## Key rates

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.

## About this resource

This activity assumes the students have experience in the following areas:

- Calculate with decimals.
- Solve problems with rates.
- Calculate with simple percentages, especially with money.

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.

# Key rates

## Achievement objectives

NA5-4: Use rates and ratios.

## Required materials

See **Materials that come with this resource** to download:

*Key rates activity*(.pdf)

## 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 an 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.

### Make sense

Introduce the problem. Allow students time to read it and discuss it in pairs or small groups.

- Do I understand the situation? (Students may need background information about currencies and exchange rates.)
- What is an exchange rate? How does an exchange rate work?
- What information has been given, and what more information might be needed?
- Can I anticipate what percentage might be lost? How?
- Does this look/sound like a problem I have worked on before? What kind of problem is this?
- What will the answer look like? (A percentage loss for each exchange system, with calculations to support the percentage.)

### Plan approach

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.

- What are the maths skills I need to work this out? (Rates are integral to the problem.)
- How could I show this problem using numbers, equations, pictures, graphs, tables, or materials?
- What strategies can I use to get started?
- Should I start with a tidy amount in NZ$? What amount would be good? Why?
- What tools (digital or physical) could help my investigation?

### Take action

Allow students time to work through their strategy and find a solution to the problem.

- Have I shown my workings in a step-by-step way?
- Does my answer seem correct? Is it close to my estimation?
- How could I make sure that I haven’t missed anything?
- Do the percentages seem reasonable?
- Do my results look the same or different to others? Why could this be?
- Is there another possible answer or way to solve the problem that is more efficient?

### Convince yourself and others

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.

- What is the percentage lost with each scheme?
- Have I shown clearly how the percentage was found?
- How would I convince someone else that my calculations are correct?
- Is there some mathematics that I need to learn?
- What does my answer mean for companies that exchange large amounts of money?

## Examples of work

The student uses currency exchange multipliers to convert between currencies and to find the percentage cost of the exchange with guidance.

The student uses currency exchange multipliers to convert between currencies and to find the percentage cost of the exchange.

The student uses currency exchange multipliers to convert between currencies and to find the percentage cost of the exchange.

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