Arithmetic Diagrams: Every Figure on the Arithmetic Pages

20 tiles in 4 groups of 5: divisible

Divisibility: Factors, Primes, GCD & LCM › What is Divisibility?

23 = 5 · 4 + 3: four full rows and three left over

Divisibility: Factors, Primes, GCD & LCM › Divisibility and Remainders

The sieve finished: only the primes remain unmarked

Divisibility: Factors, Primes, GCD & LCM › Prime Numbers

gcd(252, 105) = 21 by repeated division

Divisibility: Factors, Primes, GCD & LCM › GCD and LCM

Number line scene (single track)

Divisibility: Factors, Primes, GCD & LCM › Basic Properties

Factor pairs

Divisibility: Factors, Primes, GCD & LCM › Factors and Multiples

The ÷3 column: the multiples of 3 marked down the table

Factors and Multiples: Divisors, Pairs & Counting › Multiples

Factor set (single)

Factors and Multiples: Divisors, Pairs & Counting › Factors (Divisors)

Factor pairs

Factors and Multiples: Divisors, Pairs & Counting › Finding All Factors

Factor pairs

Factors and Multiples: Divisors, Pairs & Counting › Factor Pairs

Factor set (single)

Factors and Multiples: Divisors, Pairs & Counting › Proper Divisors

Split view (factors vs multiples)

Factors and Multiples: Divisors, Pairs & Counting › Factors vs Multiples

Common factors of two numbers

Factors and Multiples: Divisors, Pairs & Counting › Common Factors

Factor set (single)

Factors and Multiples: Divisors, Pairs & Counting › Counting Factors

Factor set (single)

Factors and Multiples: Divisors, Pairs & Counting › Sum of Factors

gcd(252, 105) = 21 in three divisions

GCD: Greatest Common Divisor & Euclidean Algorithm › Method 3: Euclidean Algorithm

Common factors of two numbers

GCD: Greatest Common Divisor & Euclidean Algorithm › What is GCD?

Common factors of two numbers

GCD: Greatest Common Divisor & Euclidean Algorithm › Method 1: Listing Factors

Prime factorizations — gcd(48, 180)

GCD: Greatest Common Divisor & Euclidean Algorithm › Method 2: Prime Factorization

Euclidean algorithm chain

GCD: Greatest Common Divisor & Euclidean Algorithm › Euclidean Algorithm Step by Step

Euclidean algorithm chain

GCD: Greatest Common Divisor & Euclidean Algorithm › Euclidean Algorithm Step by Step

48 × 80 rectangle

GCD: Greatest Common Divisor & Euclidean Algorithm › Applications of GCD

48 × 80 rectangle

GCD: Greatest Common Divisor & Euclidean Algorithm › Applications of GCD

The ÷6 column: 6, 12, 18, 24, …

LCM: Least Common Multiple & GCD Formula › Method 1: Listing Multiples

Number line scene (two tracks)

LCM: Least Common Multiple & GCD Formula › What is LCM?

Prime factorizations — lcm(12, 18)

LCM: Least Common Multiple & GCD Formula › Method 2: Prime Factorization

Number line scene (two tracks)

LCM: Least Common Multiple & GCD Formula › Applications of LCM

The ÷2 column: every other number

Divisibility Rules: Tests for 2, 3, 4, 5, 6, 8, 9, 10, 11 › Divisibility by 2

126: digit sum 9, so divisible by 3 and by 9

Divisibility Rules: Tests for 2, 3, 4, 5, 6, 8, 9, 10, 11 › Divisibility by 3

The ÷4 column: every fourth number

Divisibility Rules: Tests for 2, 3, 4, 5, 6, 8, 9, 10, 11 › Divisibility by 4

Divisibility by 5: last 1 digits of 4835

Divisibility Rules: Tests for 2, 3, 4, 5, 6, 8, 9, 10, 11 › Divisibility by 5

Divisibility by 8: last 3 digits of 53104

Divisibility Rules: Tests for 2, 3, 4, 5, 6, 8, 9, 10, 11 › Divisibility by 8

Divisibility by 9: digit sum of 8127

Divisibility Rules: Tests for 2, 3, 4, 5, 6, 8, 9, 10, 11 › Divisibility by 9

Divisibility by 10: last 1 digits of 5230

Divisibility Rules: Tests for 2, 3, 4, 5, 6, 8, 9, 10, 11 › Divisibility by 10

Divisibility by 11: alternating sum of 9273

Divisibility Rules: Tests for 2, 3, 4, 5, 6, 8, 9, 10, 11 › Divisibility by 11

gcd(252, 105) = 21: the factor that reduces 105/252 to 5/12

Equivalent Fractions: Simplify & Find Common Denominators › Simplifying Fractions

Counting round a wheel of 6: the remainder is the slot you land on

Modulo: Remainders, Congruence & Clock Arithmetic › What is Modulo?

