Math whizzes come out and help me...

May 1, 2007 6:27 PM

4 teachers, 5 groups of kids: help me make a schedule please!

For a musical workshop this weekend we will have five groups of kids and only four teachers. We want each group to get a fair deal, but we don't want to do a complete rotation of teachers (the most logical solution).

We have a total of 6.5 hours of lesson time over two days, and my plan was to divide it into chunks of an hour or so, both to keep it fresh and to make sure no group spends too long without a teacher.

Let's call the groups by number and the teachers by letter.
Group 1: main teacher A, secondary teacher B
Group 2: main teacher C, secondary teacher A
Group 3: main teacher B, secondary teacher D
Group 4: main teacher D, secondary teacher C
Group 5: main teacher D, secondary teacher C

As you see, teachers A and B have only two groups each, while teachers C and D have three groups. This is logical only for reasons that aren't worth explaining here.

Our time frame is Saturday from 3-5:30 and Sunday from 10:30-12:30, and 1:30-3:30. To complicate things even further, group 4 will be absent on Sunday afternoon.

I was thinking of something like the following, but I would love to find a simpler solution.

Saturday afternoon:
3:00-3:45
Group 1: Teacher A
Group 2: Teacher C
Group 3: Teacher B
Group 4: Teacher D
Group 5: no teacher

3:50-4:35
Group 1: Teacher B
Group 2: Teacher A
Group 3: no teacher
Group 4: Teacher C
Group 5: Teacher D

4:40-5:30
Group 1: Teacher A
Group 2: no teacher
Group 3: Teacher B
Group 4: Teacher D
Group 5: Teacher C

(continue similar pattern on Sunday)

Obviously Group 1 gets the best deal, since no teacher sharing is required. Any and all suggestions on how to make this easy and fair would be much appreciated!

posted by purplefiber to grab bag (5 comments total)

Can you clarify something: Why is the number of groups of kids set in stone? Why can't you rearrange them into four groups?
posted by winston at 6:31 PM on May 1, 2007

Unfortunately not- it's a musical workshop for quartets- these kids are in preformed groups already.
posted by purplefiber at 6:38 PM on May 1, 2007

So, Sunday afternoon you have no problem - 4 groups of kids and 4 teachers. Let's consider just Saturday afternoon and Sunday morning then.

Those periods add up to 4.5 hours. Give groups 1, 2, 3, and 5 each 1 hour without a teacher. Group 4 gets half an hour without a teacher, as "compensation" for not being able to get any instruction Sunday afternoon.

So something like this ("X" indicates no teacher)

Saturday
3:00 - 4:00 1-A 2-X 3-B 4-C 5-D
4:00 - 5:00 1-D 2-A 3-X 4-B 5-C
5:00 - 5:30 1-C 2-D 3-A 4-X 5-B

Sunday
10:30-11:30 1-B 2-C 3-D 4-A 5-X
11:30-12:30 1-X 2-B 3-C 4-D 4-A

1:30-2:30 1-C 2-D 3-A 5-B
2:30-3:30 1-A 2-B 3-C 5-D

As an added benefit of this schedule, each group gets at least one hour with each teacher.
posted by DevilsAdvocate at 9:21 AM on May 2, 2007

Thanks DevilsAdvocate- that helps a lot, and we will go with that unless we can figure out a way to keep the primary/secondary teacher setup (where each group spends time with two or three teachers only). The reason being that sometimes with musical instruction, too many cooks spoil the broth and it becomes confusing/overwhelming for the student.
I do like your solution to the group 4 situation!
posted by purplefiber at 9:47 AM on May 2, 2007

I think I understand now - I wasn't quite getting what you were saying about the main/secondary teachers when I wrote my previous response. Try something like this instead.

Saturday
3:00 - 4:00 1-X 2-B 3-C 4-A 5-D
4:00 - 5:00 1-B 2-A 3-D 4-C 5-X
5:00 - 5:30 1-A 2-B 3-C 4-X 5-D

Sunday
10:30 - 11:30 1-B 2-X 3-D 4-A 5-C
11:30 - 12:30 1-A 2-B 3-X 4-C 5-D

1:30 - 2:30 1-B 2-A 3-D 5-C
2:30 - 3:30 1-A 2-B 3-C 5-D

Groups 1 and 2 have A and B as their teachers; 3 and 5 have C and D as their teachers; while group 4 has A and C. Groups 1 and 2 have B slightly more than A, and groups 3 and 5 have D slightly more than C, to offset the time A and C spend with group 4.
posted by DevilsAdvocate at 10:26 AM on May 2, 2007