Junior volumes 1–8 · a visual companion
Little Blue Book, Visualized
Seven books are seven districts and their chapters are stations; the 23 problem-solving methods of Volume 8 are metro lines running through every district. Drag, take apart, guess — then go back to the book.
Key: openopening soon (dashed)visitedlearned ✓
By book
Map too small? Here is the same content as a list. 82 of 82 stops are open.
Vol. 1Factorization TechniquesAlgebra jigsaw · 13 stops
- Ch. 0 What Is Factorization? Concept
- Ch. 1 Taking Out a Common Factor Skill
- Ch. 2 Using the Formulas Skill
- Ch. 3 Factoring by Grouping Skill
- Ch. 4 Splitting and Adding Terms Skill
- Ch. 5 The Cross Method Skill
- Ch. 6 Quadratics in Two Variables Skill
- Ch. 7 Putting It All Together Method
- Ch. 8 Linear Factors of a Polynomial Concept
- Ch. 9 The Method of Undetermined Coefficients Skill
- Ch. 10 Cyclic and Symmetric Expressions Concept
- Ch. 11 Factoring over the Reals and the Complex Numbers Concept
- Ch. 12 Irreducible Polynomials Concept
Vol. 2Equations and Systems of EquationsBalances and graphs · 18 stops
- Ch. 1 Look at a and 1 Concept
- Ch. 2 Linear Equations in One Unknown Skill
- Ch. 3 Linear Equations with Letter Coefficients Skill
- Ch. 4 Using and Rearranging Linear Equations Skill
- Ch. 5 Linear Systems in Two Unknowns Skill
- Ch. 6 Linear Systems in Several Unknowns Skill
- Ch. 7 Learning to Complete the Square Skill
- Ch. 8 Solving Quadratic Equations Skill
- Ch. 9 The Discriminant Concept
- Ch. 10 Vieta's Formulas Concept
- Ch. 11 Higher-Degree Equations Skill
- Ch. 12 Fractional Equations Skill
- Ch. 13 Radical Equations Skill
- Ch. 14 Quadratic Systems in Two Unknowns Skill
- Ch. 15 Integer Solutions of Equations Method
- Ch. 16 Integer Roots of Quadratic Equations Method
- Ch. 17 Word Problems with Equations Skill
- Ch. 18 A Map of Equations Concept
Vol. 3Linear and Quadratic FunctionsGraphs that move · 7 stops
- Ch. 1 Linear Functions: Graphs and Properties Concept
- Ch. 2 Quadratic Functions: Graphs and Properties Concept
- Ch. 3 Functions and Quadratic Equations Concept
- Ch. 4 Functions and Quadratic Inequalities Concept
- Ch. 5 Maxima and Minima of Functions Skill
- Ch. 6 Problems on Integer Roots Method
- Ch. 7 Applications of Functions Skill
Vol. 4Triangles and QuadrilateralsGeometry you can drag · 16 stops
- Ch. 1 Triangles: Basic Concepts and Properties Concept
- Ch. 2 Triangle Area and Side–Angle Theorems Concept
- Ch. 3 Congruent Triangles Skill
- Ch. 4 Similar Triangles Skill
- Ch. 5 Theorems on Proportional Segments in a Triangle Concept
- Ch. 6 The Four Centers of a Triangle Concept
- Ch. 7 Triangles Inscribed in a Triangle Concept
- Ch. 8 Right Triangles Concept
- Ch. 9 Isosceles Triangles Concept
- Ch. 10 Equilateral Triangles Concept
- Ch. 11 Quadrilaterals: Basic Concepts and Properties Concept
- Ch. 12 Parallelograms Concept
- Ch. 13 Rectangles and Rhombuses Concept
- Ch. 14 Squares Concept
- Ch. 15 Trapezoids Concept
- Ch. 16 Cyclic and Tangential Quadrilaterals Concept
Vol. 5CirclesWhat a circle keeps fixed · 11 stops
- Ch. 1 Perimeter and Area of Circles, Sectors and Segments Concept
- Ch. 2 Symmetry of the Circle Concept
- Ch. 3 Angles in a Circle Concept
- Ch. 4 Points, Lines and Circles: Relative Positions Concept
- Ch. 5 Tangents to a Circle Concept
- Ch. 6 Concyclic Points Method
- Ch. 7 The Power of a Point Concept
- Ch. 8 Power of a Point: Applications Skill
- Ch. 9 Ptolemy's Theorem and Its Applications Concept
- Ch. 10 Circumcenter and Incenter of a Triangle Concept
- Ch. 11 Miscellaneous Circle Problems Method
Vol. 6Divisibility, Congruences and Diophantine EquationsA microscope for numbers · 12 stops
- §1.1 Divisibility: Definitions and Basic Properties Concept
- §1.2 Primes and Composites Concept
- §1.3 Greatest Common Divisor and Least Common Multiple Skill
- §1.4 The Fundamental Theorem of Arithmetic Concept
- §2.1 Congruences: Definitions and Basic Properties Concept
- §2.2 Residue Systems and Their Uses Concept
- §2.3 Fermat's Little Theorem and Its Uses Concept
- §2.4 Odd and Even Numbers Method
- §2.5 Perfect Squares Concept
- §3.1 Linear Diophantine Equations (and Systems) Skill
- §3.2 Common Methods for Diophantine Equations Method
- §3.3 The Pythagorean Equation Concept
Vol. 7Fun Problems in CombinatoricsProblems you can play · 5 stops
Vol. 8Problem-Solving Methods and StrategiesMethod lines across the whole map · 23 lines
- M1 Completing the Square
- M2 Substitution
- M3 Discriminant and Vieta
- M4 The Principal Variable
- M5 Symmetry
- M6 Bounding
- M7 The Area Method
- M8 Translation, Rotation and Reflection
- M9 Building Similar Triangles
- M10 Using Circle Properties
- M11 Algebra for Geometry
- M12 Parity
- M13 Prime Factor Analysis
- M14 Choosing a Good Modulus
- M15 Estimation
- M16 The Pigeonhole Principle
- M17 Coloring and Assigning Values
- M18 Cases and Enumeration
- M19 Recursion and Induction
- M20 The Extremal Principle
- M21 From Local to Global
- M22 Generalize and Specialize
- M23 Guess, Then Prove