Here's a problem that becomes real for my older students once a year.
Each November we conduct a Speech Festival at our school. We invite students from area schools to learn and recite a "speech" (poem, story, etc.) in front of an audience. This involves clearing five classrooms and renting enough chairs to accommodate in those rooms the approximately 220 people who will be participating and watching.
The problem I give to my Grade 4-6 students (in a multi-aged group) is: 1. How many chairs do we need to rent? 2. How should they be arranged in each room, given certain specifications (side and center aisles, space at one end of room left for speaker, classrooms accommodate unequal numbers of chairs, etc.)?
The students are given the number of registered speakers. They then need to count the number of useable chairs in the school, estimate a suitable number of chairs for guests, and then work out the number of chairs we need to rent. Having arrived at that number, they then work out how to arrange the chairs in the different classrooms. Finally, the students have to organize themselves to actually set the chairs up. This last component doesn't address any specific mathematical skills, but by definition any real-world problem includes such components.
Paul Murray Franciscan Cre-Act School Pocatello, ID firstname.lastname@example.org