The purpose of this multi-level task is to engage students in using ratios to find a common ratio (scale factor).

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

This task may be 'scaffolded' with instructions that lead to a solution, and/or the students might be given a value for the area of the family pizza in order to have a concrete focus when they apply the process that leads to the solution. The approach should be chosen in sympathy with their skills and depth of understanding.

Task: A family sized pizza is baked in a pan that has twice the base area of a standard pizza pan.

Find how much bigger the radius of the family pizza pan is than the standard (ie find the scale factor for this enlargement).

### The arithmetic approach (show more)

- The student is able to find a decimal scale factor, using concrete examples in their calculations.

### The procedural algebraic approach (show more)

- The student is able to find an exact (surd) scale factor, using concrete examples in their calculations.

### The conceptual algebraic approach (show more)

- The student is able to find an exact (surd) scale factor, using algebraic generalisations.