The purpose of this activity is to engage students in an investigation that requires them to use rates, decimal and currency calculation to find a percentage difference.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
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 following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The student uses currency exchange multipliers to convert between currencies and to find the percentage cost of the exchange, with guidance.
Click on the image to enlarge it. Click again to close.
The student uses currency exchange multipliers to convert between currencies and to find the percentage cost of the exchange.
Click on the image to enlarge it. Click again to close.
The student uses currency exchange multipliers to convert between currencies and to find the percentage cost of the exchange.
Printed from https://nzmaths.co.nz/resource/key-rates at 1:37pm on the 27th April 2024