Comparing non-unit fractions

Display the learning object L2803 Fraction fiddle: comparing non-unit fractions to the class on an interactive whiteboard (or projector and screen).

Screen grab from L2803 Fraction fiddle: comparing non-unit fractions.
Source: © Education Services Australia Ltd, 2011 

• Work through a task together, pausing for students to make predictions.
  •  Which fraction do you think is smaller/larger?
  •  Why do you think that?
• Encourage students to notice the relationships between the numerator/denominator and the construction of the fraction bar.
  • What happens to the bar as the denominator gets larger?
  • What happens to the bar as the numerator gets larger?
• Encourage students to notice the position of the fractions on the number line.
  • Look where \(\frac{3}{4}\) is located. Where would \(\frac{1}{4}\) be? What about \(\frac{1}{2}\)?
  • Is \(\frac{2}{5}\) going to be closer to 1 than \(\frac{3}{4}\) or further away? Why do you think so?

Students can work in pairs at computers to complete a set of tasks. The printed record of their findings can be the basis of further discussions about strategies for solving similar tasks without the learning object.

• What can you do to help you work out which fraction is larger or smaller?
• Why can’t you decide just by looking at the denominators?