This is a rather broad question. There are so many different
variations beneath the surface of the actual question of teaching
several children at once. Are we speaking of teaching children
across grade levels, ability levels, all the various individual
interests that each child may or may not have. However, any teaching
scenario that involves multiple children will certainly involve multiple
teaching approaches. With homeschooling, parents will generally choose
the technique that best fits their child and their family situation.
This is a great advantage that homeschooling has over the traditional
schoolhouse.
Depending upon the subject matter some kids of different ages can be
taught the same material if it is new to both and at a high enough level
for one while being a low enough level for the other. Field trips to
various businesses can be an excellent source for this. While one child may
enjoy learning about how the business is run while the other may enjoy
how the product is made. For subjects, math, and reading for example may
require more precise level driven teaching than would say geography or
history that would not have the pre-requisites to learning.
Such things as science or biology projects can certainly involve the
whole family with the older child being more involved in the actual
detail of the project itself.
If one of your kids needs some time for special attention try to
arrange so in as much as advance as you can. This will give you time to
prepare studies for the others to do while you have some one on one time
with one of the children. Make use of the older children actually
tutoring their younger siblings. This will give them a sense of
responsibility and pride when they too are involved in teaching
children.
The great advantage of teaching your child at home is the ability to
tailor your schedule and your time in a fashion that best meets the
child's educational needs and those of a busy family.