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Mathemagic

Level 2 · Performance Magic

Leapfrog Addition

Ask someone to write down two numbers. Build a sequence of 10 by Fibonacci rules. Then announce the sum of all 10 — before they finish adding.


How to Perform It

  1. Ask a volunteer to write any two numbers (you can even have them choose).
  2. Have them generate 10 terms: each new term = the sum of the previous two.
  3. While they write, glance at the 7th term.
  4. Multiply it by 11 (using the Elevens Trick!) — that's your prediction.
  5. Announce the total before they finish summing all 10.

Worked Example

Starting numbers: 3 and 7

3, 7, 10, 17, 27, 44, 71, 115, 186, 301

7th term = 71. Prediction: 71 × 11 = 781

Actual sum: 3+7+10+17+27+44+71+115+186+301 = 781

Why It Works

Call the two starting numbers a and b. The 10 terms are: a, b, a+b, a+2b, 2a+3b, 3a+5b, 5a+8b, 8a+13b, 13a+21b, 21a+34b. Their sum is 55a + 88b = 11(5a + 8b) — which is exactly 11 times the 7th term.

💡 Teaching Tip

This trick beautifully combines two skills from earlier in the curriculum: Fibonacci sequences (a pattern recognition skill) and the Elevens Trick (multiplying by 11). Use it to show how tricks build on each other.

Try It Yourself

Interactive Sandbox

Leapfrog Addition

Σ

Pick any two starting numbers (1–99). Ten Fibonacci-style numbers will be generated.

Enter two starting numbers to generate the sequence and predict its sum.

Practice offline

Free Worksheet — Leapfrog Addition

10 Leapfrog performance scripts with different starting pairs, plus a blank template for students to create their own. Ideal for classroom demonstrations.

  • 20 graded practice problems
  • Step-by-step answer key
  • Student reference card (wallet size)
  • A4 and US Letter formats
Download Free Worksheet (PDF)

Free. No account required.