Looking for an engaging math trick to get your students excited while practicing mental math? This “Always 15” mind-reader puzzle is a fantastic classroom favorite.
No matter what starting number your students choose—whether it’s 5, 100, or 1,000—the final answer to this math trick will always be 15.
It works brilliantly as a self-checking task: if a student ends up with an answer other than 15, they know a calculation error happened along the way and can retrace their steps to find it!
Have your students grab a piece of paper or individual whiteboard and follow these simple steps:
Pick any number. (Example: 100)
Multiply by 3. (100 × 3 = 300)
Add 45. (300 + 45 = 345)
Double the result. (345 × 2 = 690)
Divide by 6. (690 ÷ 6 = 115)
Subtract your starting number. (115 – 100 = 15)
I like to use a math trick like this at the start of a math lesson as a quick mental warm-up, or whenever there are a few precious minutes to spare at the end of class that need to be filled with something educational.
Mental Math Warm-Up: Display the steps on the board and have students work through the steps mentally or on whiteboards.
Error Analysis Practice: Remind students that if they don’t hit 15, they need to swap papers with a partner to debug their calculations.
Early Finisher Challenge: Ask students to see if the trick still works with negative numbers, large multi-digit numbers, or decimals.
If you teach upper primary or middle school, you can use this trick to introduce algebraic thinking by writing the steps on the board using $n$ for the starting number:
Start with n
Multiply by 3: 3n
Add 45: 3n + 45
Double it: 2(3n + 45) = 6n + 90
Divide by 6: {6n + 90}/{6} = n + 15
Subtract n: (n + 15) – n = 15
Showing students that dividing the added constant (90 ÷ 6) equals 15 unveils the mystery behind the algebra!
