### Rationals Between...

What fractions can you find between the square roots of 65 and 67?

### There's a Limit

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

### Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

# Circuit Training

##### Age 14 to 16 Challenge Level:

It is worth spending some time discussing the strategies pupils have adopted.

Another question might be:
What is the ratio of the speeds of the two runners if they are to meet at the start after $1$ lap, $2$ laps, $3$ laps... $n$ laps?.

What is the relationship betweent he ratio of the speeds of the runners and where they meet?