Daniel Walker (a secondary school maths teacher) devised the prompt for his year 10 class. An inquiry might start with students exploring the difference of squares of other consecutive numbers and verifying that a2 - b2 = a + b. After the initial phase, the inquiry has the potential to develop in different directions. The following changes could be made to the prompt:
- Make the difference between a and b greater than one;
- Make the powers greater than two;
- Express, under the teacher's guidance, the difference of two squares as (a + b)(a - b);
- Expand the brackets to show (a + b)(a - b) = a2 - b2;
- Represent the numerical and algebraic forms visually (see Daniel's power point).
On the last point, students, even those experienced in inquiry, rarely suggest an alternative mathematical representation spontaneously (see Moving between forms of representation). For this reason, the teacher might introduce the idea of a visual representation in order to deepen the students' understanding of the prompt.