Here's the kaleidoscope base to this block. The Dear Jane blocks measure 5 inches unfinished so I made the octogon wedges a bit bigger than necessary, then cut them to size after piecing them together. Then I added the four light triangles on the corners and trimmed again.
Next I appliqued four triangles to the base of each of the light wedges to make the starburst. To applique, I traced the finished size template from the Dear Jane book onto freezer paper. Then I ironed the freezer paper triangle to the back side of the fabric. I cut around the shape leaving a seam allowance and then ironed the seam allowance back around the triangle on the two short sides. For these triangles, I only have to applique the two short sides. And to iron the seam allowance, I don't bother with spray starch. I just spritz it with a little water and that is enough to get a lasting sharp fold. Then I pinned the shapes to the block and sewed them on by hand.