### Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

### 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?

### Comparing Continued Fractions

Which of these continued fractions is bigger and why?

# Not Continued Fractions

### Why do this problem?

For experience of reasoning about the integer part of a number and working with fractions.

### Possible approach

Challenge the students to invent their own problems of this type.

### Key question

What is the integer part of $N$?