pairs and multiples within 100; prime and composite numbers
  • Number and shape patterns from a given rule
Learning Objectives
  • Use four operations flexibly to solve multi-step real-world problems and judge reasonableness
Number & Operations in Base Ten
Topics
  • Digit in one place = ten times the place to its right
  • Read, write, compare, and round multi-digit numbers
  • Fluently add and subtract multi-digit numbers (standard algorithm)
  • Multiply up to 4-digit × 1-digit and 2-digit × 2-digit; divide 4-digit ÷ 1-digit
Learning Objectives
  • Generalise place-value understanding for multi-digit whole numbers
Number & Operations — Fractions
Topics
  • Fraction equivalence; compare fractions with different numerators and denominators
  • Add and subtract fractions and mixed numbers with like denominators
  • Multiply a fraction by a whole number
  • Decimal notation for fractions; compare decimals to hundredths
Learning Objectives
  • Build fraction operation fluency and connect fractions with decimal notation
Measurement, Data & Geometry
Topics
  • Convert measurements within a single system
  • Area and perimeter formulas for rectangles
  • Angle measurement; measure and sketch angles with a protractor
  • Classify 2D figures by parallel/perpendicular lines and angle types
  • Lines of symmetry
Learning Objectives
  • Solve measurement problems and understand angles as geometric figures measured in degrees
  • Classify shapes by properties of their lines and angles

Year focus: Fraction operations, decimal operations to thousandths, volume, and the coordinate plane.

Operations & Algebraic Thinking
Topics
  • Numerical expressions with parentheses, brackets, braces; order of operations
  • Patterns and relationships; ordered pairs on a coordinate plane
Learning Objectives
  • Use grouping symbols and structure to evaluate and interpret expressions
Number & Operations (Base Ten + Fractions)
Topics
  • Place-value system including powers of 10; decimals to thousandths
  • Fluently multiply multi-digit whole numbers (standard algorithm)
  • Divide up to 4-digit dividends, 2-digit divisors
  • Add, subtract, multiply, divide decimals to hundredths
  • Add/subtract fractions with unlike denominators; multiply/divide fractions
Learning Objectives
  • Extend place-value understanding to decimals; perform decimal operations fluently
  • Achieve fluency with fraction addition/subtraction; develop fraction multiplication and division
Measurement, Data & Geometry
Topics
  • Convert standard measurement units within a system
  • Understand volume; measure by counting unit cubes; apply V = l × w × h
  • Graph points in the first quadrant of the coordinate plane
  • Classify 2D figures into categories based on properties
Learning Objectives
  • Understand volume as an attribute of solid figures; relate to multiplication and addition
  • Use the coordinate plane and reason about shape category hierarchies

Year focus: Ratios and rates, division of fractions, rational numbers, expressions and equations, statistical thinking.

Ratios & Proportional Relationships
Topics
  • Ratio concepts and language; unit rate
  • Rate/ratio problems using tables, tape diagrams, double number lines
  • Percent of a quantity; unit conversions
Learning Objectives
  • Reason about ratios and rates to solve real-world and mathematical problems
The Number System
Topics
  • Divide fractions by fractions; interpret quotients
  • Fluently divide multi-digit numbers and operate with multi-digit decimals
  • Positive and negative numbers; number lines and coordinate plane
  • Absolute value and ordering of rational numbers
Learning Objectives
  • Extend the number system to include negative rational numbers
Expressions & Equations
Topics
  • Expressions with whole-number exponents
  • Properties of operations to generate equivalent expressions
  • One-variable equations and inequalities; solutions on number lines
  • Dependent and independent variables
Learning Objectives
  • Use variables to represent and reason about quantities and relationships
Geometry & Statistics
Topics
  • Area of triangles, quadrilaterals, and polygons
  • Volume of right rectangular prisms with fractional edges
  • Coordinate plane polygons; surface area using nets
  • Statistical questions; center (mean, median), spread (range, IQR)
  • Dot plots, histograms, and box plots
Learning Objectives
  • Solve real-world problems involving area, surface area, and volume
  • Develop understanding of statistical variability and summarising distributions

Year focus: Proportional relationships, operations with rational numbers, linear expressions, and probability.

