Two classic questions - putting a steel band around the earth, and marking out a running track. Given as a short practice assignment to Maths B early in year 11, but suitable when studying circumference of a circle in year 9 or year 10. Probably too difficult for most year 8 students. Answer is supplied by Dr. Math. Printed with tiny margins and tiny print, it fits onto 3 sheets of paper.
Kids enjoy looking for patterns in the digits.
The Expanding Rail Line Imagine that there is a section of railway line one kilometre long, made without gaps, and fixed at each end so that it cannot take up the expansion on a hot day. Determine whether the teacher is correct. Repeat with the same 3 triangles but put equilateral triangles on the 3 sides. This article will help. I had my students evaluate several different series to 2500 terms in the space of a few minutes, once they got the knack of setting the things up.