The challenges in this book are mainly designed for able mathematicians in elementary or middle school although many of the tasks are appropriate for a much wider range of ages. Extensively trialled through the author's work as a Mathematics Advisor in Kent, UK. Each task has a Task Sheet describing the challenge and Explanatory Notes that include learning objectives, resources implications, advice, answers and possible further study. Teachers and parents will find it invaluable. The challenges are graded in terms of their accessibility to a wide range of ability (rather than in terms of difficulty). Many of the challenges are presented as practical problems to help pupils develop their mathematical thinking.