Like We'll Bang the Drum
, the interactivity in this problem has plenty of scope to be used to explore areas of mathematics not covered by these particular questions. The way the problem has been written allows opportunites for you to highlight ideas about factors, multiples and symmetry with the children.
You might like to introduce the problem by "playing" two examples of rhythms on the wheel, one with a steady beat and one with no steady beat. Asking for differences between the two will help pupils understand what we mean by "steady" in this context and they should be able to explore the first parts of the problem in pairs using the interactivity. After a few minutes, it would be worth bringing
the whole group together to talk about how they are remembering what rhythms they have tried. In this way, they will be encouraged to think about how to record what they are doing.
These recordings of ideas can lead to interesting discussions as to the sameness/difference of the rhythms. For example:
Similarly having discussions about these further three examples could prove very valuable:
You could also make more of a specific link to musical notation. Placing 3 - 8 drum beats within one turn of the wheel can easily be related to having a bar of music available for a drum beat rhythm that equates to four-four time (four crotchet beats in a bar). Since we have 8 spaces, each one would be equivalent to a quaver in length. Listening to the beat of the drum can give an illusion that
when there is one space on the wheel after a drum beat, the beat length increases by a quaver.
Here are twelve examples of putting either 3 or 4 beats for different effects:
So for example in number 6 when the "bottom" drum sounds it appears to last for 4 quaver beats before the next drum beat sounds. That second beat appears to last for 2 quavers, as does the last beat.
In example 9, the first appears to last for 4 quavers, the second and third beats last just 1 quaver each and the last beat lasts for 2 before the rhythm starts again.
If you want to take the note values further you might look at the eight quaver values in one complete turn. Then the twelve examples shown above include notes of value 1, 2, 3, 4, 5 and 6.
These could be recorded as follows: