The prompt was designed to expose and correct a common misconception among secondary school students. When shown the prompt, they will often claim that fifty divided by a half is 25 and 20 divided by a fifth is four. Therefore, they reason, the two sides are unequal and the equation is false.

The inquiry normally starts in one of two ways. Either there will universal agreement that the prompt is not true, or one student or a few will argue that it is. (If the majority can explain why it is true, then the prompt is not appropriate for the class because it will hold no intrigue.)

• In the first case, the teacher should assert the equation is true and ask each student to think why that might be before students pair up to discuss and then share their thinking. Often, at this point, students will speculate that the reason is related to 50 x 2 = 20 x 5.

The teacher, using a diagram if appropriate, should link the speculation to the fact that there are two halves in one whole, four halves in two, six halves in three and so on. Following the pattern, we have 100 halves in 50. Similarly, there are five fifths in one whole, 10 fifths in two, and 100 fifths in 20.

• In the second case, the teacher will draw on the existing knowledge of one or a few students to co-construct a convincing argument.

Once the class accepts the prompt is true, the teacher might structure the inquiry by following the first line of inquiry below. Alternatively, if the class has experience in carrying out inquiries, the teacher might offer a selection of regulatory cards: