Type of question:
"How can your subjects (algebra and calculus) best be explained progressively to children and young people to enable them to develop their understanding gradually to grasp the principles involved in these abstract subjects, so that they can demonstrate their understanding in applying it in a practical way to everyday problems?"
"How can such learning be communicated so as to be a fun thing, rather than cold, formal and analytical, as is often taught?"
(Children will often attempt to understand the subjects by learning by rote formulas and the like without any comprehension of how their understanding can be applied. This makes the subjects boring for them when, with the right teaching techniques, it could be fun! If children can be taught at every step of the way in terms of what they already fully understand, they will enthusiastically and gradually develop their understanding of more and more complex, abstract topics.)
If you're actually looking for a problem to set students, there are many examples, but the ideal problem is one that gets students to apply their understanding of mathematics in a practical way. Combining geometry with algebra, is one way. Choosing a problem that tests students' understanding of the formula for solving quadratic equations, or trigonometric identities, or rules like the sine and cosine rules, or simultaneous equations, etc., without specifically stating what methods to apply in solving the problem, is a good way of discovering students' mathematical ability in practical application. Such problems could be presented as word problems and could be expressed concisely to appear simple, but nevertheless demanding on the intellect and comprehension.