"Silent functions" - mappings, functions and graphs
This link takes you to Number and Algebra 3, a Nuffield Foundation textbook available to download from the National STEM Centre website. The relevant section is The function game on pages 91-92.
In silence learners try to identify a hidden function by putting in various values and observing, and conjecturing about, the output. The silence is very helpful because it encourages everyone to think as more and more data is developed on the board. The propensity for learners to form their own understandings of possible functions is a major ingredient of this approach.
There are potential pitfalls in introducing functions as mappings involving particular values – this starting point can embed the idea that the graph is a ‘join the dots’ exercise. However, in the example given the function is expressed in general words as well as number pairs, so can help move towards an understanding of the function in its general form.