Complete curriculum for grades 5–7. 29 weekly lessons with full lecture notes, problem sets, solutions, and contests.
Learning Hub
Curriculum & Books
Explore Prime Factor's original curriculum, developed through
more than 15 years of teaching. Across eight levels, the
curriculum is designed around problem-solving, mathematical
reasoning, and clear communication rather than memorization.
Explore what students learn at each level — and the published
math circle books by our founder.
Published by our founder
The books behind our curriculum
Written by Anna Burago and published by the American Mathematical Society, these books are used in Prime Factor classes and in math circles across the United States and abroad.
Complete curriculum for grades 5–7. 29 weekly lessons with full lecture notes, problem sets, solutions, and contests.
Sample Curriculum Outlines
Fall
- From two ends problems
- Digits in masks algebra
- Count the shapes: organized approach
- Playing with polygons
- Mister No
- Kenken and other puzzles
Winter
- Coordinates
- Cuts and pieces problems
- Tricky word problems
- Secret codes
- 3D visual geometry
- Math Kangaroo practice
Spring
- Intervals
- Logic with charts
- Balance it!
- Ancient numbers
- Time and calendar
- Tessellations
Fall
- Logic problems
- Relative comparisons
- Word problems, using tables and bar diagrams
- Cryptography
- Perimeters: smart calculations
- Symmetry
Winter
- Finding areas of complex figures
- Algebra with weights
- 3D visual geometry
- sdrawkcab gnioG
- Math Kangaroo practice
- Problems about age
Spring
- Fractals
- Binary number system
- Number puzzles
- Pascal's triangle
- Ropes and Knots
- Math Domino
Fall
- Smart out-of-the-box problems
- Systems of equations with weights
- Word problems and diagrams
- Ancient number systems
- Combinatorics
- Math Domino
Winter
- Rates problems
- Copycat robots algorithms
- Order of operations
- Venn Diagrams
- Unicursal figures
- Math Kangaroo practice
Spring
- Square and triangular numbers
- Circle geometry with hungry goats
- Area of triangles
- Four colors Theorem
- Ratios problems
- Fibonacci the beautiful
Fall
- Magic squares
- Logic of Knights and Liars
- Special word problems
- Positional number systems
- Speed and motion
- Geometry: angles, lines, triangles
Winter
- Combinatorics
- Combinatorics game
- Tricky areas
- Pythagorean Theorem
- Paths on a grid
- Towers of Hanoi
Spring
- Circles: circumference and area
- Number Theory introduction
- Pentomino play
- 3D Geometry with cubes
- Amazing curves
- Platonic solids
Fall
- Parity and alternations
- Percent
- Averages
- Counting and probability
- Fake coins algorithms
- Math Auction
Winter
- Decimal system
- Binary and other systems
- Tournaments problems
- Invariants
- Arithmetic sequences
- Number Theory topics
Spring
- Double counting method
- Cryptography
- More cryptography
- Introduuction to strategic games
- Math Olympiad prep
- Puzzles
Fall
- Problem potpourri
- Proof methods
- Pigeonhole principle
- Coloring method
- Geometry: triangles
- Linguisitics puzzles
Winter
- Geometry: areas
- Combinatorics
- Pascal's triangle
- Sticks and stones method
- Introduction to Graph theory
- Math Domino
Spring
- More graphs
- Geometry: similar triangles
- Geometry: special triangles!
- Divisibility and remainders
- Triangle inequality
- Endgame analysis
Fall
- Sets and Logic
- Intro to circuits
- Logic gates
- Binary adder
- Modular arithmetic
- Euclidian algorithm
Winter
- Invariants
- Induction
- Double counting
- Recurrence relations
- Fibonacci identities
- Math Auction
Spring
- Graph Theory
- Trees
- Algorithms on graphs
- Cryptography
- Geme Fight
- Set theory intro
Fall
- Foundations: screen geometry and broadcasts
- Conditionals
- Using Variables and counters/li>
- Multiple screens, visual effects
- Collilsion detection and scoring
- Random numbers
Winter
- Logic and game mechanics
- Working with Lists
- Working with strings
- Geometry of spirals
- Walking in a maze
- Clones
Spring
- Creating Art
- Game: clones in action
- Hangman project
- Visual illusions
- Creating games
- Scrolling worlds and advanced animation
Fall
- Mobile app design
- Buttons and events
- Variables and counters
- Logic and conditionals
- Animation
- Functions
- Loops
- Interactive graphics
- Holiday Card project
Winter
- Lists
- Drawing apps
- Timers
- Multi-screen apps
- Arcade games
- Canvas graphics
- Pixel art
- Double loops
- Space Wars
Spring
- Secret image decoder
- Strings
- Coding challenges
- Hangman
- JavaScript objects
- Databases
- Game Lab
- Platform games
- Final game project
Fall
- Math operators and data types
- Variables, for loop
- Conditionals
- Random; logic operators
- Functions
- Turtle module
Winter
- Strings
- Lists
- List functions
- While loop
- Caesar cypher
- List algorithms
Spring
- Events in turtle module
- Function ontimer
- Local and global variables
- Introduction to dictionaries
- Introduction to recurison
Fall
- Lists, strings, dictionaries
- Problems-solving practice
- Modular arithmetic problrms
- Reading from/writing to text files
- Problems that receive their input from text files.
Winter
- Sorting
- Sets
- Problems related to calendar
- 2D lists
- Variable scope
- Function parameters
- Projects with turtle module
Spring
- Dynamic programming
- Using pygame package
- Classes
- Introduction to class inheritance
- Challenges from CS competitions
Fall
- Operations, conditionals
- Integer arithmetic
- While loop
- Algortihms on Strings/li>
- Booleans, Logic
- For loops
Winter
- Character type
- Arrays
- Reading/writing with files
- Lists, array lists
- Java classes, foundations
- Class constructors, "this" keyword
Spring
- Base and derived classes
- Classes inheritance, polymorphism
- Sets
- Recursion
- Maps
- 2D arrays
- Time complexity