Here are four fractions all jumbled up: 1/2, 1/3, 2/3, 5/6. If I asked you to line them up from smallest to biggest, which one would you put first? What is tricky about doing that when the bottom numbers are all different?

Each fraction is shaded on its own strip, and every strip is the same length. The further the shading reaches, the bigger the fraction. Watch first, then check by re-writing over a common denominator.

Now we order this set together at the board: 1/4, 3/8, 1/2, 5/8. Before each strip is shaded you predict where its shading will reach — further or shorter than the one before — and then one of you shades it and we see whether the prediction held. When all four are shaded, we read the order out loud, smallest first.

Today we order three sets, each one a step harder than the last: first 2/5, 1/2, 3/5, 7/10, then 1/3, 1/2, 2/3, 5/6, then the trickiest one 1/3, 5/12, 1/2, 3/4. We'll shade each set and read the order off, smallest first.