Purpose

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.

Activity

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

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

- Photograph your face side on. Do the proportions of your face match those on the diagram? Explain your answers, using measurements and calculations.

- 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.

Attachments

FaceFractions.pdf196.37 KB