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Engaging Maths: Higher Order Thinking with Thinkers Keys

Engaging maths: Higher

All students should be encouraged to engage with higher order thinking tasks. This book uses a critical and creative thinking tool called Thinkers Keys, adapted to be specifically mathematical.

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Cake fractions

The learning object L2801 Fraction fiddle: matching cake fractions uses the context of filling customer orders in a cake shop, where partial cakes can be ordered.

Successful predictions prompt more challenging visualisations, including shapes without division lines and shapes rotated into different positions.


A slice of cake represented as one fifth matched to the correct fraction.

Screen grab from L2801 Fraction fiddle: matching cake fractions.
Source: © Education Services Australia Ltd, 2011 

If using the learning object with the whole class, via a screen or interactive whiteboard, encourage discussion of predictions and visualisation strategies before moving to the checking stage of the activity.

Small teams of students could discuss and make each prediction, and take turns in carrying out the checking. During the checking stage, ask the students to explain what happens with the number of equal cake slices as the denominator is changed.

Students working in pairs can take turns in completing the tasks presented by the learning object, discussing their strategies and any errors. The printed record of the task solutions can be used to support a class debriefing discussion about the most effective strategies.