A mathematical model is an abstract model that uses mathematical language to describe and understand a situation. Here’s a nice video that presents a model for the Lunch Date Problem. The video below shows a step-by-step tutorial using SketchPad to build a geometric model of the problem. What is nice about this video is that it still leaves the solving to the students. The resulting geometric model leaves enough information for students to figure out a solution.

###### The Lunch Date Problem

*You and a friend arrange to meet between 12:00 and 1:00 in the afternoon. After a week neither of you remembers the exact meeting time. As a result, it is possible for you arrive at random between 12:00 and 1:00 and waits exactly 15 minutes for your friend to arrive. After 15 minutes, each of you leaves if the other person has not arrived. What is the probability that the two of you will meet?*

Mathematical modelling involves the use of mathematics to understand a real world problem. Click What is mathematical modelling? to learn more about it.