For Math Educators

The complete panel for math teachers

Lesson plans, worked examples, formula references, quizzes, and teaching tools — all in one place. Built by educators, for educators.

✦ Quadratic Formula
Worked Example — Quadratics
ax² + bx + c = 0
1 Identify coefficients: a = 2, b = −5, c = 3
2 Apply discriminant: b² − 4ac = 25 − 24 = 1
3 Solve: x = (5 ± 1) / 4 → x = 1.5 or x = 1
✓ Solutions: x = 3/2 and x = 1
📐 Geometry Tools
12+
Math Topics
80+
Worked Examples
150+
Formula Cards
40+
Lesson Plans
Browse by Topic

Everything you need to teach

From foundational arithmetic to advanced calculus — organized, referenced, and ready to use in your classroom.

➕
Arithmetic
Integers, fractions, decimals, percentages, and order of operations.
14 examples · 6 lessons
🔣
Algebra
Linear equations, polynomials, factoring, systems, and inequalities.
22 examples · 9 lessons
📐
Geometry
Angles, triangles, circles, area, volume, and coordinate geometry.
18 examples · 8 lessons
📈
Functions & Graphs
Linear, quadratic, exponential, logarithmic, and piecewise functions.
16 examples · 7 lessons
∫
Calculus
Limits, derivatives, integrals, chain rule, and applications.
24 examples · 10 lessons
🎲
Statistics & Probability
Mean, median, distributions, hypothesis testing, and combinatorics.
20 examples · 8 lessons
📊
Trigonometry
Sine, cosine, tangent, unit circle, identities, and inverse trig.
15 examples · 6 lessons
∑
Number Theory
Primes, divisibility, GCD, LCM, modular arithmetic, and sequences.
10 examples · 4 lessons
Worked Examples

Step-by-step solutions

Fully worked problems with clear reasoning. Perfect for lesson prep, handouts, or projecting in class.

