Cut two 36" squares from the blanket fabric. Sew the fabrics right sides together on all sides, leaving an opening to turn he fabric over. Turn the fabric over. Top stitch around the sides of the blanket.
Cut two 22" by 52" rectangles from the fabric for the front and back of the mat. Cut four 4" by 6" rectangles from the same fabric for the button tabs.
Cut two pieces of fabric 25" by 2" for the nap mat strap. Sew right sides together, leaving an opening to turn it. Turn the fabric over. Insert elastic. Sew the two fabrics closed. Lay one 22" by 52" rectangle right side up. Measure 10" from the bottom left and right corners. Make a mark on each place. Sew one end of the strap to each mark with a 1/2-inch seam allowance.
Stitch two of the 4-inch by 6-inch rectangles right sides together along three sides with a 1/4-inch seam allowance. Leave one 4" side open. Clip corners and turn over. Press. Topstitch the three stitched edges. Repeat with the other set of 4" by 6" rectangles. Stitch a buttonhole on each rectangle. Pin the open side of the button tabs on the right side of the 22" by 52" rectangle that has the strap stitched on. Make sure the button tabs are pointing towards the top of the mat. Sew the tabs in place with a 1/4-inch seam allowance.
Line up an edge of the blanket fabric along the length of the 22-inch by 52-inch rectangle that has nothing sewed on, leaving a 4-inch gap on the lower edge of the 22-inch by 52-inch. Make sure the fabrics are right sides together. Pin. Stitch blanket edge to the 22-inch by 52-inch fabric with a 1/2-inch seam allowance. Fold the excess blanket fabric towards the center of the mat.
Place the 22-inch by 52-inch fabric with the blanket from the last step right side up. Place the other 22-inch by 52-inch rectangle on top of the fabric right side down. Pin together. Stitch the top, bottom, and the length with the blanket attached together. Leave the other side open.
Turn mat to the right side. Measure 10-inch form the top of the mat. Stitch a line across the width of the mat, this will be the bottom of the pillow. Stuff the opening with the fiberfill. Edge stitch closed.
Press 1/2-inch of the unfinished fabric of the open side of the nap mat inside. Sew Velcro onto the open side of the nap mat.
Insert the foam inside the nap mat. Close the Velcro side.
Roll the pillow down and fold the nap mat by rolling it up. Make a mark where the button tabs hit to sew the buttons. Unfold the nap mat and remove the foam. Sew the buttons on the marks. Put the foam back in and fold the mat.