You may also like

problem icon

At a Glance


problem icon



problem icon

Gift of Gems

Four jewellers possessing respectively eight rubies, ten saphires, a hundred pearls and five diamonds, presented, each from his own stock, one apiece to the rest in token of regard; and they thus became owners of stock of precisely equal value. Tell me the prices of their gems and the values of their stocks. (Editors note: In this problem you are only given enough information to find the values of rubies, saphires and diamonds relative to the price of a pearl.)

Areas and Ratios


Why do this problem?

This problem involves a significant 'final challenge' which can either be tackled on its own or after working on a pair of related 'building blocks' designed to lead students to helpful insights. It requires students to apply their understanding of area and proportionality.

Initially working on the building blocks then gives students the opportunity to work on harder mathematical challenges than they might otherwise attempt.


Possible approach

These printable cards for sorting may be useful: Area and Ratio Cards

This task might ideally be completed in groups of three or four.
Hand out a set of building block cards (Word, PDF) to each group. (The final challenge will need to be removed to be handed out later.) Within groups, there are several ways of structuring the task, depending on how experienced the students are at working together.


Alternatively, the whole group could work together on both of the building blocks, ensuring that the group doesn't move on until everyone understands.




Key questions

What important mathematical insights does my building block give me?
How can these insights help the group tackle the final challenge?

Possible extension


Possible support