Six slots, six possible remainders: 0 to 5

Modulo: Remainders, Congruence & Clock Arithmetic › The Range of Remainders

One slot holds 3, 9, 15, …: a congruence class

Modulo: Remainders, Congruence & Clock Arithmetic › Congruence

One class, many representatives

Modulo of Negative Numbers: Truncated vs Floored Division › Congruence Perspective

The playing field mod 6: slots 0 to 5

Modular Arithmetic: Operations, Power Cycles & Applications › Operating Within a Modulus

÷1 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 1

÷2 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 2

÷3 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 3

÷4 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 4

÷5 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 5

÷6 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 6

÷7 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 7

÷8 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 8

÷9 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 9

÷10 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 10

÷11 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 11

÷12 selected, frozen

Interactive Divisibility Table › Divisibility Rule for 12

÷2 and ÷3 selected, frozen

Interactive Divisibility Table › Combining Divisors

23 tiles, ungrouped, frozen

Divisibility Tiles Interactive Visualizer › Understanding the Tiles Display

20 ÷ 5, frozen

Divisibility Tiles Interactive Visualizer › What is Divisibility?

23 ÷ 5, frozen

Divisibility Tiles Interactive Visualizer › Division, Quotients, and Remainders

3 ÷ 5, frozen

Divisibility Tiles Interactive Visualizer › When the Divisor Is Larger Than the Number

No input, frozen

Divisibility Decision Tree Interactive Tool › How to Use the Decision Tree

26 entered, frozen

Divisibility Decision Tree Interactive Tool › The Even/Odd Split

45 entered, frozen

Divisibility Decision Tree Interactive Tool › The Odd Shortcut

104 entered, frozen

Divisibility Decision Tree Interactive Tool › The Powers of Two Chain

126 entered, frozen

Divisibility Decision Tree Interactive Tool › Digit Sum Rules for 3 and 9

50 entered, frozen

Divisibility Decision Tree Interactive Tool › When the Digit Sum Fails

13 entered, frozen

Divisibility Decision Tree Interactive Tool › Only Divisible by 1: Prime Suspects

Initial grid, frozen

Sieve of Eratosthenes Visualization › How to Use the Sieve Visualization

Sieve complete, frozen

Sieve of Eratosthenes Visualization › Understanding the Grid Display

After the ÷2 sweep, frozen

Sieve of Eratosthenes Visualization › The First Pass: Multiples of 2

After the ÷3 sweep, frozen

Sieve of Eratosthenes Visualization › The Second Pass: Multiples of 3

After the ÷5 sweep, frozen

Sieve of Eratosthenes Visualization › Why Start at p²?

After the ÷7 sweep, frozen

Sieve of Eratosthenes Visualization › The Last Pass: Multiples of 7

252 and 105, frozen

Euclidean Algorithm Visualizer › Getting Started with the Visualizer

36 and 36, frozen

Euclidean Algorithm Visualizer › Why the Algorithm Works

462 and 198, frozen

Euclidean Algorithm Visualizer › Short Chains: When a Remainder Divides Its Divisor

1071 and 462, frozen

Euclidean Algorithm Visualizer › The Textbook Example: 1071 and 462

54 and 35, frozen

Euclidean Algorithm Visualizer › Coprime Pairs: When the GCD Is 1

144 and 89, frozen

Euclidean Algorithm Visualizer › The Worst Case: Fibonacci Pairs

84 and 56, frozen

Euclidean Algorithm Visualizer › Special Cases and Corner Behavior

mod 6, idle, frozen

Modular Arithmetic Wheel Visualizer › Getting Started

mod 6, placing 17, frozen

Modular Arithmetic Wheel Visualizer › Run Controls and Speed

mod 6, class 2 pinned, frozen

Modular Arithmetic Wheel Visualizer › Hovering and Pinning Classes

mod 6, zero class pinned, frozen

Modular Arithmetic Wheel Visualizer › The Zero Class — Why It's Special

mod 2, 20 placed, frozen

Modular Arithmetic Wheel Visualizer › Adjusting Divisor and Count

mod 6, run complete, frozen

Modular Arithmetic Wheel Visualizer › Reading a Complete Run

100 in base 10, frozen

Base Conversion Visualizer › Decimal: Base 10

100 in base 2, frozen

Base Conversion Visualizer › Binary: Base 2

100 in base 8, frozen

Base Conversion Visualizer › Octal: Base 8

100 in base 16, frozen

Base Conversion Visualizer › Hexadecimal: Base 16

100 in base 36, frozen

Base Conversion Visualizer › Base 36: Every Digit and Every Letter