This inquiry is suitable for students in years 5-8 (grades 4-7). The prompt is adapted from one designed by Theo Giann (a PGCE student at the University of Brighton, UK, during 2011-12). In his original version, the fourth circle contained a question mark, rather than a hexagon. However, it is possible for students to interpret the question mark as a teacher's closed question and, hence, limit the inquiry to finding the next polygon in the sequence. In its form above, the prompt might lead to more open lines of inquiry, such as the ones below that have been generated by students' questions and comments:
- names of two-dimensional shapes;
- perimeters of polygons;
- methods to inscribe shapes in a circle;
- the circumference of a circle;
- regular polygons (including interior and exterior angles); and
- areas of polygons.
Theo tried his prompt with a year 8 class as part of a Masters-level research project on encouraging autonomy. As this was Theo's first inquiry with an unfamiliar class, he decided not to use the regulatory cards and instead gave the students a limited choice of working in their books, making a poster or completing a worksheet.
You can read more examples of how this inquiry has developed in the classroom in the primary section of the website.