Pizza pans

Purpose

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

Description of Mathematics

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.

Activity

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.

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