Scenario
Lia is the mother of a 4-year-old boy named Charles, and she is hoping to find a babysitter so that she can go on a date with her husband sometime this weekend. She already has a list of preferred babysitters, two of which she would be perfectly happy leaving Charles with. The third babysitter is perfectly capable, but not preferable because she is less active and engaging with Charles.
Lia starts by contacting her first babysitter, Ben. She tries to reach him on the phone, but he's in classes most of the day and so the phone goes to voicemail. Instead of leaving a voicemail and waiting for him to call back, she sends him an email. She asks if he is free on Friday night, since that is the night she was hoping to be able to have her date.
Ben receives the email, but has already scheduled a babysitting job for Friday night. Now Lia has to decide if she should contact the next babysitter, who might also end up being busy on Friday night, or continue trying to schedule with Ben. Lia sends an email to Ben asking about Saturday, and at the same time sends an email to her second choice babysitter, Hannah. The next morning, Hannah writes back saying that she is free on Friday night, and after negotiating the time in a few more emails, they agree for Hannah to watch Charles on Friday.
Design Sketches
Liz Simon
Design 1: A week by week calendar where you can click and drag to create events. Overlapping events might be shown in a few different ways: (1) decreasing the width to fit them side by side and cutting off the information. (2) Decreasing the width and color-coding with a key on the side or (3) Combining them into one item with all possibile babysitters/families listed.
Design 2: A small screen interface. Only one day can be viewed at a time.
Design 3: A full month calendar view. A large span of dates can be seen at once, but not all information will be visible without clicking. In the babysitter view, there would be a green dot on each day that the babysitter is marked as free. Similarly, the parent view would have a dot on each day they posted a job.
Storyboards
Design 1:
When a parent wants to find a babysitter for a particular job, they will go to the jobs tab and click create new.
They will use an interface similar to a calendar to select which times would be best for this job, and which times would work if need be. The user will click and drag over all the appropriate times to paint them with whichever color is selected - green meaning the time is good, and yellow meaning it's OK. If they accidentally color a time they didn't intend to, they can click it to erase the coloring. They will also enter a title for the job and the length of time for the job. Separately, babysitters fill out a similar interface to indicate their availability, which will be under their profile tab.
The parents then receive a list of babysitters that are available at any of their specified times, and a separate list of babysitters that indicated they could be free if necessary. They can then invite some or all of these babysitters to apply for the job.
The babysitters receive a notification that they can apply for a job, and can apply by clicking "see details". 
Babysitters can also view all jobs they've been invited to under their jobs tab. They can decline a job by clicking on the small X to the left of it. 
When a babysitter clicks on a job, they select the start time that is preferable to them and then applies.
The parent will then receive notifications of which babysitters respond and can choose whichever they prefer. They can also leave useful information for their babysitters on their profile, so babysitters can easily look this up while on the job.
Analysis
Design 1: This design is very efficient because painting over all times which work can be done very quickly. It might be a bit confusing to learn without text explaining what to do for at least the first time. It is somewhat safe since there is an easy method for undo-ing mistakes, but mistakes will be very common because any time a user accidentally drags across a time with the mouse down it will get colored.