Face fractions


The purpose of this activity is for students to apply equivalent fractions and fractions as operators. The context is about maintaining proportionality of features on a face with reference to the total length of the face.

Achievement Objectives
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
NA4-4: Apply simple linear proportions, including ordering fractions.
Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.


Drawing faces is a lot easier if you know about proportions. The following diagram provides guidelines for the positioning of the facial features.

  1. Now calculate the proportions for these famous self-portraits. Do the proportions match the guidelines?

  2. Photograph your face side on. Do the proportions of your face match those on the diagram? Explain your answers, using measurements and calculations.
  3. Here is a caricature of Albert Einstein. Are his facial features in proportion? Why do you think the artist has drawn him this way?

The procedural approach (show more)

  • The student uses visual perception or fractions as operators to see if the lengths match the desired measures.

The conceptual approach (show more)

  • The student uses knowledge of equivalent fractions or ratios to check whether or not the measures are in proportion.

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