### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

### Cereal Packets

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

# Play a Merry Tune

## Play a Merry Tune

Have you ever heard of a gourd? A gourd is a hollow, dried shell of a fruit from a family of plants which grow in parts of Africa, Asia and the US. They have lots of uses, one of which is as a musical instrument, and that is the focus of this problem.

Below you will see that you have five different gourds, each one makes a different note from the others when it is played. You can listen to them by dragging them onto positions on the wheel. As the wheel turns, you will hear the sound of the gourds.

You can place any gourd on each of the eight places on the wheel and you can leave spaces too.

You could start by limiting yourself to using only two different gourds. For example, how many different tunes could you make just using these two:

You could decide on your own "rules" for making a tune: Do you need to use at least one of each gourd? Are you allowing yourself spaces?

Explore other combinations of different gourds too.

Try listening to this tune:

Now compare it with this tune:

You might want to listen to them more than once.
How are they similar?
How are they different?
Can you create another tune which relates to these two?

You could investigate other "families" of tunes too.
Send in some of your ideas!

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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: