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# dy/dan: Bet your coffee

16-22 April is UK Coffee Week, a nationwide celebration of coffee that unites the industry and their customers to raise funds for the communities that grow our coffee. All of the donations received from UK Coffee Week go to Project Waterfall, an initiative dedicated to bringing clean water facilities to coffee growing communities. Dan Mayer’s ‘Three Act Math’ task ‘Bet your coffee’ is an ideal way to link UK Coffee Week with mathematics.

The problem shows a picture of an offer in a coffee shop. For every ten coffees bought, a free coffee is offered. As an alternative, you can put your card in a bowl and on New Year’s Eve a card will be drawn, the winner receiving a free coffee each day for a year. When should we keep our free coffee card? When should we bet it?

The particular feature that I like about this activity is that it gives a chance to explore expected value in a context other than the usual ones involving games of chance. Another nice feature is that the option of exchanging a loyalty card gives a probability of 1, we are guaranteed a free coffee.

If we decide to put our card in the bowl, then the expected value is the product of 365 and one divided by the number of cards in the bowl. We are best to keep the card if the bowl has more than 365 cards, and bet the card if there are fewer.

A suggestion for gentle introduction to the problem is to alter the offer to receive a free coffee for seven days. An extension could be to alter the offer to give several prizes. Students could be asked to formulate their own offer and make the relevant calculations.

If you give this activity a go then please leave a comment to this post and let the community know how your students work on the problem, and any extensions they come up with.

We have recently added Dan Mayer’s ‘dy/dan Three Act Math’ materials, this example being ‘Bet your coffee’.

You can also join us at the National STEM Centre in York to experience ideas for teaching through understanding on Enthuse funded courses, details of which are here.

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Age 11-14, 14-16 0