Asking a student to cut a piece of wood exactly in half will require a fraction. At least one. Remember? It's the kerf from the saw. Kerf defined is the part of the wood that turns into saw dust. Depending on the saw, it could be anywhere from a 16th of an inch up to 3/16ths of an inch.

First we need to teach the basic use of the tape measure. I draw an enlarged view on the board. A huge inch. It includes each little line within the inch. Some small, some big. Take a close look at your tape measure. The biggest lines are for the full inch. The next longest line is for the 1/2", then 1/4", the 1/8th and finally 1/16". having this on the board will assist the students. They should also have this written down. Letting the student employ the smallest set of lines, and simply counting how many 16ths are involved in the measurement, will simplify their project.

Have students start a small cut in the wood. Then measure the cut. That's the kerf. Now that they have the 16ths on the board, they should be able to accurately measure the gap.

So, we now have the gap. They should now be able to measure the piece of wood and deduct the gap. Once the gap measurement is subtracted, they could be asked to cut the wood in two.

Questions: how long is each piece of wood?
How long would one of them have been if we didn't have a kerf to deal with?

More exercises with tape measures and a saw...
Cut a piece of wood in half and end up with two pieces exactly the same length. (remember the kerf.)
Ask them to cut a piece to an exact length.
Ask them to cut at a 45degree angle.