This is an easy interactive toy for toddlers and preschoolers to learn about physics and problem-solving.

Materials:

There are a couple of options for the actual ball run pieces:

6 feet of 9/16" x 1-3/4" cove moulding and
1"x2"x6' sanded pine

1"x3"x6' sanded pine and
2 1/4" square dowels (that's 2 quarter-inch dowels, not 2.25" dowels)

Everything else you'll need:
1 piece of 2'x4' pegboard
2 1/4" round dowel rods (again, that's 2 quarter-inch dowels)
Small hinges (optional)
Wood glue

Tools:
Drill with 1/4" bit
Hand saw
Circular Saw (optional)
Chop saw, miter saw or jigsaw (optional)
Hammer

Step 1: Glue the Run Pieces Together

You've got either a 6-foot piece of cove moulding and a 6-foot 1x2, or a 6-foot 1x3 and a couple pieces of square dowel. Glue the bottom of the moulding to the 1x2 or glue the square dowels along one edge of the 1x3. Clamp the pieces together and let them dry for several hours or over night.

Step 2: Chop Up the Run Pieces and Attach Dowels

With a pencil, mark several varieties of lengths, from 2 inches to 5 inches or more, onto the glued-together wood. Using a chop saw, circular saw or hand saw cut the single 6-foot length of wood into many smaller pieces. Sand as necessary after cutting.

Using a 1/4" bit, drill a hole into the side of each piece of 1"x2" (or 1"x3"), at the center point (i.e., if it's a 3 inch piece, drill the hole at the 1.5 inch mark).

Cut a 1/4" dowel rod into 1.5" pieces. Sand each piece as necessary after cutting.

Coat the end of each piece of dowel in a little wood glue, then use a mallet to hammer them into the holes you drilled. Let them dry for several hours or overnight.

Step 3: Prepare Pegboard

I made my pegboard into a folding easel-like arrangement by cutting a 2'x4' piece of composite pegboard in half and attaching hinges. I also gave it some rounded corners with a jigsaw, though I wouldn't recommend this given how flimsy and hard to work with composite is. (Note the bits of scrap wood where the screws for the hinges come through the pegboard. Pegboard is very thin, there's no screw in the universe that would securely hold a hinge onto a piece of standard pegboard without popping out the other side. Hence the pieces of wood.)

You could instead attach the pegboard to a wall (using spacers so there is space for the dowels to enter the holes), or use a single piece of pegboard and just lean it up against a wall when it's time to play.

You can paint your pegboard with non-toxic paints, use Mod Podge and wrapping paper to cover it (poke the holes out with a pencil or spare piece of dowel), or leave it as-is.

And that's it, you're done. If you don't get too fancy, this whole thing can be done in an hour or two (plus time for the glue to dry).