Once again, I'm giving you my way of doing this. You may choose to use a completely different method. If you do, please share. I know that this can be appliqued if you want, which would certainly be easier than piecing.
For this method you will need freezer paper and a disappearing fabric marker (fine point if possible). You can possibly use a pencil, but I have found pencil marks to show through on the right side of the fabric, especially if stitches will be going directly through them.
Print or trace the block pattern onto the dull side of freezer paper.
Carefully cut out the sections on the lines and iron them onto the WRONG side of your fabric, half onto your main fabric and half onto your background fabric. Make sure to leave ample room for seam allowances, especially on the edges that will be the outside edges of your block.
Cut out the pieces leaving a ¼" seam allowance all around. Make these seam allowances as accurate as possible, especially on the curved edges. Leave at least ½" to ¾" around the outside edges. (I didn't and had a close call.)
Using the fabric marker, trace around the edges of the freezer paper, marking your stitching lines. Extend these lines all the way to the end of the fabric (see the second photo). This will make lining up the pieces easier when you're ready to sew.
Clip the seam allowance of the concave pieces to within 2 or 3 threads of the stitching line. Fold each piece in half to find the centre of the curved edge and mark. You can use your nail to just crease the fabric or use a pin. For the concave edge, I just made sure I clipped at the center point.
Also mark the side seams on each piece.
Remove the freezer paper.
With the right sides together, match up a background piece with a main color piece, matching the center and side seam markings. (See the bottom of this post for my method for lining up markings.)
VERY IMPORTANT TIP: Make sure that the two fabric pieces line up on the corner. I actually pinned it in place and only removed the pin once I had stitched about ½" of the seam.
Make sure your sewing machine is on the "needle down" setting, where the needle will stay in the fabric when you stop stitching.
Now s-l-o-w-l-y stitch the seam, keeping the clipped concave edge lined up with the convex edge as you go.
You will end up with something that looks like this:
Press the seam allowance toward the outside edge of the piece. I tried always pressing toward the darker fabric but found that the block distorted when I pressed toward what will be the center of the block. There will be some bulk here, but the pieces will be straighter. (See the top right piece in the photo? That's the one where I didn't line up the corner before stitching the seam - wonky)
At this point I used the corner of a ruler to make sure that I had a 90 degree angle on my inside corners. If the corner wasn't 90 degrees, I redrew the seam line with the fabric marker, starting at the corner. This is that wonky piece again - a close call.
Now here's my method for lining up seam lines before stitching. If this makes no sense to you, ignore it and use whatever method you normally use.
Push a pin through the top fabric piece exactly on the seam line. Here I'm trying to ensure that the edges of the quarter circles will be in line.
With the right sides of the fabric facing, place the pin's point on the seam of the other piece of fabric exactly where you want the two to line up.
Now push the pin all the way through both layers of fabric and sandwhich them together so that the pin sticks up through the bottom at a 90 degree angle to the fabric.
Holding the fabric in place with your left hand, pull out the pin and reinsert it to pin the two fabric layers together.
Do this at intervals along the seam line, especially where you want existing seams to line up.
Sew the pieces together following the photo of the block and a four patch method.
You will probably end up with something scary like this:
That's where that ½" to ¾" seam allowance you left on the outside edges comes in handy.
Making sure to center the circle within the block (I used my 4½" square ruler like I did in D-3, although I think I'm going to go get a 5" one), trim the block down to 5".
If you're still alive, you'll have a block.