🧮 Maths hiding in magic

The tricks and their maths

• The Magic Number 1089: Place value, and reversing a three-digit number (roughly Years 4 to 6).
• The Secret Number Cards: Binary: every number built from 1, 2, 4, 8, 16, 32 (roughly Years 4 to 6).
• The Lightning Calendar: The nine times table, and the middle of a square (roughly Years 3 to 5).
• The Heads or Tails Mind Reader: Odd and even, and what one change does to a count (roughly Years 2 to 4).
• The Birthday Mind Reader: Multiplying through brackets, and a constant left over (roughly Years 5 to 7).
• The Answer Is Always 3: Doing and undoing: inverse operations (roughly Years 2 to 4).
• The X-Ray Dice: Opposite faces of a die always add to seven (roughly Years 2 to 4).
• The Calculator Prediction: Factors, and why 12345679 × 63 does that (roughly Years 5 to 7).
• The Countdown Card: Counting on and back to the same place (roughly Years 2 to 4).
• The Magic Clock: Counting round a dial: arithmetic that wraps (roughly Years 3 to 5).
• The Nine Times Fingers: The nine times table, and why the digits of 9 × n add to 9 (roughly Years 3 to 5).
• The Knuckle Calendar: Months and days, and a pattern you can feel (roughly Years 2 to 4).
• The Book Test: Place value again: why every reversal sum lands on 1089 (roughly Years 6 to 8).
• The Instant Magic Square: Adding rows, columns and diagonals; working with an unknown (roughly Years 6 to 8).

Why it never fails

A maths trick works because the steps cancel out whatever number the audience started with, or because every possible answer ends up in the same place. In the shop each one has a "why it works" box written in a child's words, and every one was checked over every possible input before it went up: all the three-digit numbers for 1089, all 216 ways to stack three dice.

For example, The Answer Is Always 3: Doubling a number and adding 6 and halving it leaves their number plus 3. Taking their own number away leaves 3, and it does that whatever they started with, including a huge number or a fraction.

Using it in class

Perform the trick first, and let the class try to break it with their own numbers. When they can't, ask why. The working-out is the lesson, and the trick is why they want to do it.

The maths magician quiz asks which maths is in which trick, and the classroom Top 10 lists the ten with year groups.