The purpose of this activity is to engage students in applying their knowledge of fractions in a geometric context.

In readiness for this problem, the students should have familiarity with each of the following components of mathematics. The problem may be solved with different combinations of these components.

- naming polygons
- regular polygons
- length
- congruent shapes
- area
- non standard units of area
- using fractions to express a proportion

This activity may be carried out with guidance, or by allowing the student to follow their own method of solution. It may be attempted practically, or by using measuring construction techniques. The approach should be chosen in sympathy with students’ skills and depth of understanding.

Here are two equilateral triangles. One has sides that are 3cm long and the other has sides that are 6cm long.

What fraction of the large triangle’s area is the small triangle?

### The procedural approach (show more)

- The student is able to resolve the larger equilateral triangle into a tessellation of smaller equilateral triangles and use this to pattern to find solve the problem.

### The conceptual approach (show more)

- The student is able to find and express a smaller area as a proportion of a larger.