Draw a diagram that shows 1/5 times 30 equals 6

1) ∵∵∵∵∵∵

2) ∵∵∵∵∵∵

3) ∵∵∵∵∵∵

4) ∵∵∵∵∵∵

5) ∵∵∵∵∵∵

30 groups of dots: 6 in each row and 5 in each column. I selected 1/5 of the dots, which equals 6 groups of dots.

There are 16 students total.
1/4 (4 students)--> Yellow Costumes
6 students--> Purple Costumes
(?) students--> Orange Costumes.

We know that one fourth of the students is 4 students by doing simple division.
6 students are wearing purple costumes. 
Add these together.
4+6 = 10

The remaining students are wearing orange costumes.
There are 6 students remaining.
Therefore, 6 students are wearing orange costumes.

6 Students