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Number Theory

Primes, factors, GCD, LCM, and divisibility rules - the building blocks of number sense.

To find GCD(a,b): repeatedly replace the larger with the remainder until 0. Then LCM = a×-b ÷ GCD.

Visual Methods

Number theory approach board showing divisibility, GCD, and LCM structure
1Approach
Divisibility rules board for 462 and 724
2Divisibility Rules
Prime check board for 97
3Prime Checking
Euclidean GCD board for 48 and 18
4GCD: Euclidean Algorithm
LCM from GCD board for 12 and 18
5LCM from GCD

Level Visual Guides

30 levels. Each level opens as 6 visual blocks.

Level 1 visual plan for Primes (≤ 30)

Level 1 - foundation

Primes (≤ 30)

6 image blocks

Level 2 visual plan for Primes (≤ 50)

Level 2 - foundation

Primes (≤ 50)

6 image blocks

Level 3 visual plan for Primes (50-200)

Level 3 - realistic untimed

Primes (50-200)

6 image blocks

Level 4 visual plan for Primes (100-500)

Level 4 - foundation

Primes (100-500)

6 image blocks

Level 5 visual plan for Divisibility intro (2, 3, 5)

Level 5 - foundation

Divisibility intro (2, 3, 5)

6 image blocks

Level 6 visual plan for Divisibility (2-6)

Level 6 - foundation

Divisibility (2-6)

6 image blocks

Level 7 visual plan for Divisibility (3-9)

Level 7 - foundation

Divisibility (3-9)

6 image blocks

Level 8 visual plan for Divisibility (all small rules)

Level 8 - realistic untimed

Divisibility (all small rules)

6 image blocks

Level 9 visual plan for GCD (small, ≤ 30)

Level 9 - foundation

GCD (small, ≤ 30)

6 image blocks

Level 10 visual plan for GCD (≤ 50)

Level 10 - foundation

GCD (≤ 50)

6 image blocks

Level 11 visual plan for GCD (≤ 80)

Level 11 - build-up

GCD (≤ 80)

6 image blocks

Level 12 visual plan for GCD (≤ 120)

Level 12 - build-up

GCD (≤ 120)

6 image blocks

Level 13 visual plan for GCD (≤ 200)

Level 13 - realistic untimed

GCD (≤ 200)

6 image blocks

Level 14 visual plan for GCD (≤ 300)

Level 14 - build-up

GCD (≤ 300)

6 image blocks

Level 15 visual plan for GCD mastery (≤ 500)

Level 15 - build-up

GCD mastery (≤ 500)

6 image blocks

Level 16 visual plan for LCM (≤ 12)

Level 16 - build-up

LCM (≤ 12)

6 image blocks

Level 17 visual plan for LCM (≤ 18)

Level 17 - build-up

LCM (≤ 18)

6 image blocks

Level 18 visual plan for LCM (≤ 25)

Level 18 - realistic untimed

LCM (≤ 25)

6 image blocks

Level 19 visual plan for LCM (≤ 35)

Level 19 - build-up

LCM (≤ 35)

6 image blocks

Level 20 visual plan for LCM (≤ 50)

Level 20 - build-up

LCM (≤ 50)

6 image blocks

Level 21 visual plan for LCM (≤ 60)

Level 21 - mastery

LCM (≤ 60)

6 image blocks

Level 22 visual plan for LCM mastery (≤ 80)

Level 22 - mastery

LCM mastery (≤ 80)

6 image blocks

Level 23 visual plan for Rules - small (2, 3, 4, 5)

Level 23 - realistic untimed

Rules - small (2, 3, 4, 5)

6 image blocks

Level 24 visual plan for Rules - even (4, 6, 8)

Level 24 - mastery

Rules - even (4, 6, 8)

6 image blocks

Level 25 visual plan for Rules - digit-sum (3, 9)

Level 25 - mastery

Rules - digit-sum (3, 9)

6 image blocks

Level 26 visual plan for Rule for 7

Level 26 - mastery

Rule for 7

6 image blocks

Level 27 visual plan for Rule for 11

Level 27 - mastery

Rule for 11

6 image blocks

Level 28 visual plan for Rule for 12

Level 28 - realistic untimed

Rule for 12

6 image blocks

Level 29 visual plan for Rules - all (small N)

Level 29 - mastery

Rules - all (small N)

6 image blocks

Level 30 visual plan for Rules mastery (4-digit N)

Level 30 - mastery

Rules mastery (4-digit N)

6 image blocks

Practice this category

Use the same method on live number theory levels.

Start Number Theory Workout

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