This inquiry is suitable for older secondary school students who are familiar with the inquiry process. They need resilience to unpick the prompt - to explain the formula (or request a teacher's explanation) and to identify the constraint. Once the prompt is clear, students seem quick to speculate that it must be false because there are "so many types of numbers". However, when
- What does the prompt mean?
- Why is the volume of a cylinder
*πr*^{2}*h*? Is it always the same? - Can you explain the formula?
- What are
*r*,*h*and*n*? - Is
*n*a whole number? - Does the answer depend on the value of
*n*? - Why do
*r*and*h*have to equal*n*?
After a lengthy orientation phase, classes have decided to test the prompt by developing a collaborative inquiry with groups or pairs of students exploring for different values of
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