The capacity of a standard alkaline AAA is about 1000 mAh but the capacity also depends on discharge rate. The faster you discharge the battery the less capacity you'll get. Just for the sake of this example we'll disregard that and assume that the capacity is set at 1000 mAh. To use up 1000 mAh in 10 minutes you would have to draw about 6 A of current out of the battery.
Capacity = Current draw*battery life
So
1000 = I*.1667hrs
I ≈ 6A.
You will have to connect a resistor between the positive and negative terminal of the battery to drain it but you have to make sure to choose a resistor suitable for this.
Since V = IR, to draw 6A we divide the battery voltage of 1.5 by the current 6
R = V/I = 1.5/6 = .25 Ω
Once agian to bound the problem we'll assume that battery voltage is constant even though it will decrease as the battery gets discharged.
The other consideration you need to address is the amount of power this resistor is going to have to dissipate. All the resistor is doing in essence is converting the stored energy from inside the battery into heat. If you don't size the resistor accordingly, it can burn up. To determine how much power will be dissipated use the equation:
P = IV
I = 6A
V = 1.5
So P = 9W
You need to make sure that the resistor is rated for at least 9W. Somewhere along the lines of 15W to 20W would probably be best.
Since I don't know how easy it's going to be for you to find a .25Ω resistor what you can do instead is place 4 1Ω resistors in parallel. That will have an equivalent resistance of .25Ω. it will also have the added benifit of spliting up the current draw and the power disipatted between the 4 resistors.
Each of the 4 resistors will only carry 1/4 of the total current and will only have to dissipate 1/4 of the total power so you can get away with 4 1 Ω 5W power resistors. like this:
Now all tha being said, I wouldn't suggest you wait until the science fair to try this. The battery will get hot and so will the resistors. Maybe to unsafe levels. Try this first in your garage or something with the kids far away.