Ratios & Proportional Relationships
Topics
  • Unit rates with ratios of fractions
  • Proportional relationships; constant of proportionality
  • Multi-step percent problems — interest, tax, markup, discount, tip
Learning Objectives
  • Analyse proportional relationships and use them to solve real-world problems
The Number System
Topics
  • Add, subtract, multiply, divide rational numbers (including integers and negatives)
  • Additive inverses; rules for operating with signed numbers
  • Convert rational numbers to decimals; terminating/repeating decimals
Learning Objectives
  • Apply and extend operations to all rational numbers
Expressions & Equations
Topics
  • Add, subtract, factor, expand linear expressions
  • Multi-step real-life problems with rational numbers
  • Equations: px + q = r and p(x + q) = r; inequalities
Learning Objectives
  • Use linear equations and inequalities to model and solve problems
Geometry & Statistics / Probability
Topics
  • Scale drawings; triangle construction; cross-sections of solids
  • Area and circumference of a circle
  • Angle relationships; area, volume, surface area of 2D/3D figures
  • Random sampling; comparing data distributions
  • Probability of chance events; compound events
Learning Objectives
  • Draw, construct, and describe geometrical figures; solve measurement problems
  • Investigate chance processes; use sampling to make inferences

Year focus: Linear equations and functions, systems, integer exponents, the Pythagorean Theorem, and bivariate data.

The Number System
Topics
  • Rational vs. irrational numbers; approximate irrationals
  • Estimate values of expressions (e.g., π²); locate irrationals on number line
Learning Objectives
  • Understand the real number system including irrational numbers
Expressions & Equations
Topics
  • Integer exponent properties; square roots and cube roots; scientific notation
  • Slope; graph proportional relationships; unit rate as slope
  • Linear equations in one variable
  • Systems of two linear equations
Learning Objectives
  • Analyse and solve linear equations and pairs of simultaneous linear equations
Functions
Topics
  • Function as a rule assigning one output to each input
  • Compare functions in different representations
  • y = mx + b as a linear function; construct functions to model relationships
  • Qualitative functional relationships from graphs
Learning Objectives
  • Define, evaluate, compare, and use functions to model relationships
Geometry & Statistics
Topics
  • Congruence and similarity using transformations (rotations, reflections, translations, dilations)
  • Pythagorean Theorem and its converse
  • Volume of cylinders, cones, and spheres
  • Scatter plots; association; fit a line; two-way tables
Learning Objectives
  • Use transformations, the Pythagorean Theorem, and volume formulas to solve problems
  • Investigate patterns of association in bivariate data

Year focus: Linear, quadratic, and exponential relationships — the cornerstone high-school course.

Number & Quantity
Topics
  • Rational exponents; work with radicals
  • Quantitative reasoning and units as a modeling tool
Learning Objectives
  • Use units and quantitative reasoning as a tool in modeling
Algebra
Topics
  • Structure of expressions; factoring; completing the square
  • Operations with polynomials
  • Create equations/inequalities in one and two variables
  • Linear, quadratic (factoring, completing square, quadratic formula), and systems
Learning Objectives
  • Master solving and modeling with linear, quadratic, and exponential equations
Functions & Statistics
Topics
  • Function notation; key features (intercepts, max/min, end behavior)
  • Linear, quadratic, exponential functions; compare rates of change
  • Arithmetic and geometric sequences; function transformations
  • Single-variable data (center, spread, outliers)
  • Two-variable data; linear models; correlation vs. causation
Learning Objectives
  • Interpret, analyse, and build functions to model relationships
  • Interpret data and use linear models; distinguish correlation from causation

Year focus: Congruence, similarity, trigonometry, circles, geometric measurement, and proof.

