The Nine PatternFROM A PATTERN TO A PROOF

Tap an equation term to connect it to the picture.

A pattern you can explain

Choose a two-digit positive whole number. Add its digits, subtract that sum from the original number, then add the digits of what remains.

47 → 4 + 7 = 11 → 47 − 11 = 36 → 3 + 6 = 9

  1. Follow the steps with Next, or jump to any lesson.
  2. Change the number or its individual digits. All views stay linked.
  3. Tap an equation term to see its meaning in the model.
  4. Use Graphs for the staircase and number line; tap the plot to choose an input.
  5. Use Reading for a flowing page, larger explanations, or a short screen.

The main lesson uses base ten and inputs 10–99. The final two lessons explore larger numbers and other bases. No sign-in is needed; this file works offline. Lesson links become shareable after you host the file.

A graph dot represents an allowed whole-number input. Lines between dots, where shown, are visual guides.