Trachtenberg Speed Math for Kids

Lesson 1: Multiply by 11

Add each digit to its neighbor.

Example: 23 × 11 → 2 _ 3 → 2+3=5 → Answer: 253

Practice: 45 × 11, 67 × 11

Lesson 2: Multiply by 12

Double each digit and add its neighbor.

Example: 34 × 12 → Double 4 = 8 + 3 = 11, Double 3 = 6 → 3 6 8 → Answer: 408

Practice: 23 × 12, 56 × 12

Lesson 3: Multiply by 5

Half the number and add a zero.

Example: 48 × 5 → Half of 48 is 24 → Add zero: 240

Practice: 36 × 5, 82 × 5

Lesson 4: Multiply by 9

Multiply by 10 then subtract the number.

Example: 32 × 9 → 32 × 10 = 320 → 320 − 32 = 288

Practice: 45 × 9, 76 × 9

Lesson 5: Multiply by 4

Double the number twice.

Example: 13 × 4 → 13 × 2 = 26, 26 × 2 = 52

Practice: 15 × 4, 27 × 4

Lesson 6: Multiply by 25

Divide by 4 and add two zeros.

Example: 20 × 25 → 20 ÷ 4 = 5 → Add two zeros: 500

Practice: 40 × 25, 12 × 25

Lesson 7: Multiply by 99

Multiply by 100 then subtract the number.

Example: 47 × 99 → 47 × 100 = 4700 → 4700 − 47 = 4653

Practice: 58 × 99, 23 × 99

Lesson 8: Square numbers ending in 5

Multiply the first digit(s) by the next number, add 25.

Example: 35² → 3 × 4 = 12 → Add 25 → 1225

Practice: 45², 65²

Lesson 9: Multiply by 15

Multiply by 10, then add half the number.

Example: 40 × 15 → 40 × 10 = 400, Half of 40 = 20, 400 + 200 = 600

Practice: 20 × 15, 36 × 15

Lesson 10: Check with Reverse

Multiply and divide back to check.

Example: 23 × 11 = 253 → 253 ÷ 11 = 23 ✅

Practice: 12 × 11, then check; 15 × 9, then check