Congruence
Topics
  • Transformations in the plane (rigid motions)
  • Congruence via rigid motions; triangle congruence (ASA, SAS, SSS)
  • Prove theorems: lines, angles, triangles, parallelograms
  • Formal geometric constructions
Learning Objectives
  • Use rigid motions and deductive proof to establish congruence and geometric theorems
Similarity, Right Triangles & Trigonometry
Topics
  • Similarity via dilations; prove similarity theorems
  • Trigonometric ratios: sine, cosine, tangent; solve right triangles
  • Laws of Sines and Cosines (some pathways)
Learning Objectives
  • Apply similarity and right-triangle trigonometry to solve problems
Circles, Coordinates & Modeling
Topics
  • Circle theorems; arc length and sectors
  • Equation of a circle and parabola in coordinates
  • Coordinate proofs (distance, slope, midpoint)
  • Volume of cylinders, pyramids, cones, spheres
  • Geometric modeling — density, design problems
Learning Objectives
  • Prove and apply circle theorems; connect algebra and geometry via coordinates
  • Use geometric measurement and modeling to solve real-world design problems

Year focus: Polynomial, rational, radical, exponential, logarithmic, and trigonometric functions; advanced statistics.

Number & Quantity
Topics
  • Arithmetic with complex numbers; quadratics with complex solutions
  • Fundamental Theorem of Algebra (introductory)
Learning Objectives
  • Extend the number system to complex numbers and use them when solving equations
Algebra
Topics
  • Polynomial arithmetic; Remainder and Factor Theorems; zeros and factors
  • Rational expressions; rational and radical equations (including extraneous solutions)
  • Systems including nonlinear systems
Learning Objectives
  • Manipulate and solve polynomial, rational, and radical expressions and equations
Functions
Topics
  • Polynomial, rational, exponential, logarithmic, and trigonometric functions
  • Inverse functions; exponential/logarithmic equations
  • Periodic phenomena; unit circle; radian measure
  • Pythagorean identity
Learning Objectives
  • Extend function families and model a wide range of real-world phenomena
Statistics & Probability
Topics
  • Normal distribution and standard deviation
  • Statistical experiments, surveys, observational studies; randomisation
  • Conditional probability, independence; probability rules
Learning Objectives
  • Make inferences and justify conclusions from statistical studies and probability models

Year focus: Advanced functions, trigonometry, vectors, matrices, sequences/series — preparation for Calculus.

Functions & Trigonometry
Topics
  • In-depth analysis of polynomial, rational, exponential, logarithmic, trigonometric functions
  • Inverse trig functions; trigonometric equations
  • Trig identities (sum/difference, double-angle, half-angle); Laws of Sines and Cosines
  • Polar coordinates and graphs; parametric equations
  • Limits and continuity (introductory — bridge to calculus)
Learning Objectives
  • Develop fluency with advanced functions and trigonometry needed for calculus
Vectors & Matrices
Topics
  • Vector operations (magnitude, direction, components)
  • Matrix operations; matrices for systems and transformations
  • Determinants and inverses of 2×2 and larger matrices
Learning Objectives
  • Use vectors and matrices to model and solve problems
Conic Sections, Complex Numbers & Sequences
Topics
  • Equations and properties of parabolas, ellipses, and hyperbolas
  • Polar and rectangular forms of complex numbers; De Moivre's Theorem
  • Arithmetic and geometric sequences/series; sigma notation; Binomial Theorem
  • Combinatorics (permutations, combinations)
  • Probability distributions and expected value
Learning Objectives
  • Analyse conic sections and complex numbers in multiple representations
  • Work with sequences, series, and combinatorics; apply expected value to decisions
Exam Preparation

Part 2 — PSAT & SAT Mathematics

Digital PSAT 8/9, PSAT/NMSQT, and Digital SAT Math — content domains, weightings, and a preparation pathway.

Entry point of the PSAT-related suite. Establishes a baseline and identifies areas for growth before high school. Digital, adaptive — calculator (Desmos) allowed throughout.

