Play a Merry Tune

The questions in this problem focus on ideas of combinations and sequences. At first pupils could think of the gourds as numbers 1 2 3 4 5 and think about the combinations in this way, and it may be useful for 0 to indicate a space on the wheel. There is also the idea of symmetry (which is explored in more detail in Beat the Drum Beat ), such as 1, 2, 0, 3, 3, 0, 2, 1 and perhaps 1, 1, 2, 1, 1, 2, 1, 1 and so on. In fact, the five notes produced by the gourds are actually A B C D E as on a keyboard, which you could make explicit. The exploration can lead to many trials of tunes and then the ability to save them is of course useful in comparing.

However, encourage your pupils to find ways of recording what they try out too - you can have a good discussion about the significance of leaving a place blank. Once ways of recording have been explored then further discussion can take place about what is seen when they investigate their different tunes.

Recording in a table like this below can sometimes lead to a purely mathematical investigation that leaves the gourds and the wheel behind while sequences and the ways of generating possibilities are explored.

Using a picture-type recording that more closely resembles the computer screen representation, might be more helpful for some pupils, for example: