The prompt has the potential to cover a wide range of topics in the school curriculum, including the areas of polygons and the circle, fractions, Pythagoras' Theorem, trigonometry, similar shapes and use of formulae. It has led to open inquiries that combine student questioning with teacher instruction in a mutually supporting process.

At the start of the inquiry, the teacher should establish that the three shapes are divided into five strips of equal width, perhaps by confirming a student's observation, and that the triangle is isosceles. Examples of students' questions and observations that have arisen in classroom inquiry are:

• The fractions shaded of each of the shapes are not the same.

• What fractions of the triangle and circle are green?

• Which shape has a greater fraction shaded?

• Is the triangle equilateral? Is it isosceles? Is the fraction shaded the same for an equilateral and isosceles triangle?

• Do we need to know the height of the triangle to work out the area?

• The base of the triangle and the diameter of the circle are divided into five equal parts.

• To work out the area of the green part of the triangle, should you use the formula for a trapezium?

• Over half the circle is shaded green.

• Is the fraction of the circle shaded green smaller or bigger than three fifths?

Three-fifths of the square is shaded; for the triangle, the fraction shaded is greater than three-fifths. As finding the fraction of the circle shaded poses a much greater challenge (see mathematical notes), the teacher might guide students towards inquiry pathways involving other quadrilaterals, such as the trapezium, rhombus or parallelogram, before considering the circle.