To determine how many bottles of hand sanitizer Ms. Nelson's students will use in 10 weeks, we can multiply the amount they use per week by the number of weeks.

Each week, the students use $\frac{1}{4}$ of a bottle, and this happens for 10 weeks. So, the total number of bottles used in 10 weeks is:

$\text{Total} = \frac{1}{4} \times 10 = \frac{10}{4} = 2.5 \text{ bottles}.$

Therefore, Ms. Nelson's students will use 2.5 bottles of hand sanitizer in 10 weeks.

Would you like more details or have any questions?

Here are 5 related questions to extend your understanding:

1. If the students used $\frac{1}{3}$ of a bottle each week, how many bottles would they use in 10 weeks?
2. How many weeks would it take to use exactly 5 bottles of hand sanitizer at the rate of $\frac{1}{4}$ of a bottle per week?
3. If Ms. Nelson bought 3 bottles of sanitizer, how many weeks would that supply last for the students?
4. If the usage rate doubled to $\frac{1}{2}$ of a bottle per week, how many bottles would be used in 10 weeks?
5. How many bottles of sanitizer would be used in 12 weeks at the same rate of $\frac{1}{4}$ of a bottle per week?

Tip: To solve problems involving rates, always remember to multiply the rate by the total time or units given.