The Task

Put these fractions in order from smallest to largest:
3/4     1/3     11/22     5/4      1/6
Use the Fractions Lab compare box to check your answers.

Teachers' Notes

Students often answer incorrectly, using a) 1/3; 1/6; 3/4; 5/4; 11/22 or b) 1/3; 3/4; 5/4; 1/6; 11/22. It is worthwhile discussing this solution with students because it can come about due to two different incorrect approaches:

1. 1) Students who answer a) have ordered the fractions according to the numerator, and where two numerators are the same, they look to the denominator to make a decision (i.e. 3 is less than 6);
2. 2) Students who answer b) have ordered the fractions according to the denominator, and where two denominators are the same, they look to the numerator to make a decision. While this is correct to some extent (i.e. 3/4 is less than 5/4), they omit to compare the two fractions with the others within the list (so 5/4 is not less than 1/6).

This task also encourages logical thinking as when they are using Fractions Lab, students can compare two fractions at a time in the comparison box and compare fractions visually. Discussing how to order five fractions using the comparison box might be appropriate.

You can also read how to compare fractions by reading the Quick Start Guide, "The operations box: compare, add or subtract".