London Bridge
Very short, and almost entirely stepwise — a good tune to read rather than play from memory, because your ear will try to run ahead of your eye.
"London Bridge is falling down"
How to play it
It sits across the D and A strings — open A and 1st finger on the A string, 3rd finger and high 2 on the D. The line drops from the A string to the D string on 'falling' and climbs back. Move the whole arm for that crossing; keep the bow light and the strokes short. Read it a note at a time — don't let the familiar tune rush you.
"My fair lady"
How to play it
Four notes to close: 1st finger on the D string, up to the open A, back to high 2 on the D, and settle on the open D — a half note, held, ringing. Two string crossings in four notes, so go slowly and let the arm lead each one.
The one thing this tune is for
Reading a line by step and skip while your ear insists it already knows the tune. Trust the page: name each note, find its string, then play. It's a short line — use it to practise looking.
The usual mistake
Letting the familiar tune run ahead of your eye — playing from memory and drifting off the written notes. Read it a note at a time, out loud, the first few times through. And scraping the string crossings between the D and A strings: lead each one with the whole arm, slowly.