Solving a Quadratic Equation Medium
Solve: 2x² − 5x + 3 = 0
  • Identify: a=2, b=−5, c=3
  • Discriminant: b² − 4ac = 25 − 24 = 1
  • Apply formula: x = (5 ± √1) / 4
  • Two solutions: x = 6/4 = 3/2 and x = 4/4 = 1
✓ x = 3/2 and x = 1
Factoring a Polynomial Easy
Factor completely: x² + 7x + 12
  • Find two numbers that multiply to 12 and add to 7
  • Pairs: (1,12), (2,6), (3,4) → 3 + 4 = 7 ✓
  • Write as: (x + 3)(x + 4)
  • Verify: x² + 4x + 3x + 12 = x² + 7x + 12 ✓
✓ (x + 3)(x + 4)
Solving Linear System Medium
Solve: 3x + 2y = 12 and x − y = 1
  • From equation 2: x = y + 1
  • Substitute: 3(y+1) + 2y = 12 → 5y = 9
  • Solve: y = 9/5, then x = 9/5 + 1 = 14/5
  • Check in eq. 1: 3(14/5) + 2(9/5) = 42/5 + 18/5 = 60/5 = 12 ✓
✓ x = 14/5, y = 9/5
Completing the Square Hard
Rewrite in vertex form: y = x² − 6x + 2
  • Take half of −6: −6/2 = −3, square it: (−3)² = 9
  • Add and subtract 9: y = (x² − 6x + 9) − 9 + 2
  • Factor perfect square: y = (x − 3)² − 7
  • Vertex is at (3, −7)
✓ y = (x − 3)² − 7 · Vertex: (3, −7)
Area of a Triangle Easy
Triangle with base = 8 cm, height = 5 cm. Find the area.
  • Formula: A = ½ × base × height
  • Substitute: A = ½ × 8 × 5
  • Calculate: A = ½ × 40 = 20
✓ Area = 20 cm²
Pythagorean Theorem Easy
Right triangle: legs a = 6, b = 8. Find the hypotenuse c.
  • Apply: c² = a² + b²
  • Substitute: c² = 36 + 64 = 100
  • Solve: c = √100 = 10
✓ c = 10 units (classic 6-8-10 triple)
Volume of a Cylinder Medium
Cylinder with radius r = 4 cm, height h = 10 cm. Find the volume.
  • Formula: V = π r² h
  • Substitute: V = π × 16 × 10
  • Calculate: V = 160π ≈ 502.65 cm³
✓ V = 160π ≈ 502.65 cm³
Circle: Arc Length Medium
Circle with radius 9, central angle θ = 120°. Find arc length.
  • Convert angle: 120° = 2π/3 radians
  • Formula: L = r × θ
  • Calculate: L = 9 × 2π/3 = 6π ≈ 18.85
✓ Arc length = 6π ≈ 18.85 units
Basic Derivative Easy
Find f'(x) for f(x) = 3x⁴ − 5x² + 7x − 2
  • Power rule: d/dx [xⁿ] = n·xⁿ⁻¹
  • Differentiate each term: 4·3x³ = 12x³
  • Then: −2·5x¹ = −10x, then 7, then 0
✓ f'(x) = 12x³ − 10x + 7
Chain Rule Hard
Differentiate: y = sin(3x² + 1)
  • Outer function: sin(u), inner: u = 3x² + 1
  • Outer derivative: cos(u)
  • Inner derivative: du/dx = 6x
  • Chain rule: dy/dx = cos(3x²+1) · 6x
✓ dy/dx = 6x·cos(3x² + 1)
Definite Integral Medium
Evaluate: ∫₀³ (2x + 1) dx
  • Find antiderivative: ∫(2x+1)dx = x² + x + C
  • Evaluate at bounds: F(3) = 9 + 3 = 12
  • Subtract: F(3) − F(0) = 12 − 0
✓ Integral = 12
Limit at Infinity Medium
Evaluate: lim(x→∞) (3x² + 2x) / (5x² − 1)
  • Divide numerator and denominator by x²
  • Get: (3 + 2/x) / (5 − 1/x²)
  • As x→∞, terms with x vanish: 3/5
✓ Limit = 3/5
Mean, Median, Mode Easy
Dataset: {4, 7, 7, 3, 9, 7, 5, 6}
  • Sort: 3, 4, 5, 6, 7, 7, 7, 9
  • Mean: (3+4+5+6+7+7+7+9)/8 = 48/8 = 6
  • Median (n=8): avg of 4th & 5th: (6+7)/2 = 6.5
  • Mode: most frequent value: 7 (appears 3×)
✓ Mean = 6 · Median = 6.5 · Mode = 7
Standard Deviation Medium
Find σ for: {2, 4, 4, 4, 5, 5, 7, 9}
  • Mean: μ = (2+4+4+4+5+5+7+9)/8 = 40/8 = 5
  • Squared deviations: 9,1,1,1,0,0,4,16 → sum=32
  • Variance: σ² = 32/8 = 4
  • Std dev: σ = √4 = 2
✓ σ = 2
Probability: Complement Easy
Probability of rolling a 6 on a fair die at least once in 3 rolls.
  • P(no 6 in one roll) = 5/6
  • P(no 6 in 3 rolls) = (5/6)³ = 125/216
  • Complement: P(at least one 6) = 1 − 125/216
✓ P ≈ 91/216 ≈ 42.1%
Z-Score Medium
Test score = 85, class mean = 72, σ = 10. Find z-score.
  • Formula: z = (x − μ) / σ
  • Substitute: z = (85 − 72) / 10
  • Calculate: z = 13/10 = 1.3
  • Interpretation: 1.3 standard deviations above the mean
✓ z = 1.3 (above average)
SOHCAHTOA Easy
Right triangle: hypotenuse = 13, opposite = 5. Find sin, cos, tan of angle θ.
  • Find adjacent: adj = √(13²−5²) = √(169−25) = √144 = 12
  • sin(θ) = opp/hyp: 5/13
  • cos(θ) = adj/hyp: 12/13
  • tan(θ) = opp/adj: 5/12
✓ sin=5/13, cos=12/13, tan=5/12
Trig Identity Proof Hard
Prove: sin²θ + cos²θ = 1 using the unit circle definition.
  • On unit circle: point is (cos θ, sin θ)
  • Distance from origin = radius = 1
  • By distance formula: √(cos²θ + sin²θ) = 1
  • Square both sides: cos²θ + sin²θ = 1 ∎
✓ Proven via unit circle definition
Solving a Trig Equation Medium
Solve: 2sin(x) − 1 = 0 for x ∈ [0, 2π]
  • Isolate: sin(x) = 1/2
  • Reference angle: x = π/6
  • Sine is positive in Q1 and Q2: x = π/6 and x = 5π/6
✓ x = π/6 and x = 5π/6
Law of Sines Medium
Triangle: A=45°, B=60°, a=10. Find b.
  • Law of Sines: a/sin A = b/sin B
  • Substitute: 10/sin(45°) = b/sin(60°)
  • Solve: b = 10·sin(60°)/sin(45°)
  • Calculate: b = 10·(√3/2)/(√2/2) = 10√3/√2 = 5√6 ≈ 12.25
✓ b = 5√6 ≈ 12.25
Quick Reference

Essential Formula Cards

Print-ready formula reference for your classroom or students' notes.

