Stop Thief - Teacher Notes
A bank manager says that an armed youth stole a bag containing £5000 in £1 coins and ran away.
Write a report for the insurance company! Tell them if they should pay up, or prosecute the bank manager for attempted fraud.
Explain your reasoning carefully! Tell the insurers exactly what information you used, and what assumptions you made.
The bank manager's story is / is not suspicious because...
Teachers' notes for Stop! Thief!
Time: about 40 mins
We recommend that pupils work in groups of 3 or 4.
Pupils know what a pound coin looks and feels like, but few pupils will have factual knowledge (weight and volume) needed to solve the problem.
Some teachers have brought in kitchen scales, bathroom scales, and some pound coins to give students some relevant practical activities.
A: Introduce the problem - you might choose to read it aloud to the class or show the powerpoint with task description including a short video clip showing a youth running with a bag.
B: Small group discussions [10 minutes]
What do we need to know, to solve the problem?
There is opportunity for discussion about lots of unknowns, and how to deal with them, for example:
- How heavy will the bag be?
- How big will it have to be?
You could weigh and measure the coins as part of the estimation procedure, as an activity in front of the whole class, or by allowing each group to weigh coins in turn.
Alternatively, you could give students the information (or could ask them to find it for themselves, for homework, the night before the lesson).
In mathematics, pupils are normally given information explicitly - here, there is quite a lot of information contained contextually in the video: pupils can not identify the exact dimensions of the bag, but they can see it is about the size of an ordinary brief case. The youth is a big strong lad, and he is able to run quickly with the bag - would this be possible with 5000 pound coins in it?
Pupils may not know much about how insurance works, and particularly the process for making claims on insurance. The information at the end could be used to give them some understanding of the process.
C: Group work [20 minutes]
Discourage 'busy work' and spurious accuracy.
Some teachers have brought in kitchen scales and bathroom scales.
[The one pound coin weighs 9.50 grams. It has a diameter of 22.50 mm and a thickness of 3.15 mm [see http://en.wikipedia.org/wiki/British_One_Pound_coin].
Encourage pupils to take the 'audience' seriously. Do their answers provide all the information the insurers need? Is the reasoning clear? Is the style of writing appropriate?
D: Class Review [10 minutes]
You might nominate particular pupils to read their answers, or to simply report their ideas.
A £1 coin weighs about 10 grams - so 5000 coins would weigh nearly 50 kg.
Pupils can compare this to their own weight measured on bathroom scales.
You might talk about baggage limits on aeroplanes (usual allowances are around 20-25 kg; the heaviest bag allowed is 32kg), to give pupils a sense of the reasonableness of running carrying 50kg.
Even though 5000 coins could fit into a relatively small bag, it will be too heavy for someone to run off with.
Key Ideas to Discuss
Different approaches to estimation - does weighing coins give the same results as the official data?
Things to include in the advice to the Insurers - assumptions made, and the likelihood of being wrong.
In any insurance the principle is that a person pays a fixed price (the premium) for the insurance company to bear the risk of an event such as their house burning down - usually because the cost of that event would cause the person a real problem. The insurance company makes money by insuring a lot of people for such risks and only having to pay out on the few occasions where the event happens.
It is easy for an insurance company to check whether a house has burnt down, but it is much less easy for them to know whether, for example, a claim for a burglary is truthful. The company will run checks on samples of claims to try to ensure that people are honest in making claims on insurance policies. This might be sending an assessor out to look at the damage to a car and checking that old bumps and scrapes are not being included as damage to be repaired because of a recent accident.
In this case, the idea is to check on whether the manager's claim that the youth ran off with 5000 pound coins in a bag could really have happened.