A research platform for task design
Hazel turns a textbook problem into a mathematical modelling task. You bring a problem you already teach; it argues from twenty-seven worked exemplars and cites them by number.
Taking part in the study? Your slip code goes in the same box.
Scroll to exploreFour routine problems, and the modelling task each one becomes. The arithmetic does not change. What changes is who decides what counts as an answer.
Routine
The tank holds 12 m³. How long does it take to fill? Every quantity needed is given and nothing superfluous is.
Modelling task
The butt ran dry in the third week of a dry spell. How big would it need to be? The capacity is now the unknown, and the dry spell to design for is a decision rather than a fact.
Routine
To three significant figures. What is assessed is whether the solver picks tangent rather than sine. The tree is a costume.
Modelling task
Report a range you are willing to defend. A canopy has no unique highest point, the ground is not level, and asking for a range makes disagreement visible.
Routine
80 km/h, and equally compatible with a coach that sat still for twenty minutes and one that held exactly 80 the whole way.
Modelling task
Kick-off at 14:00, and a driver who remembers the trip taking “about an hour and a half, but once nearly two”. Recommend a departure time and say how likely it is to work.
Routine
A 10 m square, 100 m². The pen is rectangular because the question says so, there is no wall to use, and there is no gate.
Modelling task
Nine panels of 1.8 m, one side already a solid wall, and a gate wide enough for a wheelbarrow. The optimum stops being a square and the perimeter is quantised.
Designing the thing is the first half. The second half is finding out whether it works on someone who has never seen it.
Ask what a relationship looks like and you get the curve, not a paragraph about the curve. Hazel plots functions, sketches the situation, and marks an assumption where it would otherwise slip past.
A committed task comes with a class-facing version: the situation in student language, a picture, and the questions to ask a group that has stopped. You edit it before anyone sees it, because it is your class.
Publish a task and a solver works it through the seven transitions of the cycle. Where they stall comes back to you, stage by stage. The difficulty in modelling lives at the transitions, so that is where it is measured.