Why do this problem :

This problem explores the connect between decimal and fraction representations. The preliminary activity should be part of every thinking child's experience of mathematics.

Possible approach :

Start with a preliminary investigation into which fractions make recurring decimals.

Allow students to use electronic calculators and also (essential) to experiment with a standard non-calculator method for the division, to acquire a feel for the elements involved in 'decimalising' a fraction.

Once the group can see which fractions will lead to recurring decimals, and can really understand why, present the Tiny Nines problem.

Key questions :

How can a fraction like $2/7$ or $5/12$ be turned into a decimal representation ?

Without using a calculator ?

When will I get recurring decimals ?

(pointing to the Tiny Nines problem) what pattern to you see and can you make a generalisation ?

Can you demonstrate that ? That the pattern persists, for ever.

Check that the group can also change any recurring decimal into a fraction form, and make this a mini-investigation over time if they are fortunate enough not to have already encountered the standard manoeuvre.

Possible extension :

Sept 03

Possible support :

Activity which concentrates on changing decimals to fractions and fractions to decimals to important work. Ask students to make up a set of eight fractions which don't seem particularly related. Ask then to guess the order of the fractions, smallest to largest.

Direct them to convert each fraction to its decimal form and compare, and then challenge them to find a way to get this ordering right every time, whatever the fractions.