The letter Qq is a great one for introducing the concept of 'quarters'.  We combined this with quilt to spice things up a bit.

• Print the template and color in the Q q.  Point out to the child which is the capital Q and which is the lowercase.
    
• Have the child color the template pieces.
    
• While the child is doing that, trim construction paper to different sizes -- we had:
  • one full sized piece of red and one full sized piece of green
  • one medium sized red and one medium sized green (we trimmed an inch off all the way around)
  • four small sized pink and small sized blue (we folded the pieces into quarters and cut them, then trimmed about an inch off the edges)
  • You can use whatever colors you want!
      
• Now, you take the full sized red piece and give your child the green (or vice versa).  Show them how to fold the piece in half lengthwise and then in half again, but this time the other way to make QUARTERS.  Cut or rip with a ruler.
    
• Repeat the process with the other pieces... you can work on cutting them while your child folds them or you can do each step together.  While you work, talk about other things you can cut into quarters (pie, pizza, etc)
    
• When you're folding the pink and blue pieces, think about different ways to make quarters.  Instead try folding the second time to make a triangle or to make a long rectangular piece.
    
• Now assemble your quilt squares -- set aside the 4 largest squares and place the others where your child can get them.  
  • Give your child one of the largest squares as a base for their work.  Take one of them for yourself.  
  • Mix and match the pieces to make fancy patterns and designs.  
  • You make one too!  (or you make one, daddy makes one, big sister makes one *grin*) so your child can see how symmetry and pattern works by watching you.  
  • You don't have to interfere much with their quilt square, if you have a habit of working together over time they'll catch on.  Don't worry if theirs isn't a perfect pattern.
      
• Take a piece of black or white construction paper and glue all the quilt squares onto it to form your quilt.  Cut out the Qq and glue them on top of the whole thing.
            

• Whenever I do these projects with Kaitlyn, I get to draw pictures of words that start with the letter and then she gets to color them.  This time, though, our quilt was so beautiful that Kaitlyn didn't want anyone drawing on it.