Quadratics
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Δ = b²−4ac is the discriminant
Geometry
Circle Formulas
A = πr²
C = 2πr
L = rθ (arc)
θ must be in radians for arc length
Trigonometry
Pythagorean Identity
sin²θ + cos²θ = 1
tan²θ + 1 = sec²θ
Derived from unit circle
Calculus
Power Rule
d/dx [xⁿ] = n · xⁿ⁻¹
Works for any real exponent n
Calculus
Chain Rule
d/dx [f(g(x))] = f'(g(x)) · g'(x)
Outer × inner derivative
Statistics
Standard Deviation
σ = √[Σ(xᵢ−μ)²/N]
Use N−1 for sample std dev
Geometry
Volume Formulas
Cylinder: πr²h
Cone: ⅓πr²h
Sphere: (4/3)πr³
All require r in same unit as h
Algebra
Binomial Expansion
(a+b)² = a²+2ab+b²
(a+b)³ = a³+3a²b+3ab²+b³
See Pascal's Triangle for higher powers
Calculus
Fundamental Theorem
∫ₐᵇ f(x)dx = F(b) − F(a)
F is the antiderivative of f
Classroom Ready

Lesson Plan Library

Structured lesson outlines with learning objectives, activities, and assessment ideas.

01

Introduction to Functions — Mapping and Notation

Domain, range, function notation, vertical line test, and real-world examples.

Algebra II 60 min
02

Understanding the Derivative — Rate of Change

Graphical interpretation, limit definition, and connection to slope of tangent lines.

Calculus 75 min
03

Probability Trees and Conditional Events

Drawing tree diagrams, compound events, P(A|B), and the multiplication rule.

Statistics 50 min
04

The Unit Circle — Radians and Exact Values

Converting degrees to radians, memorizing key values, symmetry properties.

Trigonometry 60 min
05

Graphing Parabolas — Vertex Form and Transformations

Shift, stretch, reflection. From standard form to vertex form via completing the square.

Algebra II 65 min
06

Introduction to Limits — Approaching a Value

Intuitive definition, one-sided limits, limit laws, and indeterminate forms.

Pre-Calculus 55 min
Test Your Students

Interactive Quiz

Sample questions across topics — great for warm-ups, exit tickets, or review.

Loading...
Question 1 of 10
Math Dictionary

Glossary of Key Terms

Precise definitions with examples — ready to print as student handouts.

Derivative
The instantaneous rate of change of a function with respect to a variable. Geometrically, it's the slope of the tangent line at a point.
e.g. If f(x) = x², then f'(x) = 2x
Asymptote
A line that a curve approaches but never touches. Can be vertical, horizontal, or oblique.
e.g. y = 1/x has a vertical asymptote at x = 0
Eigenvalue
A scalar λ such that Av = λv for a square matrix A and non-zero vector v. Fundamental to linear transformations.
e.g. Used in PCA, quantum mechanics, and graph theory
Modular Arithmetic
A system where numbers "wrap around" after reaching a certain value (the modulus). Also called "clock arithmetic".
e.g. 17 mod 5 = 2 (because 17 = 3×5 + 2)
Bijection
A function that is both injective (one-to-one) and surjective (onto). Every element in the codomain is mapped to by exactly one domain element.
e.g. f(x) = 2x+1 is a bijection from ℝ to ℝ
Determinant
A scalar value computed from a square matrix that encodes volume scaling and orientation of a linear transformation.
e.g. det([a,b;c,d]) = ad − bc
Congruence
Two geometric figures are congruent if they have exactly the same shape and size. Denoted with ≅.
e.g. ΔABC ≅ ΔDEF means all sides and angles are equal
Composite Function
A function formed by applying one function to the result of another. Written as (f ∘ g)(x) = f(g(x)).
e.g. f(x)=x², g(x)=x+1 → (f∘g)(x) = (x+1)²
Tools & Downloads

Teaching Resources

Printable worksheets, calculator guides, and classroom tools ready to use.

📋

Printable Worksheets

Differentiated practice sheets for each topic — beginner, intermediate, and challenge levels with answer keys.

Browse worksheets →
🖩

Graphing Calculator Guide

Step-by-step instructions for TI-84, Desmos, and GeoGebra covering all common classroom tasks.

View guide →
📊

Rubrics & Grading

Standards-aligned scoring rubrics for problem-solving, proofs, and explanatory writing.

Download rubrics →
🎯

Learning Objectives Bank

A full library of measurable learning objectives mapped to Common Core and IB syllabuses.

Explore objectives →
🃏

Flash Card Sets

Printable and digital flash cards for formulas, definitions, and common integrals and derivatives.

Get flash cards →
🗓️

Annual Curriculum Map

Week-by-week pacing guides for Algebra I, Algebra II, Pre-Calculus, and Calculus courses.

See pacing guides →