Since the poster explicitly stated the requirements of the homework exclude the use of Collections an alternative approach would be to use System.arraycopy(). In such an approach you only maintain a single array and as you add items to it you use System.arraycopy() to copy the old array into a new larger array. System.arraycopy() is relatively fast and is actually how ArrayList expands its size.
If you are concerned about the cost of using System.arraycopy() you could use it only when your array is full and create a new array with more space. E.g.
Create and array of size 20. When it gets full copy it into and array of size 40. When that gets full copy it into an array of size 60...
Interestingly ArrayList increases its size by
int newCapacity = (oldCapacity * 3)/2 + 1;
when the old array is full. Presumably the writers of this put some considerable thought into how much to grow the array by when needed. It might be worth doing the same.
