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Practising Mathematics: Developing the mathematician as well as the mathematics

How can your students work like mathematicians?

An engaging selection of tasks contain activities from many areas of mathematics including: Number work, Ratio and Proportion, Algebra, Geometry, Probably and Statistics.

 

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Home > Topdrawer > Fractions > Misunderstandings > Using rules blindly > Comparing non-unit fractions

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).

Non-unit fractions to represent the breakfast of two birds, in order to determine the larger fraction.

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?