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 $N$?