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Step-by-step build — 6 steps. Also available as a print sheet.
Clamp the two side blanks face to face and mark the dado positions across both at once.
Mark them separately and your treads will be out of level — on a stool someone stands on, that's not a cosmetic problem.
3/4" wide, 1/4" deep, across the inside face of each side, at both tread heights.
Test the fit on a scrap of your actual tread stock. 'Nominal 3/4"' maple is rarely exactly 3/4". You want a fit that pushes together with firm hand pressure — tight enough to hold itself, loose enough that glue has somewhere to go.
Draw an arch at the bottom of each side, leaving about 2" of foot at each corner. Cut with a jigsaw and sand the curve fair.
The arch means the stool stands on four feet instead of two long edges. On any real floor, a full-edge stool rocks; a four-footed one doesn't.
Assemble dry — both treads into the dados, back brace in place.
Check it's square, sits flat, and doesn't rack when you push the top. Fix anything wrong now. Once glue is in the dados you have about five minutes.
Glue in the dados, seat the treads, add the back brace, clamp across the sides.
Check square with a tape across the diagonals while the clamps are still moveable.
Optionally drive two screws per tread through the sides into the tread ends — countersunk and plugged. The dados are doing the work, but a stool is a load-bearing object with a child on it, and I'd rather over-build it.
Round over every edge generously. This gets grabbed by hands and stood on by bare feet, and a sharp maple arris is unpleasant on both.
Sand to 220. Milk paint for the traditional look (it chips and wears in a way that gets better, not worse), or hardwax oil to show the maple.
Then stand on it. Bounce a little. If it doesn't creak or shift, you cut your dados right.