We integrated the ”Make It Sound” international Smart Hands workshop in the maths lesson Ratios, proportions and mean(arithmetic and harmonic mean) for the 9th graders from Colegiul National Emil Racovita.

The lesson started with a structured discussion around the following questions:

1. Do you know any string instruments? Do you know anything about the arithmetic or geometric mean of 2 positive numbers? Or the harmonic mean of 2 positive numbers? What about the octave, quint or quart?
2. Is there any connection between the 3 means of 2 positive numbers (or just one of them maybe) and the octave, quint and quart? If so, which is the connection?

Then, the students were asked to make monocords (the process has been tested in the Make It Sound workshop) with different string lengths: 90cm string length, 45cm string length, 60cm string length, 67.5cm string length and to compare the sounds produced by the 4 monocords.

In groups of 4 (each student in the group had a different string length for their monochord) the students worked together to investigate the connection between the sound and the length of the string and to identify different properties of musical proportion. During the group work activity, the students solved the tasks related to the musical proportion, the relationship among the musical proportion and the proportion made with 2 positive numbers, the arithmetic mean and their harmonic mean, harmony of sounds, the frequency of the sounds produced by the 4 monocords (they used FizzIQ app to measure the frequencies) and the relationship between the musical notes and the string frequency.

The lesson ended with the students’ reflection on their work.