How to fix bed slats?
Metal plates will be nice and fast to repair that, but in my opinion, You need one for each side and - the longer the better. Some glue for wood may be nice to use before fitting.
Remember not to use too-long screws to avoid matress damage. Alternatively You can use bolts and drill holes for them before fitting together.

Optional fix can be done by removing all of these wooden bars (these come bound together from Ikea as I recall - my kids got similar beds) and remove broken one with new one (You can buy it in probably every shop like Castorama in Eastern Europe). Replacing this would be most elegant way, I guess.