Key rates

Purpose

The purpose of this multi-level task is to engage students in an investigation that requires them to use rates, decimal and currency calculation to find a percentage difference.

Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

The task can be presented with graded expectations to provide appropriate challenge for individual learning needs.

Activity

Task: In March of 2014, NZ and China brokered a deal to allow direct exchange between their two currencies (NZ$ and CNY, the Chinese Yuan). This removed the need to use in intermediate step of exchanging into US$.

Use the exchange rates below to investigate possible savings if a sum of NZ$ is changed into CNY and then back into NZ$ with and without this direct exchange deal. Find the percentage of the sum involved that is 'lost' within the transactions.

NZ$ → US$    0.846
US$ → NZ$    1.168
US$ → CNY    6.213
NZ$ → CNY    5.314
CNY → US$    0.160
CNY → NZ$    0.188

The arithmetic approach (show more)

  • The student is able to use currency exchange multipliers to convert between currencies and to find the percentage cost of the exchange, with guidance.

The procedural algebraic approach (show more)

  • The student is able to use currency exchange multipliers to convert between currencies and to find the percentage cost of the exchange.

The conceptual algebraic approach  (show more)

  • The student is able to use currency exchange multipliers to convert between currencies and to find the percentage cost of the exchange.

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