The purpose of this activity is to engage students in finding a pattern from multiplying dimensions and to generalise this pattern with a rule.

The background knowledge and skills that need to be established before and/or during this activity are outlined in the diagram below:

Click to show example questions for each heading

The students are encouraged to work with natural (counting) numbers for trials of scale factors. This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.

If a triangle is enlarged by scale factor 2, what is its increase in area?

What if the scale factor was 3?

What if the scale factor was n?

### The arithmetic approach (show more)

- The student is able to find the areas of an original triangle and an enlarged triangle, and to relate the scale factor to the increased area of the enlarged triangle.
- The students are encouraged to work with natural (counting) numbers for trials of scale factors.

### The conceptual approach (show more)

- The student is able to find the areas of an original triangle and an enlarged triangle, and to generalise the increase in area, in terms of the scale factor.
- The students are encouraged to work with natural (counting) numbers for trials of scale factors, generalising by using n.