Algebra
  • Linear equations in one and two variables
  • Linear functions and their graphs
  • Systems of two linear equations
  • Linear inequalities
Advanced Math (Foundational)
  • Equivalent expressions
  • Introduction to nonlinear functions and graphs
Problem-Solving & Data Analysis
  • Ratios, rates, proportional relationships, units
  • Percentages
  • One-variable data: distributions, center, spread
  • Two-variable data: scatterplots and models
  • Probability and conditional probability
  • Inference from sample statistics
Geometry & Trigonometry
  • Area and volume
  • Lines, angles, and triangles
  • Right triangles and basic trigonometry

The PSAT/NMSQT (Grade 11) qualifies students for the National Merit Scholarship Program. Same digital adaptive format as the SAT. Calculator (Desmos) allowed throughout.

Algebra (~35%)
  • Linear equations in one and two variables
  • Linear functions; systems of two linear equations
  • Linear inequalities
Advanced Math (~35%)
  • Equivalent expressions and rewriting
  • Nonlinear equations in one variable and systems
  • Nonlinear functions (quadratic, exponential, polynomial)
Problem-Solving & Data Analysis (~15%)
  • Ratios, rates, proportional relationships, units
  • Percentages; one- and two-variable data analysis
  • Probability, conditional probability, statistical inference
Geometry & Trigonometry (~15%)
  • Area and volume; lines, angles, triangles
  • Right triangles and trigonometry (sin, cos, tan)
  • Circles

Multistage adaptive: two modules; performance on Module 1 determines difficulty of Module 2. Calculator (Desmos) allowed on the entire Math section. Includes multiple-choice and student-produced response (grid-in) questions.

Algebra (~35%)
  • Linear equations in one and two variables
  • Linear functions; systems of two linear equations
  • Linear inequalities; interpreting and modeling with linear relationships
Advanced Math (~35%)
  • Equivalent expressions (factoring, rational, radical, exponent rules)
  • Nonlinear equations in one variable and systems in two variables
  • Nonlinear functions: quadratic, exponential, polynomial, rational
  • Function notation, transformations, and modeling
Problem-Solving & Data Analysis (~15%)
  • Ratios, rates, proportional relationships, units; percent change
  • Distributions; measures of center and spread; scatterplots
  • Probability and conditional probability; inference; margin of error
  • Evaluating statistical claims
Geometry & Trigonometry (~15%)
  • Area and volume formulas in context
  • Lines, angles, triangles (similarity and congruence)
  • Right triangles and trig: sin, cos, tan, Pythagorean Theorem
  • Circles: equations, arcs, sectors, radians, central/inscribed angles
General Preparation Strategy — PSAT → SAT Pathway
  1. Build the foundation early — consistent Grade 8–11 math mastery is the strongest preparation.
  2. Master the built-in Desmos graphing calculator — fluency provides a meaningful speed and accuracy advantage.
  3. Practice full-length digital tests — build pacing and familiarity with the two-module adaptive structure.
  4. Target Algebra and Advanced Math first — together they make up ~70% of the Math section.
  5. Review error logs by domain — Algebra, Advanced Math, Problem-Solving, Geometry — to focus practice where it has the most impact.
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Deepti will assess your child's current level against this curriculum, identify exact gaps, and design a personalised learning plan — at no cost or commitment.

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Common Questions

Frequently Asked Questions

MathsWonder follows the Common Core State Standards (CCSS) for Mathematics, used by 41+ US states. The curriculum covers Grade 3 through Grade 12, progressing through elementary math, middle school math, Algebra I, Geometry, Algebra II, and Precalculus. MathsWonder also prepares students for PSAT 8/9, PSAT/NMSQT, and Digital SAT Math.

Yes. States like Texas (TEKS), Virginia (SOL), and Florida (B.E.S.T.) follow a closely comparable mathematical progression to the Common Core. The underlying topics and grade-level content are virtually identical — only naming conventions differ. Deepti tailors each student's programme to their specific school's requirements.

Yes. MathsWonder offers targeted preparation for the Digital SAT Math section, covering all four content domains: Algebra (~35%), Advanced Math (~35%), Problem-Solving & Data Analysis (~15%), and Geometry & Trigonometry (~15%). Preparation also covers PSAT 8/9 and PSAT/NMSQT for students in Grades 8–11.