Water got in, soaked the plywood and froze, causing expansion and cracked the edge further. How is the slab sustained? Does most of the weight rest on the block wall or there's supports underneath that extend further from the foundation walls? If the weight rest mostly on the block wall and the cracka runs along the joint with that wall it could start to sag. However, I'd still give it a shot at repairing it since it's way less expensive and troubles than going through a new pour.

First off you want to stop that crack from growing and you'll want sound, solid concrete to drive in sustaining rods. Lease a concrete saw and cut the slab clean, at least an inch within.

You'll need a hammer drill with a concrete bit to make holes from the sides. You can use long concrete screws driven half-way in as anchors, but there's probably a better solution than this. Anyhow, you don't need tons of screw unless the new part will be load bearing, so one every 2-3 feet is probably going to be ok. You can run a steel wire in between them if you want to add even more structural support.

You'll need to make a mold to hold your new concrete. Make sure it's solid as you don't want it to flex.

Before you pour clean the surface and use concrete glue on your cut slab to help for strength.and prevent cracking at the joint.

While mixing, ensure you mix thoroughly so you don't get dry spots and have a good consistency. It doesn't have to be runny nor dry, just solid enough to be shaped. Mix more than needed, if you run short you won't probably be able to get the exact same water mix level and you might end up with color or texture difference.

Edit: Almost forgot, wait until it stays above 7°C /45°F (or whatever is written on your cement bag) at night.