### Whole Number Dynamics I

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

### Whole Number Dynamics II

This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.

### Whole Number Dynamics III

In this third of five articles we prove that whatever whole number we start with for the Happy Number sequence we will always end up with some set of numbers being repeated over and over again.

# Take Ten Sticks

##### Stage: 3 and 4 Challenge Level:

This problem is good to encourage systematic thinking - working from a simple start : twosticks, three, four . . .

Encourage questions like "what could come before . . . . . and what before that" ?

Working backwards from the goal is a mathematical thinking skill.

Especially encourage explanation - accounting for pattern.

There is lots of interest in this simple mechanical process - look out for the triangle numbers!

Above all, if possible, let each insight prompt fresh questions to consider, each new question will illuminate more of the structure.