First, we need to determine the total number of students in the fifth-grade classes. Since there are 3 classes with 22 students each, we can calculate the total number of students as follows:
\[ \text{Total students} = \text{Number of classes} \times \text{Students per class} = 3 \times 22 = 66 \text{ students} \]
Next, we need to figure out how many vans are required to transport all 66 students, given that each van can take 8 students. We can calculate the number of vans needed by dividing the total number of students by the capacity of one van:
\[ \text{Number of vans} = \frac{\text{Total students}}{\text{Students per van}} = \frac{66}{8} = 8.25 \]
Since we cannot have a fraction of a van, we will round up to the next whole number. Therefore, the school will need 9 vans to accommodate all the students.
Thus, the answer is:
\[ \text{The school will need 9 vans.} \]