Using Post-It™  Notes to Explain Composition

Post-It^™ notes can be a helpful teaching tool when first introducing composition of functions.  Consider the following problem.

1.  Write the value or expression to be substituted on a Post-It note with a heavy
     black marker (so that it can be seen by the class). 

2.  You may need several Post-It copies of the same value, as seen in this problem.
     Start by piling all of the copies on top of one another next to function .  As
     you start your substitutions, grab one copy and place it in its proper location in
     function and continue until all of the necessary substitutions have been
     made.  Emphasize that you are replacing the x-values in function with the
     Post-It note value or expression.

3.  Place the Post-It note carefully in the problem so that any operations to be
     performed on the value or expression can still be seen.  When dealing with
     expressions, emphasize to students that the Post-It note expression must be
     treated as an entire quantity.  Proceed with simplifying the expression.

4.  Showing this process once is usually sufficient.  In future problems, simply "grab"
     at the value to be substituted with your hand and state "remember, it is like pasting
     a Post-It note copy."