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The notes below describe a method of engagement based around a technique called complex instruction.
Although this problem is group-worthy, it can, of course, be attempted individually if you wish.
You may want to make calculators, internet, squared or graph paper, poster paper, and coloured pens available for the Resource Manager in each group to collect. As teacher, you (or the internet) will be a resource containing knowledge of physical data, constants and formulae.
While groups are working divide the board up with the groups names as headings. Listen in on what groups are saying, and use the board to jot down comments and feedback to the students about the way they are working together. This is a good way of highlighting the mathematical behaviours you want to promote, particularly with a challenging task such as this.
You may choose to focus on the way the students are co-operating:
Alternatively, your focus for feedback might be mathematical:
Make sure that while groups are working they are reminded of the need to be ready to present some of their approximations at the end, and that all are aware of how long they have left.
We assume that each group will record their reasoning, assumptions and calculations in preparation for reporting back. There are many ways that groups can report back. Here are just a few suggestions: