On the lap course everybody starts on the dark space and moves clockwise. After the last space you carry on at 0.
With 23 steps on a ring of 5 spaces you go all the way around four times (4 × 5 = 20) and 3 spaces further. You land on space 3. That is division with remainder: 23 ÷ 5 = 4 R 3.
In the backwards puzzle you walk the route in reverse: 4 laps and then space 3 make 4 × 5 + 3 = 23 steps.
For parents
What does this exercise practice?
Division with remainder turns into a movement you can see: the remainder is the bit left over after the whole laps. That also shows why the remainder must always be smaller than the number of spaces.
Common pitfalls
The start space is often counted as the first step, and then the token lands one space too far. The first step leads to space 1. With start space 3, the start space is added to the steps before dividing.
How to practice at home
The seven days of the week are a lap course with 7 spaces: today is Monday, which day is it in 40 days? The clock is a ring too, with 12 spaces: what time is it 50 hours after 3 o'clock?
Related: Table of Values, Number Sequence