## Rex's ransom

The purpose of this activity is for students to apply metric units of length, volume, and mass to solve a problem in context.

## About this resource

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

- Choose appropriate metric units of length, volume, and mass.
- Convert between metric units of length, volume, and mass.
- Apply the place value of large whole numbers.

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.

# Rex's ransom

## Achievement objectives

GM5-1: Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.

GM5-2: Convert between metric units using decimals.

## Required materials

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

*Rex's ransom activity*(.pdf)

## Activity

Your beloved Rottweiler, Rex, is kidnapped by an international gang.

The criminals ring with a ransom demand.

You are to drop off $1 000 000 in US $100 notes at a discrete location.

The money must be packed tightly into one briefcase.

- Is that possible?
- If you can, how much will the briefcase weigh?

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 in pairs or small groups.

- What information has been given?
- What other information is needed? (Dimensions and mass of $100 notes, size of a briefcase.)
- Can I imagine (visualise) what the numbers or shapes look like?
- What do I need to find out? (How many units of $100 equal $1 000 000?)
- Is it about how many or how much? (Dimensions of a 100 Х $100 note stack, number of stacks, volume of all stacks, mass of the stacks.)

### 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? (Measurement of length, area, volume and mass, multiplication.)
- What could the solution be? What is a sensible estimate?
- What strategies can I use to get started? (Drawing a diagram, writing an equation.)
- 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?
- Am I finding out some useful information or do I need to try something else?
- How do my results look different to others? Why could this be?
- Is there another possible answer or way to solve it?

### 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.

- Show and explain how you worked out your solution.
- Can others see how I worked it out?
- How does my solution answer the question? (Will the money fit? What does the money weigh?)
- How can I clearly show what I found out?
- Which representation (text, table, graph, numbers, diagram, equations) will be easy to understand?
- Which ideas would convince others that my findings answer the investigation question?

## Examples of work

The student finds a way to enclose $100 banknotes into a briefcase without considering how the number of notes might be maximised and calculates the mass of the banknotes using appropriate place value.

The student uses a systematic strategy to find the optimal dimensions of a briefcase so the maximum number of notes can be arranged in each layer.

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